A bicycle odometer (which measures distance traveled) is attached near theebz5.jfk a4 4p w,3;xd;hzb ql wheel hub and is designed for ;f4ebz 5,z j lwx4bh ad;3q.pk27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constv8pj v9,howjht0b h:.ant angular velocity. Does a point on the rim have radia:80.hhvwo j b ,tjvp9hl 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 si fwz u-*a9gjm-ngle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a jt, u n, egf;:igud;k m(p5d6rgreater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head th;c8 rx+l zf(gi6 is.klan when your arms are stretched out in front of you? A diagram may help yokfz.ixc 6islg+; 8 (rlu to answer this.

A 21-speed bicycle hll( , n;6,pofw 20 ztdiota1novq2se 2as seven sprockets at the rear wheel and three at the pedal cranks. In which gearlwio q( pf2,oeasdoz0lt n61n2 ,t v;2 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 loe2zh d 2nvrw9m8vm ph;67fa p1wer 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 mamh7; vpvp r9n8fwm2 6 21aehzdss is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a l roj5 1p0hcau14fkn3iggfaf-7 ;go( j ong, narrow beam?

If the net force on a system is zero, is the net torque also zero? If themy d4x pqfyvj2s 9en1x9()g i9 net torque on a system is zero, is the net force zer s(91yj 9me)dnif9 px2 qyx4gvo?

Two inclines have the same 6 5mgq;c8am qnzgu06c height but make different angles with the horizontal. The same steel ball is rolled down cu mg66g0nz8qqma c;5each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One m1aj:sqjh e54 sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Wsj qmh5ej14: ahich has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the samea .4szc3*ik ;qj4b ,dh9hoz si mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bo3 s ais4d h.;o*kczqzhbj9,4ittom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most movif4cd8 bhb3 r;. kva2zbng or rotb z4crh;2.bb38ak dvfating objects eventually slow down and stop. Explain.

If there were a great migration of p*.-1:0io kmfzf kioy people toward the Earth’s equator, how would this az* io1pki-of mf k0.y:ffect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having anr2mxkvx 1:c1py initial rotation when she lea:mcv pxxkr121 ves the board?

The moment of inertia of 28y 3k sl rj-:he*jnxd9w/qks a rotating solid disk about an axis through its center of mass is /ky*q3sjxws8klh2erd -j 9:n $\frac{1}{2}WR^2$ (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 anzziw;qj4.;3)otsc x rotating stool holding a 2-kg mass in each outstretched hand. If you w4snx ; qtic.z;joz3 )suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mast38 bchsuy6/x dkgp 3g/c/2 mos. However, one is hollow and the other is solisc68y th dgm/pb/g/ cu23kox3d. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horiz /k9hw+w zl1ilontal axle points west. In what direction is the linear velocity of a point ikh l+zwwl1 9/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 increasing or decreasing?

Suppose you are standing on the edgyi gm+:9 8je atni1wbky/) o,s/w.a tve of a large freely rotating turntable. What happens if you walk toward tv,a:kwygmo1n /. j9)y/si+bt8aw e tihe center?

A shortstop may leap into the air to catch a ball and throw it quickly. Asr;+1qt r 76 tuyjcvrtdp3j.+q he throws the ball, the upper part of his bodyp1u+y6jt+;tq.q7r trcvd3j r rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, dis ucv+) xekgg0*cuss why a helicopter must have more than one rotor (or propeller). Discuss oneecgk )xuv+ g*0 or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radixg,*o( nt:9 u3y* ll)(r zibx4bucrlians: (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. Calculaj a)vi.,(kj fip.s/l lte, using the information inside the Front Cover, the anguls(pklj.l. ia/ fi),j var 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. The beam diverges v3m:qhm c-p3e(k9t vpe7k9uivmp ,g8q/u- sc at atsh c8q9( -gv3pk:kemev , uc3-9mvqpimp/u 7n 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 qc8thk3(b6irfy8wxdr gw/1u(y /ds 0l9+ qh uat a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest (8t hdwx(y8/rsby3 q 9r+6/hu 1kifdu0wgq lc 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 floor 3.5 m to another child. If the ball makesduoe snd5x28i,)o: qj 3n v0vs 15.0 revolutio8 vuo,)2end03vxds oi :sqn j5ns, what is its diameter?    m

  A bicycle with tires 68 cm in diameter oosv abip buthac ,,4l7a00+xy;i9d 9 travels 8.0 km. How many revolutions do the wheels make?09b sl bu,i4ohavyaoa ,p; tx709+cid    $rev$

  (a) A grinding wheel 0.35 m inlagp e uy+zs ;6f(mgd1:kjv7, diameter rotates at 2500 rpm. Calculate its angular velocity iv: zk ;a,ef(gjulm6 1 s+pgdy7n $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution 9gee:j ,1ua)v jiw3w ain 4.0 s (Fig. 8–38). (a) What is the3e iuvw91: awjagj )e, 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 odmr48up sqldln i)/rbd-1f)7 f the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a bejt4kc1n.-yppd;e9 dri 4l+ point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the aa yr4/rh+fvbexc h 872xis of rotation is to experience an acceler7ryab8f ch2/x v+h4eration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abo, t23)8esotp(gy- n ,wyulb zyut its center from 130 rpm to 280 rpm in 4.0 s. Det te, (o8nguylz,2s3p)-wytbyermine
(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 radiuwa *nbz:dih95 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 M;c(c aqk+wl5j)v3da,)af ppioon, astronauts aboard the Apollo spacecraft put themselves into a slow r3ivpqfl)aac+w ,( d; k5)ajc potation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a 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 unqf+3fs5ppxcojy 4:u*s rgh 8pj75k)yiformly from rest to 15,000 rpm in 220 s. Through how many revolutionsk) r8op*yfp :jhp75guys cq3+s5xf 4j did it turn in this time?    $rev$

  An automobile engine slo+zn; iqbjqo:72y)n jqh fqysee 2+- p:ws 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 tb:s jku/oejk0qv8. s (he stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions befkse sq .:(ouvj8k0j/ bore 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 accelerzq(u95ic x (x(wlvw h;ates uniformly from 240 rpm to 360 rpm in 6.5 s. How far wiwz lx(cq;(5(i9vxwu hll a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is d,c *n puos vhv *wfz-a67f5-wrunning at 850rev/min It turns 1500 revolutions before it come pu zfs-a o,76dwhwv**c5v-fns to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reducesolpecw( 94 go 9t+wtg5 its speed uniformly from 95km/h towop4(5t9wce tg g9+ol 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

  The tires of a car make 65 revolutions as the car reduces its speed uniform+o, )2c)qne ef8 nhrq+ejs/zvly from 95km/h to 45km/h The tireesz vec/f 8,nnh+q) rjq+eo2)s have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pez.z6 toa0rco )dal when climbing a hill. The peda ar)o6 t.zoc0zls 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 q8ux u9*m1ybtmu: 1*j wf; kdtof a door 74 cm wide. What is the magnitude of the torque if the force is exertedbw mu uq;x9tmyj*8t1k 1du:f*
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fi ;g46xnwz;ni dib). ltg. 8–39. Assume that a friction torque of 0.tx n6w;.l4 ;d b)ngizi4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless ro ebz9;ylron t--9m;ha d which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then releashrl; 99-eobz-;mny t aed. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder he;vn mj, dov:f c7f8;ukad of an engine require tightening to a torque of 38 ff,mou8v:7nd cv;;kj$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of ra,krp1, l5bkh bdius 0.648 m when the axis of rotation ibr5h,bp1l , kks through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in d,u gv,* goi-rniameter. The rim and tire have a combined massong-,r,g *u iv 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,vx mw72vwhr)l v0 0eo6 light rod is rotated in a horizontal circle of r) lvhw0eo 0672xwmvvradius 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 onn*uqjiw*s. 6d9 g.w)lqtc; tpax;n u/ a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction sq*jupnl/6i ;9ant*)w;.u qdcwgt . xforce 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 igjrm26+17 5n 3zza cael.gz zwnertia of the array of point objects shown in Fig. 8–43 aboutzr3j5e ncz+az216gmal .7z wg
(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 twadi) fp-zr 7(/gqm*( i oydux(o oxygen 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 cylindrical satellite spinning at thebww);b-tg rn4f q 1f zge:w:l5 correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the sa1-twqw ;b4gr zgn)fl5wfb :e:tellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a u(kz:s da 7:qutniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Caluz 7:sq k:td(aculate
(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,77e phod*i9 cfrm6qg8z7 i wd3 accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and:26kag)u;teokg vgpt ;bo,kpf6e+qj7 /)xgz is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. x:2oke jt z) ;gkvbk +7/q,;tpgog)6uagpef6$\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut pc2uiabs507 )z;fc: uwxx5yu off and is eventually brought uniformly to rest by a frictional torque of 1.25fuys7x b0 :;pi uza2u5)cwcx $m \cdot N$ 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-kl9ftdc : q;9j4da(vlx g ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm,+ v5k5nc5v3 q7jt xicx which rotates about the elbow joint under the action of the triceps iq v5nkjvx5+5tc3c x7 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 considered8m(vzi(f1e gq a long thin rod, as shown in Fig. 8–46v1e fi(mq (g8z.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses,2 k(nq9tf,y4izb edf o8je* z) $m_1$ 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 tr k9v6fq;(p daurns (revolutions) ankd69r; v (qfpad 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 :dug9p-4d5oslq :y igivk7n7 z 2cz3ha moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine dmd6mwntutc+u59xogk 0b97u + evelops a torque 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 slippi*70 d qdapyv q(mc2b8v8yda0r ng down a lane at 3.380ac8vdr *(mqd q 7daybvy2 0p $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of :o eyj*7sf fm)two terf7o:efm*j ys) ms,
(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 v.cigri6 6ecr agh6-:wgh: qy0 c+x+ ba mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution pe g we0.6-b+vhgchyg:rqi+r c66ix:c ar 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass+ zp9ve/9 locnq42c *kz( k9j4xnjk26x fzin h 1.80 kg starts from rest and rolls without slipping down a 30.4 4f z(e*oczkzxqh6n2 /ci9jpk2x9 n+nlkv 9j0 $^{\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 startsaxb1n4 trbv,h2d 5ut1 to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it 4 ut1bxvtad5b,n1 2hrhits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentumhbym / bilj: a.14x2fp6vg -eg of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at an angula12yf6jv b/h - x:aeg img.pl4br speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uvd9,+6a amy 0cr avu1zniform cylindrical grinding wheel of radi, a y0am9v1cdra+zuv6us 18 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 a platform that sx b-+*2j- dpm:motjaw)bsm2is rotating at a rate of 1.3rev/s If he raises his aw2* b 2sjt-+xmm-j) bas:dpmo rms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduczn/ 0va;q(uw s m0d hvi.jz;.oe 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 1.5 s when in the tuck positi(.uhqvzwnd miv; a.jos / 0z0;on, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ratec/ 8)/1evk(qwl vobtb of 1.0 rev qveb o (b)kv18/ wltc/every 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 throuf42t5 s k5,wvb3nny yzgh 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 dzv5 ynw32y b4,tsfk5nisk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figu79-naqufco eum +) y(lre 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 mo.f(z1 uhewd t0mentum 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 cylindricatc xzv:s6f8(shf8+t9hj l vs-l disk of moment of inertia I is dropped onto an identical disk rotating at angular (v9s c zl ft-8jhftss v:8h+x6speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at/s*1q6p rihd0 pu) w(1wavzaq 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 of a rotatd zz)jnbm9 g+/gq r, r9/w t3so+; cs:vczqu.oing merry-go-round platform of radius 3.0 msq w :cz)zg.; rrqn 9tj/co+dm v 9,obgsu+z3/ 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 freely wit7uzj;d .vfftki ;1 vox8b8c0 vs vc74hh an angular velocity of 0.8 s k .0i7 t47 8vvc;v;8uhfjc fdzvxo1b$rad/s$ 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 wlrao4:5f i zfvu/h,5 qhite 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 momentum, what wouldzaf:5l 4, uvh5iq /rof 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 exces*earhdhyx9uv +b)2 : )zfey ;fs 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 qfht o3z: w;4k$ 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, i5ivs jkgzx) kvefx3 ,8 m)-qp:d6ly i7nitially at rest, that can rotate freely without friction. The moment of inertia v yv8ex,ipfs ql- m5jkdk:i7g)x6 3)z 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 l.4 x9wmkfrc n(y;g+lthe edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of ywc g( fkl49lx;.r+mn 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 rol tws3*o*1 m;1gme6v9 p/jgari mk2kjels on the ground with the end of the rope lying on the tokgt29 a ej1swj*e6gmp3k mivm;*/ o1rp 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 that the same side always faces the Earth. Determz39bj;rc05 myy lnd g9i m r539bzy;0c lyd9gnjne the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates froua-z7-* abric(mte-my3n3d tw9-9 m . mj lqwlm rest at 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 radius 0.20 m acquifg -y 6nt:8c, dgee)i tjve::zres a rotat-fd: e vtcg8gn y :i:6eezj,)tional rate of from rest 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, each of mass 0.050 kg an o5d1mw1v -*eewa0 x8y5-o4 v zabyrpjd 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 energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long strieb*-4 5ao8w5jpx0 m o-av1ev wzy y1rdng, 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 thpc tnflb 5 *d,ws(v*4elh64pie 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 as great, were ro 9s yh.pz s0*x7ob hl1;+yktoytating 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 unifoz +9 0o.y p1xthbl7skyy;os* hrm 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 ;. wzk4m:rrvw 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 and mass 240 kg, and should be able to travel 350 km without needingwz.:r k;m rw4v 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 wf7xap+qk6,)o ;dldi 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 u-0t)nres+7,i stl 8h4fmx 0s9b qpfa on a horizontal 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 ignolem1oozsr (tq+bmn5,pk8i;usfc1 - 7re friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontmi-7+11c m(n,s5u;l pq or s efo8kzbtally 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 the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertical .hknz3icf0t6,1 g6 ebyyryo*ly on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig.g.rykt*6e1h 3czon0f,yi yb 6 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road iw+kx -77o 5j1 zmk8vsl;pb nsos making a turn with a radius The forces acting on the cyclist and l;zb1o-vkxj7 75sk on8swpm + 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 aa/kw 0/t ex+ wi3g+fzv 0.50-kg rock into a 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 1z0f/gw3k+xei /+ vtwa20 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 body as a solid cylinder and her arms as thin rods, maky m(j1 rbylrwgo91m24p 2nhs *ing reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, ajo9 wsbrl2pn21r*hymm1g4 y( nd with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two ls,i6l wx c(-hf,6 ct p0xq9i1 qd;gbrcylindrical plates, of massd c gq1x(l;r,c sh-bl q6w0ft9ipx,i6 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alom fp (w 9/+6:zxiyczpbng the looped rough track of 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 pziyx(czp/:9fw6 mb + point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not4uld(+if j h29gxta5aia 3;jo assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speedvwk8 d(3dwimxb .x9++dsjzz 3 uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each t3s+idw+(9 zbxj3mkdz8 w xv .dire? $\approx$    $rad/s^2$(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