A bicycle odometer (which measures distance traveled) is attacheddbpd yo6 t39)d near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyyodd) 3t6 bp9dcle with 24-inch wheels?

Suppose a disk rotates at constant angular velocitluui-cj u, 7p.y. Does a point on the rim have radial and/or tangential accele ci,7uj u-u.plration? 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 component of linear acceleration change?

Could a nonrigid body be dixy5,9)s a;s xmi xtk1escribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greaterbj) ,7tjak e h;-woe;a torque 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 handsdjsr dba;)4i. behind your head than when your arms are stretched out in front of you? A diagram may help you to answrs4ja );ibdd .er this.

A 21-speed bicycle has seven sprockets at the rear wheel and three9re:grms +05 pjux y adn4dg78 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 ug58d jgyesanp +79:rxr04dm to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able tnu-f:sy;iga4ya,u8zle e d 7 6o run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of myfuezn7ulda -s ;6ygi ae,84 :ass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bea4 e1bo;oh7eq.moh rk; m?

If the net force on a system is zero, is tii j7mbl;rn. o s b.h*ebgykg+. j3f4*he net torque also zero? If the net torqubis .+h.jg lb*4; fr k.e* ynmo3gi7jbe on a system is zero, is the net force zero?

Two inclines have the same heigw3ajb1fu r -lqv j+5l5ht but make different angles with the horizontal. The same steel ball is rolled down each incline. On which iu5 qfl5j3r-+j1 wlv abncline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (frowpfbl bi)qups)3a * 51m rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speedfpb1*3w 5qiup)als b) there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. Theyfq.5 z/ ctrrm70mr*nj start from rest at the 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 Kfjnr.0*tzr m5rcm7q/ E?

We claim that momentum and angular momentum are oe.uun9, :lkmes dl -0d*kjv3conserved. Yet most moving or rotating llven,e*uk.9dumk-sj 3o0 :dobjects eventually slow down and stop. Explain.

If there were a great migration of people towarhs ga o 3w;hutcta/ 10ataq,h86z19fpd the Earth’s equator, how would this affect the length of tf 8th6 gps /9;,aaot03uzh1wcthqa1ahe day?

Can the diver of Fig. 8–29 do a somersaulu v0k;k6,y nt zjp/i3pt without having any initial rotation when she leaves the b3 t ;yik0jpu6kvznp,/ oard?

The moment of inertia of a rotating solid disk about an axis throuccvfzt) 1b8q8 h+;bv fgh its center of mafc8h1);+f 8qvzc bbvtss 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 sto 08hbz4km8x (r sg*nfnol holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay thhg8f8 szn k4bx0 (nrm*e same? Explain.

Two spheres look identical and have the same mass. However, one is hollow and +)xwu8tyb6b9jh0v ) 1 as,pve1wajdvthe other is sole 06)pw v t9 +bjx1aawj8)vsdyhu,bv 1id. Describe an experiment to determine which is which.

The angular velocity u4t2d3 u7otax of a wheel rotating 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 acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel7ux 4tu2atdo3 . Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large frq77s/a2 4*, zwuac m5deunwh aeely rotating turntable. What happenacw,z 4*7qh5m e/a u7as2uwdns if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quick/gx, u,oh)c jvly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his,gvh/cj,u)o x hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of coniry4um),;ptkew h.s ; servation of angular momentum, discuss why a helicopteruehis ty)m;rpkw,4 . ; must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles ic+zzeuz g3)2in 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 Earth because of an amazi9dif7cc09mcq0lbw7u: *li2 if2v yck ng coincidence. Calculate, using the information inside the Front Cover, the angul0id cq0l:y7iwfcb 2 99fvku cm c2*i7lar diameters (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 frun1 qm r em.lrg;u2d4/om Earth. The beam diverges at an qnurgmur.4md/l e; 12angle $\theta$ (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. Whe tpc5ds 4(qrdh4a,9(j 0ra kqjn the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow dowj44a0sjqr hpd 9,r( d cka5qt(n?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another cxhj x0s b66k:l1 f48 nhiob2nxhild. If the ball makes 15.0 revolutions, what is its diameter? f21oxxi j 64 6b8:0lshnbhxkn   m

  A bicycle with tires 68 cm ink,ho3: kvil i5 diameter travels 8.0 km. How many revolutions do the wheels mak,i: 3klk o5hive?    $rev$

  (a) A grinding wheel 0.35 m in diameoc3um((5vx zxkl fe+5 ter rotates at 2500 rpm. Calculate its angular velocity im+(oku l3xx(v5ezc5 fn $rad/s$ $\omega$ =    $rad/sec$
(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 (Fig. 8uln.1k3no;pn s ;zb0iicb 0-p–38). (a) What is the linear speed0 nuinib 0cks n3o; ;zbp.1lp- of a child 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 of7f;o2/gp se7jcasi00rjbx ir 62q lb+ the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin9ehl 3hascldrv0ka0r r27+ -umd y +y.t
(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 rot,q/m 24zrsbb jate if a particle 7.0 cm from the axis of rotation is to expj/rb,msb4 2z qerience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly h mxv s+.sb;xco b-z9-about its center from 130 rpm to 280 rpmbv.;ob s-xs+-c zhxm 9 in 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 9tga(bfi)/ zks $R_1$ 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 g )fd5:5us3xbi m)mbcowd81s 2 ku1mqApollo 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 every minute during a 12-min time interval. The spacecraft can be thought of as a cylindemu 2ssmb8wob1g m)55qd1c k3:)u dxfi r 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 sq y1ygq f9v(+i. Through how many revolutions did it turn in tqg1fy iy+v q9(his time?    $rev$

  An automobile engine slows down from 4500 r*p2iqxa2wv xrl 2-cm;*3wb xtpm 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 o.25r-ffnse;h6e tlnhf flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to fehhe;lt. 5 6fn2n-sr turn through 20 complete revolutions before reaching 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 rxfk36c 5fu+hw pm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time u+3xhf6wf5 ck?    m

  A cooling fan is turned off -1ib/o+j *h io.wcq 0x3p wmmowhen it is running at 850rev/min It turns 1500 revolutijc ib*.q31- whiwx o0m+pmo/ oons before it 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 car reducesp gm,w2.vbbl ) its speed uniformly from 95km/h to 45km/h The tires have a diametb)m.v gl,p2 wber 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 ma8b++pv febg 59xp njsri4c 6l9s +-oyake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h Tj-5+s ib 9+48vfr xp c e+g9nlpyao6bshe 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 ridin*okfcizcd f gc2 43c-et3m*ra/ uij+8g a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a ci3je 8*4uif*rg -io+2f cdak z3mcct/crcle 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 wide. Whjd94 )volxuq* at is the magnitude of the torque if the f9x*oluvd) q4jorce 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 Fi83: su +wsmgudg. 8–39. Assume that a friction torque of 0 g3+:8sudws mu.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the endez0* ynf:7h(n ojk t6/2g mr 9jsmcd7ks 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 and direction of the net torque on this s *od fe ty/9zn0k:rs6km(7g7cmnjh j 2ystem.

  The bolts on the cylinder he5p s;mqnt4ke)pvi*b jiq59-e ad of an engine require tightening to a torque of 38peets4)5vk9;bjiq qn- 5*mip $m \cdot N$ 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 sph k5cpnuo6 /1)z 8ayhgyere of radius 0.648 m when the axis of rotation ih)a y/ogpc186k nz 5uys through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Thz1/f nmaq5) rte rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?)1 mat/zrf5nq).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotat,icu j42e q.lbg8zg (eed in a horizontal circle8bg(lieceu z42q.j , g of radius 1.2 m. Calculate
(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 rotz 2 jwegqh26 l1z() igcm)ke7lating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N 6hcm)kelgl72(jg 1w)eqzi z2 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 of5 : kwpg:q*to +ysrtx/ point objects shown in Fig. 8–43 +op:xrksq tyg *5 :/wtabout
(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/oama jq+yx-g/y- -mq 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 cylismdv;/70xl aendrical satellite spinning at the correct 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,d0ea7 xv/s;m l 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 uniform cylinder with a radius of 8.50 cm and a qb cn /u)s.u.,un.taj mass of 0.580 kg.)sn, ..unu./j ctu bqa 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, accelerating it fr5vg 1q)j 21uo g(zsvquom 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 oc ;w6 w yhyh/ulfd-ahrir;0(82aduz.h((i e wn a small hand-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 acceleration, neglectingif ad2rh 8w zhd c0aelu.w; wiyy(ur(hh;-6(/ 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 is eventually broughbbe nx*.y2 sj0t uniformly to ren bjx2y esb*0.st by a frictional 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 acceleratezg/wx 6(i9lut 0t*3h+hdb aya s 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 ekfxlp- ji;l6x o8q2- forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from r pq-6f;8je l 2lxx-kioest 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 canq .hbiyqqzjd;( kd14 9 be considered a long thin rod, as shown in Fig. 8–46. bzd1 (.qd;qykjh4q9i
(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 mvi: (,xwsdz.fp,r-jbasses, $m_1$ 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 u;b6jjo*xf 55tdzf,ikkiaf8qpewj) 73p,3xfull turns (revolutions) and releases it at d,pj8tkifxxau3i5o5fb ) jk6 ;*7 3jqpz,wef 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 huw:,i ffugu 7xoy2v - 9,oay,cjnmoa .11)vv nas a moment of inertia 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 torque, s7r11l)iy)ocivcbg9 h0pkn 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 rollsdgi v.v) /vgnc.fc 2(1nu+lad without slipping down a lan+a c n( ni21gg.u)lvv fv/ddc.e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to thee 8rj+2dyl;d l7bl)+m, q vwjv Sun as the sum of two l j+yvr dq,8de mvl;+)w2 bj7lterms,
(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 of 1640 kg and a radius of 7.50 m. How mucahm .lr7f4m) hh net work is required to accelerate it from reshmam)r7 .f 4hlt to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 ck4 )-2hjk+aszy)j0ea qvqel, m and mass 1.80 kg starts from rest and rolls without slipping down a vhjqk0e 4ql2- )+a eyazj,sk )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 tip. It starts tp 1nwg uc/.5f(v ijum*dc:nx5 o fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]du invn xp:/ cu51f5*w.mj (cg    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on .ne1*xow z 8hfthe end of a thin string in a circle of radius 1.10 m at an angular speed*nz1 f8.ho xew of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-k s(wj1 5u g.ffcnhd0r3n 4l f1gii:i9zg uniform cylindrical grinding wheel of radius 18 cm when rotating at 150grf(f njc13 lihi:1u g5zwds4if.0n90 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 at his side, on a platform t9l 2i jvsyodrv 8tq1)-hat is rotating at a rate of 1.3rev/s If he raises his armivr-os1q 8jlt ) 92dyvs to a horizontal position, Fig. 8–48, the speed 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 her momegk8bx) m3 xbh7:+nc/h pp.d*7qhbq d nnt of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotationnx. h7:ghb3h n d)dp8+*qc xp7kbm/qbs 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 rotation rate from an initial rate of 1.0 4hu u:ex7gdetr*t 35zrev evezhdx 5 *u:trtu 4g7ee3ry 2.0 s to a 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 around a vertical axis through its center at a freq v7 6uxql7yv0aas7g*iuency 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 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 g6i 7*ua7 vaqx7ly0v sit?    $rev/s$

  (a) What is the angularby d dsh,h80twn h43u,uy:u:f momentum of a figure skater 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 momentum of the Eaki711 wlxddf/zb0 y.aywa3) - o hrwp;rth
(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 cylinde 0sr if*yebow ql30m4,vxb4)rical disk of moment of inertia I is dropped onto an identical disk rotating at an l3,r0fsb q*ex0o)bw yv44 eimgular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2gl0 flyw:qnv -qi7i :).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 stanqsk9nk)2k(- dm 3 agsqds at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertiamk d nsaq2g(9k -)qs3k 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-gj( ub d-3c8 nvk.i,uv)vzoh d,o-round is rotating freely with an angular velocity of 0.8, d (kbzo)- c. v,uujvvnh83di $rad/s$ 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 icxcwv,o 7a 1cx3a3y g(nto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing 1(,aw7ccyv o3cxg3 axradius. 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 windy9ctw+y zxf** yq;9sia pk2)ys in 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 nhqlpifwsyr :a+n1 afr/bw 9 i(6:p5+ $ 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, that can *hmvhh-k 3(qi rotate freely without friction. The moment of inertia of the pervhk- *mh3iqh(son plus 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 oxlz;df7;lr-gtu )d16.5-m diameter merry-go-round turntable that is mounted on frictionless bearr) ldx;uf7 d-g1ztl;oings 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 ozzz t-zl oo4c6oghb*mfoz46; 03c 5e dn the ground with the end of the rope lying on the 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 length of rope unwinds from the spool? How fmz36eot4zh fz 0-z4c lo6ogo ;*cdzb5ar does the spool’s center of mass move?

  The Moon orbits the Earth such that the sa5 lf s- j65goz:y8bqu2kzlli ,me 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 latter case, treat the Moonzlu,5l5:f b6qis8 z -l2 joygk as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rat s+x)q6rvk (dkj)kv7iu w(k 9ce 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 cylinde+g b)fhvl7o2 k;z pt+wr of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at 2z+v p ohgbk7)+tfw l;constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and cv z//.m88ih83urkawz x b( xhdiameter 0.075 m, joined by a (concentric) thin solid cylindrical hub 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 sbu8v k/xza3cm88 wh irx.(/z htring, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angu- km-kbt7 pz5ylar 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 ofnfy*d /mdwt:k/: m:gs our Sun, but with mass 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 sphere at all times, and that the lost tw :ymfdgmks/ *:dn: /mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy storedp3z pghp1 y+5i in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical fly ipyg15pp 3+hzwheel 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 illustratesk8sukvrqb+- ( 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 hor /ewq)p7u31a v (wnbu)u ,dkuqizontal surface 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 fric.zdg;7l4gpwbue* + -ch3xjhe tion) 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) the angular acceleration of the rod, and (b) the linear acceleratilbp;ejc* x.dhg4+uz3g e 7 wh-on 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 floor, and x77vmd 8j1rgx we want to exert a horizontal force F at itsxgjd 7r x7m18v 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 *3kjeag;j*x4*m;bn72 eeli yr4 iny j a turn with a radius The forces acting on the cyclist and cycle are the normal yi ;a jk*ie;mje2x jngb 4e7*y34n*lrforce $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 ) t+qhx1iiu z3vt5 9mnm 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 u+mz tqii91xhvn5)t 3 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder anp5z6cw gx + 9lo(w8n3uof r+ffd her arms as thin rods, making reasonable estimates for the dimensions. Then calcul+5 lf8pnfor w36cwof9(gz+x uate 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 clutch assemblyn. hry(f9 e9oi n08+uz r,epnf8sx/iv which consists of two cylindrical plates, of mass 9x nsf e,o88ze9ivp i.r0( ny un/frh+$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radiw; lq 5js)y )qwpk16gzus r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h twkzsqy1;pg 5) j6)wlq hat 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 do not (lnlgtu18 3gsd 3pf/b assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly x )5mpxs 5e8qr+s zu:qfrom 90km/h to 60km/h The tires have a diameter of 0.90 m.sxp)+ xe8q:qm5 z5u sr (a) 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