A bicycle odometer (which meas 6 ff s(9hcwxrx4l2 hf.j8z rr)k;url;ures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-ink9rj;f (;r.8r6z chr)4 wuflx hslxf2ch wheels?

Suppose a disk rotates at constant angular velocity. Does a pdjgvu(5.sovr: z-f8to b) us4-d1zj woint on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either :jj-dsz(sub5oz wt .d-gfo) 14vur8vcomponent of linear acceleration change?

Could a nonrigid body be described by a p:-)m+iuvwl-qn)s vdur , jz+single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque-6w tyr o0+gqh than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your headxdv1;w nfnz+b +v l49c jlc80v than when your arms are stretched out in froln l czbx9+v v80;v1cf4 wn+jdnt of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three a32w5mtx/ zorb t the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Whyrt5/om2b3z w x?

Mammals that depend on being able to run fast have slender lower9p vbyshyl .g;/l ie:k*,j x)fq+ijk. legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynp+xl.9jyyiie j ;/f )bsv k*qhk,g .l:amics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow71+ +gpxnklei beam?

If the net force on a syste gz z xbh4sgyu,)6-vb2m is zero, is the net torque also zero? If the net torque on a system is zero, 2,gg)bs4h-yvx zbu 6 zis the net force zero?

Two inclines have the same height but make different angles wi+xs0q6;wrvt-c hjv p, th the horizontal. The same steel ball is rolled dv+;r,ps-xtj 6q0cv w hown each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down anosz 3.i*ay gb74jo n;e incline. One sphere has twice the radius and twice the mass ofa.4y;s inebo3jz 7* go the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They startt7p928 *grqfu ws7b uq from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greart9b7qgqp* s278uu f wter total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentu+ov; am*qk6t al;i( vum and angular momentum are conserved. Yet most moving or rotating objects eventually slow dowaq; umt;lov+k a *i6v(n and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woulu:w47fc7imqo6 n4 ro gd this affect the o6:ng uw474i cqrmo7f length of the day?

Can the diver of Fig. 8–29 do a sro*d iurak7 0z1dc11 jomersault without having any initial rotation whendkd7c z* riru111 aoj0 she leaves the board?

The moment of inertia cb/aztp8n1u./ev c6 sof a rotating solid disk about an axis through its center of ma /nbpt /eca6cv 8suz1.ss is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outls6d.:r1u a ysstretched hand. If you suddenly drop the masse:s1. s 6dlrauys, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identicalqgq)fzvn s-y; 5e .b6x and have the same mass. However, one is hollow and the other is solid. Describe an experim xnvgqs5-y6 q)bfz; e.ent to determine which is which.

The angular velocity of a wheel rotating)soz8u rxn;z7 on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular accelera ns7z;uo)r8 zxtion points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a lav,f8 dyx :vt6 u7vii2mrge freely rotating turntable. What happens if you wa: tyii678xvvvf 2 ,mdulk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly*v*hktwu3 u /n. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice thatu*uhwt /vnk*3 his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, din )3j-u sw3s9m 7og gupqg;;ixscuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second props3mg gqpsuiu 9gxn ;jw -)o37;eller can operate to keep the helicopter stable.

  Express the following angles in ra;9-0fm9f* s3qxskr wf sxbz v(dians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth bec.uey.413.qffjfd:tl a+v2,hs xc gmiause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameterscd.4 gfftsfq+ji1.xem2y , uah .:3vl (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. Tni ewy,8 e*o 1*y+auwdu xe)7zpmpe6,he beam diverges at an anguanx +) y*,de6upyw*7,e ize8 mo1pewle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. Wher9e a9,/ txp4* nck uc)inhwrsu2g0a 2n the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelerwa2c0ir ekugrp) n949u / ,xc 2saht*nation as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m thyr+a+ lhlajm 5s j29bdv/phfb+x9-,o another child. If the ball makes 15.0 revolutions, what is its diameter/j5 hr9d2+ lj+a 9mhbh avslbx,p fy-+?    m

  A bicycle with tires 6twb/1z;gl,u fbh; pm08 cm in diameter travels 8.0 km. How many revolutions do thef hb/mtzwl u;pg0,;b 1 wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its anpo.sqq (hs07 x-xy q+cgulaxpss+ qxh. 0 q(oqc7y-r velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (F vuxi:/vrfsx3;a:nk 7ig. 8–38). (a) What is the linear speed of a chinfs;7:xav /r v xuk:3ild seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around3t rja,d+ zbw,bkff5 hw+q(;:yx (osgj)tqe7 the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of p, zqx27 9+oev yj.0xyh8t.c bl :z4tu d9nuhpa point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if m-t )obq(af2j a particle 7.0 cm from the axis of rotation is to experie(aqof m-tb2)j nce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center ,az/u* fa (t7-al,ukmanh n 72xrhe 3yfrom 130 rpm to 280 rpm z*nalf,he y(,m u krx3u/h2 7aaant- 7in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu yrn/zme /;w/rs $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo nenuov)0ny:f18rx u e o :sr hr*x-47dspacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter ofx rvxu y7 or ::sn4udh)1 e0e-8nofrn* 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 2,h0fst*z5 qc+eb;t v q20 s. Through how many revolutions did it tus bztc,eqf+hq v*;t 05rn in this time?    $rev$

  An automobile engine slows down from 450/e1sdvsho )x5 0 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “hu rbett vj8y :58ivy+(kman centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before v8rt: b58ki+tey( y jvreaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelbu :u,p/wnhg8 erates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have tuu 8gw nb,:h/praveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 8bfs w5goomr tv w/3d :+5-+ wbb;hvgarevolutions before it comes a8+o md5sb;o-gb w f5tvbv :r3+hwgw/to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutionirf9grpg;.g6 xswkzd7k* v)5s as the car reduces its speed uniformly from 7w).kvir zkgdrp;fsx 56g*9g95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniyfd.m29wcfzh e94ji. formly from 95km/h to 45km/h The teym 2h.w jffz.d99i c4ires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbs6hgo83wyw8xg .tsg 7 zd:ge5ing a hil3th7 es:s6xy.g8gg 5woz8g w dl. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wibg8q32 uf1zzm de. What is the magnitude of the torque if the qz2fb38 1mzugforce is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig.pr;u-cmol1 q qdso81. 8–39. Assume that a friction torqu.uql 1 -omq1pd8cosr;e of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, a07hz vzhe55x89+ d ypvez bf+ure attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position azexh+ +vu7b58 vphy f59ze z0dnd then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder k4c4b2 hrk8;giebv(ssgg h xz g4/c8.head of an engine require tightening to a torque of 38 gsg g(h.4rbke;h2 c zs88gc4 4kxvib/$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg spherernpc5fx0om2 x+ sgc+2 of radius 0.648 m when the axis of rotation is through m+s+02 xgocc fnr 5xp2its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle whv :jp o9,f9km3ggfs( heel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (ws3mg f ,( vfh9:kg9opjhy?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontalt4 lh/fzbp/2u uk9h .u circle of radius 1.2 m. Calc9uk zp h 2u/./btuh4flulate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular speqs j/a-hx:(p6j7aq qxatra4lj 0dm. 1 ed (Fmt djq 0l.q 4s(- :rxxjhaa7a/ q6a1pjig. 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects ;32s tdvry4xjshown in Fig. 8–43tv; 3dj 2sryx4 about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consm8m5(r6 o2yxf4a3ej v8.tvh /x dgrap ists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylinqr7pse73,ekjkw. 6 dp8h uvu+drical satellite spinning at the correct rate, engineers fire four djueh pp6 u+3v7k., 8e sq7rwktangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifo6d 8fo/qj61 68wg)mgqvtasiwf8 o t3orm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. g8itvf 6)3sow1f6 adtog8w68/jmoq q Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, 47uwe*/zip3oy+w y lq wn 3,swaccelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small ha kif +f9yg)gvas4u 0kj, rp06hnd-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculatevh)6fkypf +i a 0r4gu0 sk9g,j the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut ort-31tj /9g kmz*hf yk2jgc.rff and is eventually brought uniformly to rest by a frictional2jk9 /3rh zy*g.cgrm1j t- fkt torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3. l(eg9 r/sf c7vbctp .1v1qzt96-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is t1ce3fe e+5dn ehrown solely by the action of the forearm, which rotates about the elbow joint under the action cn+1f5deee e3 of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod a,fjeh4vuaqk*: l+jgsc8ixo2e:**l , as shown in Fig. 8–468l* akhc2 j* e xoq:li4,+ vsfjegau:*.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses,k)dhj6zodk ed1ctb6 )bz5; oa k+de() $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the npadr1lidau *6 mh qmw)6e*mo(-hn/,hammer from rest within four full turns (revolutions) and releases it at a speed of 28 mdah6p uiq*/m)6(w lo,hn d 1* ream-n$m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inerts:.p4,7wrz4bx a8z(fn5n q b eak3 mcvia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a v :b(xhpylo4* torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without sfozmgkmg1 r6i8f *:m jq 7;af+lipping down a lane at 3.3:ro k+8m6;z g7* ifmj1q fgmaf $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with lo75fqi*djbm4ma2; l o1 c 6wyrespect to the Sun as the sum of two terl 6m7 i;q41bjoml2fc a 5wdy*oms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass oohvenfu77l9a*v+ w b( f 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution vh f79*av+w(beo n lu7per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and roy1bgp6l h hu8yl3.meqy*:(9a q)wad xlls without slippmy(h3up w9 1q gyybd)*6hxlaq a:.el8ing down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tid25.eitd59 k ;blpj vtp. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the popt.divdkbe l5;9jt 25le just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end ydfabv bidf9/ 2:wx7,.m z/md of a thin stringiayw/2fm 7d zx,/dmb dbf.v:9 in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg unifo)ne qym ptf8aj1)* yw0rm cylindrical grinding wheel owepyq)8y1f 0m )*t ajnf radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands atq tch492h6/eksof(tl , q ti2u his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed olco22ik6(4sqqt, h9/ eut thff rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8ic1l asv-t p7q3tl (z3–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. Ifzliqpa(l3t c-7s3vt1 she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin ro :n2wk 8,qflkaal:u-ztation rate from an initial rate of 1.0 rev every 2.0 s to a final rate ol8l ,zw2 -: qkaka:fnuf 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical a*7cu*; zvt0fqd c9u vwxis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of cl 9vw uqctu0c*f;z* vd7ay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5 j5)cx1 efgqe rpwjep* *,* 7b9itkbf0$rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the E4 chys(wd-5mm arth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk 8roqvbc,jpf,n8ykw 2hbvb/ 47 k(v4 b of moment of inertia I is dropped onto an identical disk rotating at angular spekb v8cy4b k7(,v w,h q2pr48vnbjb/ofed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 0 58y rb0ksgy//sdz px2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg standz1j pjq ld2-+r5 b+emjibt y(;;ss7tes at the center of a rotating merry-go-round platform of radius 3.0 m and moment of +p2yblr;jm 7tz sj ;tej5+e1(-i dqsb inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is r;tc.- ,):h 3eyupi)tfgnn ej gotating freely with an angular velocity of 0. ug-h)e g)3tp;ij.ty, en n:fc8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf,g 343vmfwi*azqie86 1 kr bj:+y;hzgq losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rat6q81 mk3 3fqjz:gavb;4zi * iyre+gwh e be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds 0a+tg 0uc j.r8vnj+g9 ttxdo0in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass d vym9mt+) ,d1+gp 2 yxnnp.to$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at res).rx k6hje1 tg)x h )xoezx-j/1codl8t, that can rotate freely without friction. The moment of inertia of the person plus thhr/8t1cooe)-x x) jekgl .x)hxdjz16e platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-rounx 5rm12 )awiu9z ny */m*jkizh-7hsmp(9p m fod turntable that is mounted on frictioy m9xn- zoj 5r9 (*pamm1*iwsz)2k/ u f7hpimhnless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on thed59zr7 7fs;pu5upq))wf tjaa top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What lengtr5upaz a5dp 7fj)qwt9)7s fu;h of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same :ykl*+t d7exxb/ap/i side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latx7 a p*e/l/tk+d ixby:ter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest aimx6wbgx8y1my3f/m ) r0p kn,t a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of ylaqgr n5e;ta5(4cl 3 radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deliverel rc4tl5a;yq3 g(ane5 d by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each ofo10o/8xz*hn/f :*pf t,kep/ wt xjibao.v + wp mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg andk .a0 zhtwbxo ,:ifw */pppnj*+1f8/vo/xoe t diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular spevm ajs7xor/ qrd qu-1.1empm y8/h;k1ed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times astb8 egc ,ge4u*/i(j(u,smp uz great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform spherezs 4 ugc ,emgtu, *e/(jpuib8( at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutiomra lb2g7lhis1:yq3zxhz ,vy)3spi/ w;1 ,zwn automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, andmls gzys )z;,y,vh p1rwibqxi3w1/:z 2 7hl3 a should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratg,)uul4hb(j2ix jh 4fes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal suz 35 ok(gobkj3rface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass 2r6wzno nrtlq1pz ,rif-163 uM and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The 1nrlqz6 r2 r,npiot1zw3 u-6frod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the flovafz2)ktd5lcbxb1,2fi f-y- or, and we want to e2vfk)xy-l2a t51idcf bf- z ,bxert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn with am:-xnw cnpq/95z 0edes3/. *btny kkc radius The forces acting on the cczd bp 53mce: ksk-/ /9wx0*ytnqn.e nyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sl(ns)i 1qxyc7 3zz o,kaing of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the t oxz)z,s( 7ai1qy3nc korque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin (/lkheg:3bjw2 i q xv2 ow/tf:rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and withq/w 2htviwex2 (/k gjbl3f:o: arms held tightly against her body.   

  You are designing a clutch assembly which cons d ifdeb- q73u53z pkrv/)tp-eo;w07ha.oq o lists of two cylindrical plates, of mass)h0 d iq/-5kp-t;ab7 vpo.f37 eled qwo3ru oz $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r r: 6sh2y:to,7jab lfk(v+ldakg dj+ v*olls along the looped rough track of Fig. 8–58. What is the minimum value ofdvy6o v+f2 jhk ,k llag7j:(+ad:t* sb the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but(ejdrcu(t6 h( t90cs8 aa)m nx do not assume $r\ll R$ h =    (R-r)

  The tires of a car mak), mcd4b5lmn0rz yg6,qy/idpe 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accelerationb/,rd5d mz4m,ncl0qg)ipy 6 y of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s