A bicycle odometer (whiclwug6r xvm+- m b(-+krh measures 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-kbr-gxrvm 6u+m( l+-w inch wheels?

Suppose a disk rotates at constant angular velocity. Dodps 8 rnl4e4,mes a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial ms8,lrn e44p dand/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described -q8l4,*6 fvb -z2quxai)pia7wsdlkpby a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forcoq(bap4-71c wji by 6ie? 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 y 7be7etchx :se0+y xq+our head than when your axcq bhe 77x:y+ 0et+serms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at then8;jvfql 7 ,cm rear wheel and three at 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 sprm78cv;f l ,jqnocket? Why?

Mammals that depend on being able to ru kh9 ks3au99m9vw7fc wt-:hgq n fast have slender lower legs with flesh andq9-ktm9:w 3ks h7ugf 9va hc9w muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig.ewzx:o+g 5;fp:i , vzd 8–35) carry a long, narrow beam?

If the net force on a system isj( h(kg:vi5+fxd g31f0vd cns zero, is the net torque also zero? If the net torque on a system is zero, fg (c1:xdd3ksvg+nh(fvi5 j 0is the net force zero?

Two inclines have the same height but make different angles with the hp 2ncae+fr /idp6/s,yorizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gyser2 d/c, a6p+/fnpireater? Explain.

Two solid spheres simultaneously sszn1gx ip3, f d5 63udi/qas2ctart rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom pfd n 3 3ii/,261axsgdzs5cu qof 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 sadli7w 9yy- x7ome mass. They start from rest at t7 iwd-xl9y7yo he top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are0 vm/sgd 1s9ju z.ozp nh3+p3s conserved. Yet most moving or rotating objects eventually slow down and stop. d+9s hm 1z j3 o/vsu.zs3gnpp0Explain.

If there were a great migration of people toward the Earth’s equa mz(;ci*zyovoy/ m:;btor, how would this affect the length of the b;mvomz: *y;/(ic yo zday?

Can the diver of Fig. 8–29 do a somersault without having any iniwj+9huji+ mv/tial rotation when she leaves t9i vmj/+juw+hhe board?

The moment of inertia of a rotating so*-fbbx r bu2s0kdq s,-lid disk about an axis through its center of mass is- b,ru0b2qsk- xd *sbf $\frac{1}{2}WR^2$ (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 holdingo,8btnx)9wns wo78py a 2-kg mass in each outstretched hand. If ntn w sb8xyop,o98w 7)you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identis y1x k+*+hfh m.ke45fxes*jbcal and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine wxkx*e++s1ff ke mjb.y4hs *h5hich is which.

The angular velocity of a wheel rotating on a horizontal axle points west. z1/:w znx *xowIn what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangentia/x*o1 wwzzn x:l 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 large freely rotating turntable. What ft / bk)no oo.x-+fgx9htu 7w5happens if you walk toward the center?b)5wft7n ux +ko9h-ogxf to. /

A shortstop may leap into the air to x* vnk++r 2sgm;mfq0ocatch a ball and throw it quickly. As he throws the ball, the upper part go2sq*v nr0+mmk+xf ;of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law ofu324v7ejxwxp conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller canvuex7 3pxw2 4j operate to keep the helicopter stable.

  Express the following angles il/dwk mw54 0gtq3.kr1szcidz) +y *gwn radians: (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 Ea nhtmm j3tkl hlckb r3j:06 y0jc;6/)drth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sunm k;mk jldn)66 jh3rb3/cl:c0ytjth0 and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Eazt18ncvx9n ;6qtf; yarth. The beam diverges ataxz91;tf yqt8vn;6nc an angle $\theta$ (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. When the moto 7h + 24wt-y7io*xo/2fiz ob/yrrxti er is turned off during operation, the blades slow to rest in 3.0 s. What is the anf2o2i/oo x yrewxi*-r +7hy bi/t7t4zgular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If th ;g vue(b9(hxre ball makes 15.0 ; h(9er bxgu(vrevolutions, what is its diameter?    m

  A bicycle with tires 68 cm ia0ic+:2j+4ew yyycvdt 328 9mxjvcqj n diameter travels 8.0 km. How many revolutions do the yc:qjxj0 wi3 2yy+2vmj8v+4cc9da te wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter r4iauv (t86 x.hpcfxz 3otates at 2500 rpm. Calculate its angular velocitxz6v 8xiftc4h.(a3 pu y 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 5k9b dnmvl9*u4.0 s (Fig. 8–38). (a) What is the linear speed of a childb v*k9dmu5 n9l 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 orw0r79p o; yl vkw tk(olo-m n.gm44ro4bit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spev ;gzs+ *jrs5ded of a 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 a particle 7.0 cm from the axis v i n3fcw8t wya/51qq-.jw2x lof rotation is to experience an acceleration qlcyw/13f8-w.van2i t w5qjxof 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheelgt;)c xci+dn; *tf*tw accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determnc+*g) *fdw tx ;c;titine
(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 radiusp oby 5*g60-fdopd q+e $R_1$ 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 Apo4eg ay/opxu4fx5)-xej+e k0 b c 0pr+pllo spacecraft 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 evexk0p/+5b e 4 +oe-0ypg4eaxfujc pr x)ry minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 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 220 s. Thro95)( qwlujw ;hhd -ve5gqluz ,ugh how many revolutions did it; vuhl95w gw-u5 q,(zejq)dhl turn in this time?    $rev$

  An automobile engine slows down from 4sl p53.a u;hkmtr,r(d 500 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 strepu3p4,s(ns vysses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before rp(3,vps uy4nseaching 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 accelerates uniformly from 240 rpm to 360 rpm in 6.5 sa14f;c/a ak 1q.5eanuqx s ur5. How far wux/nqa1uas5a5 q ka 4r; 1ef.cill a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off j1a6ni y/*ig a vx45w(fui +rcwhen it is running at 850rev/min It turns 1500 revolutions before itgaa1u */v 4+i j(wycif n56xir comes 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 revolutions as the -9cs io9b6p,bsc0w+ uz+q98 6siypg ayj s6sfcar reduces its speed uniformly from 95km/h to 45km/h The tires have asws0+o6siqi9zc py6 c, fub g68ajy+s b9-9sp 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 m9p+ eq/eskgufk8 l:qr5 ;n-kk ajsb-8ake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h e klk5p/;qg98+: rsu nk -8jqbkse-f aThe 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

  A 55-kg person riding a bike puts all her weight on each pedal wheq/ q57zo8h tqisir.p k;1b3-epppg:s n climbing a hill. The pedals rotate in a circle of radius 17 cm.ep8;q: iq3koz pg5bs.thqr-ps7 p /1i
(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 wide. What is t8)m .sljk )poszabzqht ; t3ehz b,5d):3g;yc he magnitude of the torque if t 3:;z;8 c5z3 s l)pebj.t)qyt oh)zgdh,bksm ahe force 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. 8–39. 7(zn0f sibmq/m8 2hw aAssume that a friction torque of 0m80nf( zmq/ 7i2h bswa.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attargefpu:ex0:wp ,;imd;el56f5 vo5 o wched to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and5f5wv6erlpw5:;x;0 p eeg ui,:omofd direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a *9njifjx -s l,torque of 38sf*j-9 l nxij, $m \cdot N$ 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 sphere of radius 0.648 m when th0czm mpf+y8x:mt 7: xee axis of rotation is y8fcmpxt +:m: mx 7ez0through its center.    $kg \cdot m^2$

  Calculate the moment of iner. 7fx4zay i (yz11 yisqdb0mo -/9bvmttia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combm(xi41 a qt0bb.zi-m yoz 91dsyv7/y fined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light +qe-oqr 1y7tkrod is rotated in a horizontal circle of radius 1.2 m. Cal+q1 t7 yqr-keoculate
(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 b)m1mht;5 w ; , xftfdnlk:ih;speed (Fig. 8–42). mw ;;m; x1fthknhib: )df5 tl,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 o(cn4u.utz c0pt:qp c: bjects shown in Fig. 8–43 upq .4 nzp0cc::t (tucabout
(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 consists of two oxygen atoms whose total mass isx79 ll.3p vy8vfb/4owrl sg h8 z,dx.z $5.3 \times10^{ -26}$ 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 cylindrical satellite spinning at the cokw;r,bqs j e utj((*4arrect rate, engineers fire four tangential 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 a(jjrwe,;tu ks4q *(b? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm (l))y)mxt ag9ehgc,oand a mass of 0.580 9 cm(a)xo),gghy )e tlkg. 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 swi fyu8 jkb7rp,aa/s/,b ngs a bat, accelerating 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 h/p.v:k d7qrl3nc+k-*n cz k nhand-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. Calculate the torque required to produce the acceleratiokpnl cdkn 3c* :-qh+rnkz.7/vn, 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 off and sbqj1*p -rn9 ki: zl/dis eventually brought uniformly to rest by a frictional torque o rpdz*nbis1 9-l:k /jqf 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 acce1 . fcem;8yu)9syd(dd;riwfylerates a 3.6-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 thrown solely by the action of the forearm, whir w;jjr( /pa 0hh9k*xvch rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acchah9r*jjxvw 0krp (;/elerated 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, as shown b7z. 9quaevz9 in Fig. 8–4bz 9azuve.97q 6.
(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 massegxmj6; cd/k -o tsr-c.s, $m_1$ 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 hammer from rest within four.+er)b;7q oa2aee ump full turns (revolutions) and releases it aou2. m+rq e7bp);eaa et a speed of 28 $m/s$ 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 inertia of km+ :se xg5jf($3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 286e:5) dn:ma6rdn nkwm0 $m \cdot N$ 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 rh hojk;d+1zq8anp,2fmo1 mhq 6; q4dy 3krv (polls without slipping down a lane at 3.3 pr vm +qqy dkk,12h4;o ao; h6fnz jdp(q38hm1$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ofe /n1pyu6j h cjuo6:l/ two term:l /cy epu j6u61jho/ns,
(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 mas 9 0r1dfwfnhz m:tw;.xm4am h-s of 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 per 8.9zrawwnm1h4:x0-m ; .fhm fdt 00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fromggie/b j7m6-b21 6w bee cqwr9 rest and rolls without slippine1jc 9 mi ewqeb6w7/gbrbg-62 g 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 on57dfn:ab2bhu q.m l86dpu 2sv its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper enpm 7 nh56 :u.d2b l8quafsbvd2d of the pole 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 of a r -q7y)hre f-x;ijkdo2hp); r thin string in a circle of radius 1.10 m at an anguhj) 7r)xfed-q; r-ph2k;ryoi lar speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angul 3ldge-4:fwd u6p-jio 87 nslffm-vd1ar momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? jl 1gf ffv76--m 8d 4w 3udole-sin:dp   $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at h9 xp9 pv.+kh+z*)c xdpd,dhr3yxvzu.is 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 speepd v3zyzpx+.c 9krupv)*d9h+x.dxh ,d of 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. 8–29) can reduce 4 a1i4h irpjsz:*on s0her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her1s4*ra0:ii4spz h njo angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate ofx. enlvc *zc lh)hb9-6 1.0 rev every 2.0 s to an6hb *9-l).cl vhezxc final rate of 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 arouw3 4rxu ylfsba*7g8nc9vurkb5ye 2. :nd a vertical axis through its center at a frequency of 1.5rev/s The wheel can be consideryy743c2a.*lw5 k:vrbn fgbxr9 s8 ueued a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, 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 skate0xtsqg c4a/q0s7ao: q)8m olwr spinning at 3.5 $rev/s$ 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 momze asmp7- g2p6entum of the Earth
(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 of moment of inertia I is dropped on)5gt mi9b 2bl fu13ox uivt,6oto an identical disk rotating at angular speeu26 o5ti ) mx 3f,ub9ob1gltivd $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.vf,jjf mw yry-2 3*b.t4 $rev/s$ 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 stands at the center of a rotating merry-go-round pl.q 5cw d0- yun kl*lcwxzpihv(46; 3mdatform of radius 3.0 m and moment of iner; mdnwx u4. i hq0pkl*lvw-c5c3(z6ydtia 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 rotating freely with an ang1; 6+kz )hfcz(l6-tdzgdu n3yqqj g:aular velocity of 0.8 az-:t(1 z)k6 j n6+qzdgh3gcdyu ;lfq $rad/s$ 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 collapx;ib2dw.,*owdje81i nwj 1i hses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% i1;.h bidwodj *n w,w82 xi1ejof its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate 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 in excess of 120 0r* ox lae /n/8/2zw9rt2wfymi ,sfjs$km/h$ 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 7m d 2qr pvu47s82)iu+siqljo $ 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 rest, thang5jt4maihr.156so +cb1b gl t can rotate freely without friction. The moment of inertia of the person plah1s6b5lgin5+g.41jrb ct m ous the 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-g u/lc o/ ,m5oq5h+hdeho-round turntable that is mounted on frictionless bearings and has a momend5hheh5cm+o , lo/q /ut 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 en)en-vr wij sdq ;m7g*;d of the rope lying on the top edge of the spool. A persons )*e md;7g -qrwijnv; 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 length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such tsn:k1pf1xx,ksy5-o o hat the same side always faces the Earth. Determine thef:os o,nxpyk1sk-x 51 ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at ar 8v(ygst.r77ntzz5; lsz z4e0unq 4 i 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 unifol v*9,k cqjppks4a(p4 rm cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the mokp 4k(qp ,vplc *saj94tor.    $m \cdot N$

  (a) A yo-yo is made ofjk /jfgorcna0.*m t/4 two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hubjng/ / 04rko.jmfcta* of mass 0.0050 kg and 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 .0 p/ uiwo/ d xtlf6e93+ixslothe angular speed 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)ittg( .e 3*r5dwzs tt 8.0 times as 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 ztie .dt3 *st5rw)t( gsphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is hdcs:,e /a4.z ist lg:for it to use energy stored in a heavyt siz c4::ldh/g.e,sa 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, and 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 illustratb1npn9d ktk 4(ktua68h 8.v qaes 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 su-oj6tw4pj8 yo2 rb)5 qwe:62exp wbxt rface 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 M and length L can pivot freely (i.e., we ignore friction)bw *zd g6yvfq4x...xi about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) thv* g.yq z.fx.6xbdi4 we 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 floorr7bvz179v ec qn e ++ra qxlwdue7:32v, and we want to exert 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 9qvewv+d2e+e 3vlc7r77:b rzquax 1 n h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat roacn 2wzeok tpw48ca sp- 7z6+7bd is making a turn with a radius The forces acting o 7e+w- pzt6aocn cs7p w84zbk2n the cyclist 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 sling of length 1.5 m and begins whirllf0btw5ok3-q:s d-u+m p b9 wcing 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 fea o0bp m39w l-st5-+q:ukcwdfbt, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid vg,x xt:l y2w.cylinder and her arms as thin rods, making reasonabgx2w.t:x ,yl vle estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutcr:pip -fop. - cp+wba .o9ub*yh assembly which consists of two cylindrical plates, of mas-o bppfcya.9wi:* urpp b-+o.s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rolls along the looped rough track of Figamfic( (r s8v /*y0bib. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track?c(iif 0*r8s mybab/( v Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dol*rw/sju*b p -f5a88rqc p 4qo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 re1 z5 av60 kaervmjv.y ;73nlyxvolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) k.evmx50yral3 6;vynav 1 7zj What was the angular acceleration 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