A bicycle odometer (which measures distance traveled) is attached ne(.ptv7b ueg; eh0-ns yar the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle wi hng.uepsy-t0;eb7 v(th 24-inch wheels?

Suppose a disk rotat1k hgym zr).c2es at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If).y c1 gzhrk2m 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 described by a single value of the angular warjj4zs j 5k-ulbzpl9* ek. 2.u2f 8ovelocity $\omega$ Explain.

Can a small force ever exert a greater to9myng36ib 4uw16 vqe4 g mg(uorque 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 jks.lbp*)b6l,x/ krito do a sit-up with your hands behind your head than when your arms are stretched out in front of you?jk./b*),xbk rl 6 slpi A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at)o+h wg,+sg6 kqk qvs3 the rear wheel and three at the pedal crank s+k)3gk6+,v qsohwq gs. 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? Why?

Mammals that depend on being able to run fast have slender lower legs witmljdjuz( ;j1 :h flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this dm;(ju dlj :j1zistribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry at8cpi)/ 4x mex). z ,jvpuwin+ long, narrow beam?

If the net force on a system is zero, is thw6j (nf-a(9 cipap amrqy8b40 e net torque also zero? If the net torque on a system pqa mpyjiw6n (9bara-0(4f8c is zero, is the net force zero?

Two inclines have the same height but make rk2 d5ziqvov8:tuti(s* l )k5different angles with the horizontal. The same steel ball is rolled down eachu8 )sdti i5v q(vorkl:kz*5t2 incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling c0t n;3ki*rcjje * :hmqmqc59(from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Wh3 9;ktm*cjmjc0r *i5qqceh n:ich 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;aed0v qt)giu a.s )-d same radius and the same mass. They start from rest at the top of )qv;0)iad.-u ad es tgan 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 au+pvu )zm9d1and angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explpa9u)z um1v+ dain.

If there were a great migration of people towara9x+sc- l,hgpdex,ybo,9; i kd the Earth’s equator, how would this affeck,coedaspyx9 gih ,xl;+9b -,t the length of the day?

Can the diver of Fig. 8–22aj9nx( 5hw nw9 do a somersault without having any initial rotation when she leaves x2 5jwn h9n(awthe board?

The moment of inertia of9r ,ndz ixy)p::2 lqhmoyf+i: a rotating solid disk about an axis through its center of mass ) +x h92oryz::inm p,: lidqfyis $\frac{1}{2}WR^2$ (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 ar+ebt-dcs 01f z,u c*k rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the mar teczc -b*kf1uds0 +,sses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and havj js5g35-yusb- 7m bune the same mass. However, one is hollow and the other is solid. Describusj m5s 37 -byngj5bu-e an experiment to determine which is which.

The angular velocity 4qja 0eoksd3f i8ls/8yhog5) 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 tangentifj3 5k84 oy/l ga qd08)iohsesal linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing onmbp g/9 6 sstdte6rltoa+und)5*,vh/ the edge of a large freely rotating turntable. What happens if you walk towa6ubte 5+)l, dvr6o* th/nsta9/gmdsp rd the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he thg(rlcy+,x hm;/ff9rer/v1t lrows the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotath+gl,frxe;( r yvrtc/ 1l9 /fme in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss 1o41 cnwpl*qvc.gaxj6k u / 2ewhy a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stwj e4xlqgu *oc/v 1np 62k1.acable.

  Express the following ang,z sc em2y7r+v t.n2ueles in 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 amazing coincidence. Calculate, aejp3p nadgv 1j0 ,75aes,g5i using the information inside the,p,3e5pdv 71en 0gjjiag aas5 Front Cover, the angular 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 from Earth. k7 : c8iv8zob wgsf/)dThe beam diverges at an an87zf ks )i/gcb8d o:wvgle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender roh 4znyzp ,f-i0tate at a rate of 6500 rpm. When the motor is turned off during operaifh4zn ,p y0z-tion, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level s rr2 z chzbofhte ,ct0;n*1o ((h)6gtfloor 3.5 m to another child. If the ball makes 15.0 revolut1()*6f0(gtecsnht2,t zhhorozcr b; ions, what is its diameter?    m

  A bicycle with tires 68 cm inl 4jd;x; x(pje diameter travels 8.0 km. How many revolutions do the wej;x(; j4xdplheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm.qb+fc -t*fc :a Calculate its angular ve*:aq-c b+ftfc locity 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(v hna*0. o) cg*vqtxg,)qcr/ hhvcu0 complete revolution in 4.0 s (Fig. 8–38). (a) What isug*c)n haqvho/rxh,)c0c0.vg t v* (q the linear speed 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 of the Earth (a) in its orbit/zvogbw4/h 9*c3p mst around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a po1 8dy5mh5(:zn(x thqys ovgxy)0;ugdint
(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 centh)):1 5 n1qliz4u-tzbkg:qu )vakfg hrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of5lun ikb:-g)u)z1f1ag4q: htz)q vkh 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly1kl6slsqs/ 9e4 r4i7 lkxjzs8 about its center from 130 rpm to 280 rpm in 4.0 s. Deter9z/rs ljksl 7s4s ie8x46lq1kmine
(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 radius ud j+dd/dazpl65+ .bx$R_1$ 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 spacecrarjk14yhcbo,n 5 ccn1z+c xdxd40 n3,rft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accele4xndh,x o dzcjc1y10c43rn +5 bn,crk rated 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 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 -aavq9 s f0ub--thu*yfwm40cz8u l i1from rest to 15,000 rpm in 220 s. Through how many revolut s -a *fb-fywzvqa u0940cumt8h-l ui1ions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.e9u f e76m*nkbypq*6x5 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 stress7 5mncmceme (:es of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its finammme75(c ecn:l 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 acceleratekkn( phthb877s uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel havk7hn 7(k pb8hte traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 reeg ty5am )1so;volutions before it comes to a stop mo1);5 sygate.
(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-y025edp5*ltjv9o l vejr)mh reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of e vpl0*5e9dhl o jm2 5)ryvjt-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 revolu*zxsvj*sf5 /c (slw.h tions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have chwfs*5ss/ x. *(j zlva 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 put+yv ir hf,/c9q1k 2:praf qcm,s all her weight on each pedal when climbing a hill. The pedals rotate in a circle o9 r2qvp qyah,:+c ,i/krc1mfff 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. What is the mag05gweoxt+ur. quo2ur7lq u7) nitude of the torqurg.ox lu0u 7+u uw2qt re)7qo5e if the 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 torq6 *viukvoxk7gbd r.:dlx r,-9ue about the axle of the wheel shown in Fig. 8–39. Assume that a fricti 6rlxub:dxk.97rdgkv, -i*v oon torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod which pives2o2j :9gy -g( psqobots as shown in Fig. 8–40. Initially the rod is held in the horizontal position :jyo(2 s2s peb- goqg9and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tighk, fcg *pk8ix5-oxlp* tening to a torque of 38g8-5 ,xfkoi p* lkp*xc $m \cdot N$ 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 od1 u04z crmst+jvpma+022bl of inertia of a 10.8-kg sphere of radius 0.648 m when the axis of ro20+2u+ z14vrpsdaot cmbjl m0tation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The 1 e v3u8azcj7 a )vup3cwf4c)yrim and tire have a combined masucy e83afu )c)43jz7wp va1cvs 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 rod is ,e0pq. ;j:kcvjj g-qk rotated in a horizontal circle of radius 1.2 m. gk0 q jj-e :.c,jvqpk;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 boww6) c yiaut7ot7 ry( b-q)8iifl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is acw(7 -irtuf86 )yy7b iq)iot1.5 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 point9;l wt1uqnqy43 xs s5o objects shown in Fig. 8–43 about 41 nxuqs395yo twq;sl
(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 atom +zd9wt tr-,.pmzss q6s+y.v ys 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 cylindrical satellite spinni)r; txwy d3;qwosi l00ng 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 o; i w0;lrs)x3yo qwt0df 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 uniform cylinder with a radius of 8.50 cm and ahq+ jpe b3,7zi mass of 0.53ehp bj7, +zqi80 kg. 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 from rest to 4dph87haxls ckvm(br 991-v k3 $rev/s$ 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 sko/cc5(k.zc zxale: 1mall hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in cxe5aokz 1.(:z/c clk10.0 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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpmhs1yfxw;w sm5odbxz3r6k ,7 4r** vc e is shut off and is eventually brought uniformly *o*x7f bszc ysmve6,k43d1xr w;5 rhwto rest 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 accelerates a 3.6-kg ball at 7 s 6zt4lxec0iw88z:)fyj rx2/xoeuz2 $m/s^2$ 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 sole mhmx*:d(-qgj0xp,q sly by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. Th:-*dmg( pq0,j x hsqmxe 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 l,7luqviqveo.i)y 79(-wda e considered a long thin rod, as shown in Fig. 8–4)e7i9dy 7iv, qao q.e ll(uwv-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 consisdb h tr ;y5uv-:y,+ggmts of two masses, $m_1$ 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 full turns qs4ojgr;q) v,c k tx55 zf5+we(revolutions)4e 5xtov5 5qk,c+ wzrfsg;jq ) and releases it at 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 dfowqz976q; yruc e 22of 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 torz)z+9n-z c+kz bfyndcrg7h1;k 4 ifbp9e;7 a xque 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 o 5v3xcgi,y,h without slipping down a lane ati3xo,5 gc ,yvh 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ofo* pdwq59ig kg 4mt8c82drv6 i two mro 4ii8pwvkd q g698*cg5d2tterms,
(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 radiu n2 0uk+a.ni amvx6y.js of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cyl.x 6n0ki 2j.myn+aavuinder.    J

  A sphere of radius 20.0 cm : hvsbqvv ;a)08vhv7 xand mass 1.80 kg starts from rest and rolls without slipping 0vs7 ax :v8bqvh;vhv)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 ba3*v**xcmgs zko .ys:alanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the spc. y v:o3smxz *ka*s*geed of the upper end 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 roq8w5(g +;*aaofrsbk btating on the end of a thin string in a circle a+* kfqrb(gsa ;5b8owof 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-kgos i4u j(l69ak1 w6dxv uniform cylindrical grinding wheel of radius 18 cm when rotat9 v4 jsiw(16 xu6dlkaoing 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 at his side, on a platform that)82ba x4puo2jcj tw5z is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreju4c tzx58o)w ab 2p2jases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown n94lgb(m w (jizc+8ij ew42ky in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight po89lkywgz(e4+jw 4j2cnm i(bisition to the tuck position. If 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 rotation rate from an initia9neg5s(b 5s6 i) u6vle4 bqzmdl rate of 1.0 rev every 2.0 s to a finalvb5 e6 dbni4gl (suq6me5 z9)s 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 thr9/isv8 1(73wkk qxwudz hq3w tough 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 clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rot8 k 7ix3wq9d/uvzw wq3hsk 1t(ating 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 spinnz25we pvh(9e 7sx4 tj,3 1gy;wlb2tv*ukot gning 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 t,+. 3zg x sz*sjops8hghe 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 droppedp;:(uaxo +n tg onto an identicanp:t; x+g(oua l disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a/no hxk 6u.h*kt 2.4 $rev/s$ 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 stands at the center .1jbnlg2jxrt3 pi:b yyt5we l.0t j 9)of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920 .b jy 5yp9jtelg1: rnt2ib lt3jw)0 .x$kg \cdot m^2$ 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 angum d, /o/-yu+dxqv e)eklar velocity of 0.8+yuxk qo/e )ve-/,dmd $rad/s$ 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 collapsecp 2l*nxpy,5 zd gvb)6s into a white dwarf, 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 momentu zp)2bgvl6 *n,pdcyx 5m, 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 cchg 2q9/il4f$km/h$ 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 xcdo ;/**2gl-. o h9y ij) y.dhzztke, +vafkd$ 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 caewc )ze2avjx yey0k -e-i605fn rotate freely without friction. The moment of inertia of the person plus th e xwc fy-0jv)y-ei60kee5a2ze 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 edgm75xaj w6 rr 7*aaltmme-b-1ie of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and hasamjeamwibar-tl*65 r771mx - 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 roll qf,dkg mn8(*fs on 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 ofkfmn,8q gdf( * rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Defubnl;.kq0 j -m6x,+infwg9ltermine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case6k wfx bin.9uj0nf-+;qm l, gl, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of;wn/d*8xw+rr 2w,+p bsyfph w 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 cylinde1ogf).h +y,pvig):qyd z- wvh r of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at cons,q y.g)g fv1h )h +od-wy:vpiztant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindriiw(pn4kfhp -xz zvexpq(*g24 eo9 2zk5q v(w 8cal disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub ofq4iove89(nxf2we(g(- p p45vq kp 2wz xkz*hz 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 the angular spblt(a.f63li o eed 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 e i/ig,shvz(njrjdm+1qp- 68 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 spgez-v/j r6jdqi1n h(s pi8+ ,meed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for fpcsxf,f+n 8- if6bys5q8 (c qa low-pollution 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 ,+f bp 58fxf sqqs(cc8ny6i-fand 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 illustrate;d6qpc-fp ng 4q,itfb0x0mx2 s 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 surface at speed v=3.3 f)o-;ftf/*9j y z yyepf+l(tgv w/.db$m/s$ 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 )pnl q qo*i46mand length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and thoq4n*l mipq6)en 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 radiusbrw x tgap1tfo,/1 8+m4 oq/h1is0xev R. It is standing vertically on the floor, and we want 1/t fomhq0obwrg8i1x41ts+x v ,pa/eto 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 h, where h

  A bicyclist traveling with speed -urzwc ;*w la g6(z3ddsdscit040 9smv=4.2m/s on a flat road is making a turn with a radius The fortwg40 za63wssc z( drmd-i 0 d;s9uc*lces acting on 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 begi:qx4 wba1ze( owoo2mj;dbc8/ns whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate /q wdocjba8w x4 b1o;mz2eo:( of 120 rpm after 5.0 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 bo( pt o2 9gmgi5f.3p x;iym6yoody as a solid cylinder and her arms as thin rods, making reasonabi(i. 6 mgt2;gpp9 oyomx53o yfle 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 clutch assembly which consists of )xhy:fz;um,g two cylindrical plates, of m ux)mhf zy:g,;ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 o/pxfmgw . mn17ah3wh6 d3 p 6tnl38dfgf Fig. 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 wim ph3hd7f ad3n3pn8f6 . tl6g1mxg/wwthout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dokr *j ;2aq0r 7flpzpwa*0o-np not assume $r\ll R$ h =    (R-r)

  The tires of a car make 8q4ig.+ gy40y- m l-di-iqmz xf5 revolutions as the car reduces its speed uniformly from 90km/h to 6ilg0iym xgfmzidyq4- . 4q--+0km/h The tires have a diameter of 0.90 m. (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