A bicycle odometer (which measures distance traveled) is attacfjv( k-q8-osaa3h8 dqy .m ej,hed near the wheel hub and is designed for 27-inch wheels. What happens if you uqyjs( dhv,aj38 qk--ao .f8e mse it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular 9j(*c abopx0s velocity. Does a point on the rim have rad0j9 p*x oab(scial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of li)t7h ,-((e)jzy2lkqn n(r.awfm dithe angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force?,a5w/ime w5) -jkmdac 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 yout eqg9tb;j ,.kr hands behind your head than when your arms are stretched out,; .eb9gjq ktt in front of you? A diagram may help you to answer this.

A 21-speed bicycle hzq(8lhus4048 uquiml l 1. dwuas seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it ha81l u8w4suz.0( lqdiumq lh u4rder 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 :zm inn5r2 a rn jycvls4-;pt6h 5r:5eon being able to 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 mass is ad;ej5ztr:a 52c :4 snr5hpry6nm-nlivvantageous.

Why do tightrope walkers (Fig. 8–35)7f8ab ql0kbf 5q6;jmz ) 9ofvj carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net -qxfb n zqeb 07;l6w7itorque on a system is zero, is the net force zerbbq 76; nilewx-f70 zqo?

Two inclines have the same height but make different angles with the hor:,m*ja:e 5j1hs8n8q svbku wgizontal. The same steel ball is rolled djqews, v: g:n*a8 hm1uk5j8bsown each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) d:u 0y ,1:zitxcfyu tr,own an incline. One sphere has twice the radius and twice the mass of the other. Which f: 0x ztcytyi ,,r1:uureaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They dek*h c3+aa.:nzxa5e 3sfq 8g start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom?: afe*+ n5dqhaa83 szcxekg3. Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are vq x:bfs- ;t)82sadfwconserved. Yet most moving or rotats f-b t:8);avw fq2sxding objects eventually slow down and stop. Explain.

If there were a great migration of peopleg9or5 5k0lu:o)nlx qld*q w0h toward the Earth’s equator, how would this affect the l qhx*5l 0kuo95l:0rw dnog)q length of the day?

Can the diver of Fig. 8–29 do a somersault without having any iz lg8q* 0f4qnenitial rotation when she leave48lf*z0geqq n s the board?

The moment of inertia of8atab13 uuf )v-bz3c1 9ddfan4 m.vb f a rotating solid disk about an axis through its center of4vb3f)mfau9-bfbava 3 cndu d 11.zt8 mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool hg/.8kn/ l jcbverx;. kolding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, d;8n / j rekglb/..cvkxecrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However,svyf vz,+m f r0z v,o5mnfp-*8 one is hollow and the other is solid. Describe an expopy*-f8zv rf,50fsvmz ,mv + neriment to determine which is which.

The angular velocity of a wheel rotating on a horg 5isd.rnsz eh8 2*6m;l8s eiy(x bco+izontal 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 wheel. Is the angular speed increass26sn x.ez(relbdy8cii5so *8m ;gh+ing or decreasing?

Suppose you are standing on the edge of a lar-v,)iz ;wuaj dge freely rotating turntable. What happens if you walk towardaui;,d-w jz)v the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As hu;twuc.vs t ;q(7i5;i:zhqv,.gll eie throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36iu.; uvi, (.vl:7g z;le hs5;tqcqwti). Explain.

On the basis of the law of conservation of angular momentum, discuss why aylq2,/xh2uo :i+ys z u helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propex+ 2uos h ,iyqlu2:/zyller can operate to keep the helicopter stable.

  Express the following. tizs( j+n sz3-jzeso09 w;yd angles 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, usie5i x81svnv3nw3q 9q nng the information inside the Front Cover, the angular diameters (in radians) of the Sun and thnv895enq33 i v1qsxwn e Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam dive 78y*xey,d mglrges at mlyyg 8e,x7d *an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at n w0k91tl4j3(gsml*xgr 6qm) ee9ni(jn7taia rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular t)n k0n(l9x9sj (6gi ee1n7w j3li t*m4 mgqraacceleration 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 g cxojzc0ph,7u*g4.b ball makes 15.0 revolutions, what is its diameteohx.c0ug4jbcp z7* g, r?    m

  A bicycle with tires 68 cm in diameten1xq fptwyyr6+ 7k 5r3r travels 8.0 km. How many revolutions do the wheels make 1y7n6r+tyf r kpw5qx3?    $rev$

  (a) A grinding wheel 0.35 m in diameter r,z3rcxewj+a ps+y a2,hwm7 5 iotates at 2500 rpm. Calculate its angulaw3p72h, ae zra5c+ i,jmw +yxsr velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round zl z.x8+m nnilw 4(a)dkr oq41makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linea (z n raz.oqklx14)+n4mwdi l8r 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 th2qaomv 6* s7lsc,h dl8e 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 pog2e*ixvd o9d7 int
(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 par;j p:sj4tb;uh ticle 7.0 cm from the axis of rotation is to experience an acceleration of 100,0ts:b 4p;juh ;j00 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 281w5z*ra d3 w e(.d1giqq mpwh20 rpm hi3p (wqwm2rg5az eq dd.1w*1in 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 radiup,5,p, 4je3l oj ylp6nbl-mui s $R_1$ 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 Apoll; blsq p(8jhybfrcl f; 1q+45ry7t r2ro spacecraft put themselves into a slow rotation to distribute the Sun’;q qb87ys5clfr2yr1rj+ p;( 4flhtbrs 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 uniformly from rest to ,irv,uirvu c1 -50iwb15,000 rpm in 220 s. Through how many revolutions did it turn in tv wiibu-r0i5r vc 1,,uhis time?    $rev$

  An automobile engine slows down from 4500 rpm toul flmcw-4*p.z89 bg -n qmh/n 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 str5n xeai7 cj-v7esses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions bef7jcxiv5n 7ea- ore 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 rpm to 360 rpm in 6.j won pl/ e).g31scduofn-67p 5 s. How far will a point on the edge of the n1pujcdop lgw-6 e/3fsn.o)7wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/mgesfdjr: 1cu; r8ak**in It turns 1500 revolutions before it comesur1das kj *r e*f;g:8c 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 c8hnzce a5k 842h0 z3r adhn/v:rilj4d ar reduces its speed uniformly from 95km/h to 45km/harjzl in2/z8c4 3 hnv rhdk eh8d054a: 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 t66 v;t,dm 6bk og2 2*tnwjbjznhe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 66otzwt*2,jg d n;bbj26 kvn mm.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing a h0ddc;y9 egy1aill. The c9dag y;d 10eypedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is thz zdc4b ua)30he magnitude of th)udcz3 h04ba ze 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 about the axle of e eyeroti g/ a*d y50aa4;2kh/the wheel shown in Fig. 8–39. Assume that*42dg/ey r 0iyk/a5heteoa ;a a friction 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 t8*jex/pl y :,z+0l*ihqh gp oeo the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and thenegelph:i8 l 0 ,yhx+/j*q poz* released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requirexs;)slt4udt 7/5brs c tightening to a torque of 38 cbt/4u sl);rss7d 5 xt$m \cdot N$ 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:3-/jh4e(yyu fvknb d of a 10.8-kg sphere of radius 0.648 m when the axis of rotation ik-vuhf:(e /dy4b jny 3s through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle(vl t14ez hh;du6p:pm ttcdb/+w x g/9 wheel 66.7 cm in diameter. The rim and tire ha9h tc61z+e /lhtv: (gdb;pp u/ mwd4xtve a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod isx+ :5hur h.qpu rotated in a horizontal circ.5p qrx:h+huule 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 aj7 d/jfu1jc0 on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The frictionfad7/ jc0 juj1 force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of poi eg:rdb88 8vownt objects shown in Fig. 8–43 awo8e:bg 8 8rdvbout
(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 ox lb9mzkrghrx21-.yr +7h r 9pedr)q3yygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrim d/ffbdm17 9 ulvqr g4lzl-s; +:l(bdcal satellite spinning at the correct rate, engineers fire four tangential rockets as shown 4mfdqmzr:v9gl+d ; -sll7f u/(d1blbin Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cyln)f9)e uw)th:o*ojcnglo * i5inder with a radius of 8.50 cm and a mass of 0.580 kg. Ca co)l5*) hu ow:f*jint 9eo)gnlculate
(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 *i6xyks 2s99z6bu njcbtf/ p0tqp *b) 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 tangentims 3xl 3n92z9p lm 0ify18fmhqally on 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 s91mlzfmx2y0 mn 38plif3hq9is 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 1;k:jy;s c .:mjy px lya5q+oe-0,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2- le ;kxcyam.5ypyoq:+j;: js $m \cdot N$ 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 acp9si2 0 elrrrvi72u/hcelerates 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 b6rk x3e,p w-rwall is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–43prx6w,k -e wr5. 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, k,, mrk;g mvqx)wn3w5 as shown in Fig. 8–465,,wvgnr;qwxkm3 k)m .
(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. :go,umfwm*hq+v6wh 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 4m+t.m3bl2xl-yxv pqq b .f/a (revolutions) and releases it a-.+3mxlab vtpy flb42/ x. mqqt 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 inerwhy7)- wds(w ftia 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 torpkjnam /02v;0spx yys0, 94uu s)vrzo que of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without acnhuf(wb (3 aurs6,j4q qx(ayx 0+9zslipping down a lane at 3.3aa yx r z4 uq6,h(qacw0(xu nfjs(+93b $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with resqin :-glh3v hu 8+8i(u9pcqg epect to the Sun as the sum of tl qp gq(8+h8ivu:3- 9nu hgiecwo 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 tgexk ayi,s i0r;0k9* radius of 7.50 m. How much net work is requiredr0ae k;gks90t,i *ixy to accelerate it from rest 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 cm and mass 1.80a . .1jiaqxw;vmr8 -ln kg starts from rest and rolls without slipping downaw n.vj .m;qlax-r i81 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 tqlki,wj(*e8r ap1n2 on its tip. It starts to 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 groundq8 nkt (iaeplr1* 2,jw? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg balm.5/ t ie/iqrtitupa *kb81et+vhx :)l rotating on the end of a thin string in a circle of radius 1.10 m at an angular speed trxp+h/*)tieeq ita8. 1u:i t/5bvkmof 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg zoccu7c/jgl lz (cm02f6u1,a uniform cylindrical grinding wheel of radius 18 cm wc(l1c,7lc6zojcf 2ag u0z/um hen 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, onexo zpzgm 16,f/rntgwkf))yd 4 9un*/ a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the spee6m) /g t9 r kd1xufgy/pn,zo* )wfnz4ed 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 redu /e4xso(pyv,nus4r, oo6nju0ce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in e jnunu40xooo(6rsv/py4 s,,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 he 8+ ,hcx,rpsvcr spin rotation rate from an initial rate of 1.0 rev ev,hvx8 p,c rsc+ery 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 cent1 mksqif /3hz(e:* gmjer 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 omj :z qe /k*fmih1gs(3f 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 angula+ u)u2bf ro 8hlmaqx.(r 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/o 3c-ko;7vucvjwr u . momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped ontod.g y:am4 jz(zf;f8,.roawah an identical disk rotda8h;a.4fym,(gf. jz w r:ao zating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2qz m4wvc0 d)oa5 3brbtng8.0q.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 of;/otgccz seio/7e x-u 1 xh7(g a rotating merry-go-round platform of radius 3.0 m and moment of inertia 920 iz/ - cx/1;t7ehc(xu oo eg7gs$kg \cdot m^2$ 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 roq vai(9.yun+4/g( qpa o z5nqntating freely with an angular velocity of 0.g.4q95i /aqpy(( anq+zunovn 8 $rad/s$ 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 collapsp5:hxqb2 c kw++3nmxr es into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existhkm q+cx:n+bp52 3x rwing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 120 kb6;5cja b*abua/ro9 $km/h$ 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 v9()jxvhz fw ($ 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, initi+ce eed 4m3/x-7/garafg ml vhr +)s-rally at rest, that can rotate freely without friction. The moment of inertia of the person -/c3rd glr)g+-efa/+am ems he 7r4x vplus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.tt -,+oy/:igihy/k; zli )pzj 5-m diameter merry-go-round turntable that is mounted on fricti; pki t-zj,y i )/zltyi:g/oh+onless 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 oncx u)8hny.v:js)n7 qy 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 )uxvc ) n78jyyn:qhs .far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sid/r;mnpn+dx7u qsa s7 0e always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about7n;up sr+a7nsd0/qm x its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate w0napuk(f, i9 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 rad3fpoqz;1 ,u7sn88hbnxj :ot wius 0.20 m acquires a rotational rate of from rest8xz;,oo :7n 8tj 3bwnus 1qhpf over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, qx *pn2tu +4l8ssub(nc:ror.c6r t9 l(9ikld each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylinqkc xtd9(2s+rl n:r .ut(*ois 8r6lb nlpu 4c9drical 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 string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is thej lu2t;:as4z3fs.4 hjiwggi* angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times t df4cu. 7w nfywsu8 3rof/0q02/ujcl as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron starf q/dc.r4s2fcnw t 0juf8uyo0/u7l w3 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 no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile isf-cvtit6 t36w;t: ysq for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travt; ttyvqt36w : cs6f-iel 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 illustrates ad- chm9jeu5y /n $H_2O$ 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 xvk sm:2v/5cy 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 f7*hxjgzk 8 +0k/5kk iyeonxx7 reely (i.e., we ignore friction) 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 acceleration of the tip of the8zk hy x/7k*jgk7o5xn +kei 0x 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 oneefcl2 hn0q w j(;6wz2 the floor, and we want to exert a horizontal force F at its axle so that it will climb a step c (f2;ew wjnlz0hqe26against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with spee:5rp kmw/mg e/d v=4.2m/s on a flat road is making a turn with a radius The forces acting on the ckgr/e5: pmmw/yclist 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.c .z c;x8 cd2 )bt.ozz1ggkaf sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the to 8c ct2;gz) bo.gdzfkc.1 ax.zrque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’2z t5zxv8qy l0 ey.e1i.mwe0vs body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate y z weq81ly0 e.2evm50x zv.tithe ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a p u 6zxeq2:fi.0s+r huhuf+ 9cclutch assembly which consists of two cylindrical plates, of msep:r hf+u.6cx +i0u9zquhf 2ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fi + sjahv.7psb-z8z tq.g. 8–58. What is the minimum value of the vertical height h that the m .h vzaj.sb-qsp8 +tz7arble 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 assu 6.vdc 2qphvp3me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revoluizh0u.6 v hnqer d;b-w+ 7/pn t/qe1pztions as the car reduces its speed uniformly from 90km/h to 60ku/vn7dqpz;t0.q w p6en+ h hb1z/er-im/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