A bicycle odometer (which measures distance traveled) is : r3r)wy3emv jattached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch whemrv jr3ey :3w)els?

Suppose a disk rotates at constant angular velocity. Does a poieudt77;k jr(b/j m uh6nt on the rim have radial and/or tangential acceleration? If the disk’s angular velocity injt khb6du7j(; 7e/ rmucreases 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 ve+ms b 12v/cxyj7k,jfklocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? rzc6 +0 gbb5 . *dj/cyh eqolcb5r2/hbExplain.

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

Why is it more difficult to do a sit-up with your hands behind your head 1 zwh,yvep9-f than when your arms are stretched out in front of you? A diagram may help you to answer this zwh vey,-1fp9.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the pedal e17,umv3k7t pne:k pl cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprockku 77p enelmvk1p,t 3:et? 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 tg:2xs 2qyp q+b z3za5t/ojl9.im 4nyv o run fast have slender lower legs with flesh and muscle concentrated high, clost3vm5 gyj.:aznxs lyb9ipq422q+z o /e 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. 8–35) carry a long, 7w zq6fcxar:,narrow beam?

If the net force on a system is zero, is the net torque also q(vr/)teq3dg:vh:memh- qn3sxz 31 u zero? If the net torque on a system is zero, is the net force q d)/ qr33- 3usnmteemzq:g:h1vhv(xzero?

Two inclines have the same he.yi 5b42mex zfight but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gr5x2e.4iybzm f eater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. Ont:(v )u-+w quvttk(l.+ d ynjwe sphere has twice the rav. (dvyttl(-j k+ n)wu:q+wtudius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same maskr3 c;alh1z7v 6x5 p*tjg;nph29 rspvs. They 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 6 rc;7nj 3;tl2*p pvh1grz5vkxps h9athe bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or r n(set 2d21jsvp(1w eldt1b j5zc 0h9lotating ol z1t9 d02vs(ps1e hj2wj l5eb(1dnt cbjects eventually slow down and stop. Explain.

If there were a great migration oftd/qe- w o.gg, kk46a zz jzq-cc.s8;d people toward the Earth’s equator, how would this affect the zce/t-4c;., 8d g-zjdawogqsz .q kk6 length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initojs c(26wofk b*wq;h+ial rotation when she leaves the boarqwhf( +*ockwb s o6;2jd?

The moment of inertia of a rotating solid disk about an axis through its centerwn -lkz7r**e xjp:eh 8gc;4ej of ma7*4kr8ecejl-:p *xhw gn j ;ezss 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 onv. 4i3vutui 9k a rotating stool holding a 2-kg mass in each outstretched hand. If you sud.uitvvu 9 k34idenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, )zr5-d qcunzx4b 3q -4qm1rnb. l ml.ione is hollow and the other is solid. Describe an ex qn mqlu1 rcx.zbdmzl)r53.b in4q-4- periment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. Ini;qks wda)+,w what direction is the linear velocity of a point on the top of the wheel? Iws, w+qda) ;kif the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a largedr1l as(/*d*n)uomcgpzt0. k freely rotating turntable. What happens if you wal ur o(0tlsz.*na1pgkd/d)* cm k toward the center?

A shortstop may leap into the air to catch a ball and tct/ x(1av,nothrow it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you w v(nactxt /,1oill notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation pzg6q- 2h6(q;hpbdkewkjy50of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or mor6(w beq62k; 0 gp5zyh-dqpk jhe ways the second propeller can operate to keep the helicopter stable.

  Express the following angleszxn)rl+6bjzf, a-g oj-hw(wkso2x-w 2+m:zs 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, using t(h, y x 2se9mhc6j.eq;h8lziis/ mes+he information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moo;+em9sz sle.8 hi/e62xqy m,( hhijcs n, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the M2uz ar.hr m44fli3ptr9 dxb2:oon, 380,000 km from Earth. The beam diverges at anub2ti3hr lad :pfr9 4xz4m.r2 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 c+m lwf (ddsx4:cg)k3 a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in4 +cx:f mdcl)wgd3k( s 3.0 s. What is the angular 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 the bal)8z;ro *wcx chl makes 15.0 revol;wxc*ro8hc z)utions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many h, t.ulu ;5 + jotn2 p-kui(-zdnrge2hrevolutions do the wh l-j htuk (u;uho5ei.2 2,zntdgrpn-+eels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its0se0d5g 2ya bf;ugul;z kh:o; angular velocitys5dfg : zy;2e0gu;aohl0 bu k; 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 cn1/vcj +w:wur qvm m*8jj 1yx.omplete revolution in 4.0 s (Fig. 8–38). (a)xr: wj.jwny+*1 ucvm8q/ vm j1 What is 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,4 hsvdom3p 3n) 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 pointx gyi98tpd92p
(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 axip(e+u tzg,rwc4rt;o z1w q ,6rs of rotation is to experience an accelr z (g,wt+ ;6rqepu,oz tc4r1weration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel *mb q)wq0kev9zdd-7 y accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determin0q bk-y 9e qzm)d*dwv7e
(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 radiusx 3 w o;:wc5n-bn9m0jf/ezxxwj t z.;j $R_1$ 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 so8dl1ywi5. xoiz 5 fq:pacecraft put themselves into a slow rotation to distribute the Sun’siod.qf 1yo 55xwil:8z energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter 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 uasoh8 wmz +aw78 1kf;s nw,jt3niformly from rest to 15,000 rpm in 220 s. Through how many revolus 8+njs8t azfmw kah7w3;o,1wtions did it turn in this time?    $rev$

  An automobile engine slows,h sqba-me 1n* down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets6a iq wj qsdqlwa,bd 4dj;yo1u8*/p ;. in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions bjyws q1aw/j*q;8p4u,i; .d aldb6d qo efore 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 accele cok,dvq6a(fg(xj 9aeqm g**.rates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edgj vqagkxm*a(g9f.c 6(* qeod,e of the wheel have traveled in this time?    m

  A cooling fan is turned off when-c, vssk2+duut rv -h/ it is running at 850rev/min It turns 1500 revolutions before it comes to a sto/+ cs u ,vrvu--sd2kthp.
(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 revolu:a)qgs/ 4 rfcutions as the car reduces its speed uniformly from 95km/h to 4aq4/ c f)srug:5km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed8d1brh iv4 *h 4fxm*lr uniformly from 95km/h toh4hf v1d*r mi8rb*l4x 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on eachkc cm;srvs0d uf:5dq - oq)0:b pedal when climbing a hill. The pedals rotate in a circle of radi0 ckds:qfd 0uq;sm v5:rcb -)ous 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 o pufp-es47w 1wide. What is the magnitudp14u o-7esf wpe of the torque 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 torque abo xca*5)xd1aiaw2 wz i/ut the axle of the wheel shown in Fig. 8–39. Assume that a friction torqxc 2x5)z/wwi*daia1 aue of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are at rxz*+df vxb7hxqm)z:b: c7 d)qg 5zf6tached to the ends of a massless rod which pivots asx+)6f7q 7b : qgxddcxbmzz*z )rh5:vf 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 system.

  The bolts on the cylinder head of an engine require tighten.sh , n0/ygwwling to a torque of 38 w,y /s gn.lhw0$m \cdot N$ 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 sphe(0ltkf*mvez2l1j+ v m re of radius 0.648 m when the axis of rotation is througvlm fm v1(+2*0 ltzekjh its center.    $kg \cdot m^2$

  Calculate the moment of inerwra)asa7)-gt o y. /fhtia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The massfrs at7-aoh )a./)wgy of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rodtd ys, (0a8iryvg1f9z is rotated in a horizontal circle of radius 1.2 m. Calcurfv 9dy 1ysaz80igt, (late
(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 a1hx++*tybfjvwdg a 8e*ream.mww i,3 bk6 e95t constant angular speed (Fig. 8–42). Thbj1 e ba8* +9wv mr,y+e*h6efg35i.wk td xwame 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 arrbpsupu n.6+gz f 60it8ay of point objects shown in Fig. 8–43piuu0g6.s 8fnpt+b z 6 about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total m:ih2+t2 m8n ,tgfe sykyc ,/iqass 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 spinning at the correct rate, enc9j ) jw4z4tree63t9jx82qf q.ng hlwggew80gineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass ofeq6 4w ztgchx9wn9 8 )r.2wg4e3q8fg etjjl j0 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with ayy*h rl5zm7c) radius of 8.50 cm and a mass of 0.580 kg. Caz7yhl5* c m)yrlculate
(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)uyyh1y+.bfi k.oo be +f*;p n 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 hand-d4, qwgb 919nyt59wjleujsdb1riven merry-go-round and is able to accelerate i9u1 jb 9j,t9541nlbdywgqsw e t 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, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating vyx- 1;msvkqds p ax0;v20,f0fpr wr4 at 10,300 rpm is shut off and is eventually brought unifopvr x4- vxp ysa0;frsk,q21df00mw ;v rmly to 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 s cv6f;wte)nf5 w-t5v 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 thecaopvr2 wi)m; y3 mgld 0wo+gxa/45c( forearm, which rotates about thelp04a+cm3 yo)wac r g(gv2md ;i/x w5o elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in F r/0eyz zrdk.,ig. 8–4 zzy,/r0.ekd r6.
(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 consianmb ,b0a)vr5-*g 1y.tahz uwsts 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 4 dpwqxq02f0o n: sai5(revolutions) and releas4opi 0qfx2qds 0wn: a5es 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 of inerqdx.;i ch wmt1e8ot*,tia 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 of 280 j-9q/ek6)mf wbfus b;$m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass x++gm s -wyw7d9t:r mh7.3 kg and radius 9.0 cm rolls without slipping down a lanex+gymhm+dr7ws- wt:9 at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as )x0g(heu5 n bhthe sum of tw)g(0 uhhx b5neo terms,
(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 7.5wdf a44-zyf7x 0 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00xff z4y74wda - s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without/3c :h gnge*qqj7 xp8j sli 3qhcn87ejg*jgx:q p/pping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall 6riilpfq/+r-3 zn.t kand its lot n/l6 +rfi k.pizq-3rwer 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.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a 6r qwfe+ (r0e fcuhv3 6*kqfz:thin string in a circle of radius 1.10 m at an angular speed of 10.4 0fr qq6wefhuec:+ f z(*r63vk $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentokkd+ a a1kg.w-ex-60z(r3r5ykf ue p um of a 2.8-kg uniform cylindrical grinding wheel of radius 18 0-+ ug ky31ef(6e.ax oa5r-krdpwzkk cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on 4u, o 1ov6 vy09cdcxgya platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speev0ocvu,16cyo9 xd yg 4d 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 mompw6 qeio.a: i)fuc 3v-ent of inertia by a factio qi.e3 wv)u cpf-:6aor 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 her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can 0x) ):vxx4q l5pg;nzupbjm n/increase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s tx mpju)px:;b x40gnl/zq)5 vno 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 frx6:z gxxe +0bb7(yxj0md)32e;ci; vo kt omwkequency of 1.5rev/s Th( bc)3je+ew2z0ykkg t6o;7xmv; 0x:ox mi xdb e 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 it?    $rev/s$

  (a) What is the angular mo77gn:f9xhl, 3m zkmwqmentum 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 Eart+q9tp6 3p0 j gfsimdxhgk/ 8k(h
(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 onto axmn::sz :,)t fl ( tpaqu6e4xq+ ce1vkn identical disk rotating at anclv,pk:+ x m)txnequt1 e(s q::f4za6gular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 0*x4wky)y ( ojf) ;xgku/fzkp at 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 xha ssa9+. a7ycenter of a rotating merry-go-round platform of radius 3.9.7 hxs asya+a0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freelhw1z1d t* rkl9y with an angular velocity of 0.8ht*d1lkw1rz9 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, lom4rznzd q; -1jsing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, wz;j-qdr1 4m znhat 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 ;t1;x pj obuj;ilwawvn215d *winds 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 5 wy2ypg) -0kfabf: oo$ 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, th)cmmpnc0k*7i. j*wji at can rotate freely without friction. T 7 m*mip*c. j0knjic)whe moment of inertia of the person 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 ed-cbxb()w+e 8 djlsw 0*gq,-tsain . dige of a 6.5-m diameter merry-go-round turntable t e . c-abn ,dd)+sb*gijisl0(tww8q -xhat is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the s,x d6mh6ywkbq(fn9vmygp00 wu/ , k(rope lying on the tdw (n0hm6b 6v9,p/ s, mwgyxk 0fkyq(uop 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 far does the spool’s center of mass move?

  The Moon orbits the Earth such t),qx4jo5knjq hat the same side always faces the Earth. Determine the ratio of the Moon) ,jo5nkx4jq q’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 aorz6 (h*/ d nmyc+iqc-t a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of rfo 9zn , s+q(kog5awi/adius 0.20 m acquires a rotational rate of from rest over a 6.0-s interkw5/oi+(z q9 a fsgon,val at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindriyuk-wfd uxki 1 a5c4h1y76ou 4cal disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energyu 7doy 1kckf-i 5xw4 huu164ay 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 speed of the rearon9s8 gk:uyx, 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 masvkqvdv(9rc25 6. +w ikiwfzi( :u z2yks 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 mass carries off cq k wz+idvw 56vkf:2yui (ik.2(z 9rvno angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile ikwqs:j(p 55 ops 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 cwj(k q5spop :5ylindrical 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 illustrat+4wl52g 1vowl nad*k esojb1.es 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 horizonta83+ uacxpa*0 /vhvemwv*j6 x cl 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 zs7k389xrr9 i)aupq y friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and u3xqy7za)8irk 9 9sr pthen released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. gdbq4w;c/jh 3It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a std3/qjh g wcb;4ep against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2(ev pwqh4ykyw j(y.;, m/s on a flat road is making a turn with a radius The forces acting on thp e (,4ywj(wyyq;v kh.e 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 ayjm89 w o)u /d.n98dfrojjfe- nd begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 599ywd/re-u)mfjoo jndf. 88 j.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 body as a solid cylinder5y5d. v9a qo oia+lfp3 and her arms as thin rods, makino5l5a+.d3 vp qy i9afog reasonable 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 cons:b7 nwh -a2zig9rq u6xists of two cylindrical plates, of mas :n-g 2 ua7ri96xhzbqws $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ,) e,3e rxt qpf0d7(ss) tgdjbradius r rolls along the looped rough track of Fig. 8–58. jx 3)r7st)fq d,0 gptese(,bdWhat 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? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dopbbd3 y4:9cf8d,k b*7yqe rwr not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformlye8o75 wkv. v;uaz. dbk from 90km/h wa.u8 k 5z7dv ;evo.bkto 60km/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