A bicycle odometer (which measures distance traveled) is attached near the wheo9n wzo08epru 5cvo5 rjw4.:kel hub and is designed for 27-inch wheels. What happens if you use it on a bc uowz8 p4 9j5rowv. en5kor0:icycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poinxnvb(g)w, nsg.o 0j4ut on the rim have radial and/or tangential acceleration? I 4)s(ovxbugwg,0n.nj f 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 describpp2 cjv1 leegk/ 5,hg;ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain.qrrs mt5z0b 3gfs )38j

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 h m5rg :1)ptr(y 8m57uwwj b/4chkxadfands behind your head than when tuh84mrra 5x/wwkm)7 1gyb5jd :(cf pyour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has s/zog c*l8s-e/q fyw 7ks4 )pam ;ayhz+even sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which kysa+fhzceas m ;o)wy4-/q/87* pglzgear 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 slere7a we1upw-xt ry3,/ nder lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotationue/r x r,tya3 w71epw-al dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walke2 ost rrm*3pi;okf2:srs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system i9lu*f3ibgd*hx / ed h(yhj9n5u :i*zfs zero, is the net torque also zero? If the net torqued(bh/d*3hnu5zulj * i 9*fx:efyi9g h on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horivu9epdj738/ td8pl3s evpj)2 h* hvgizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.*/si t38p v u2v)d p7e9dl jgehj8p3hv

Two solid spheres simultan2c o4mgklj4 t:eously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which :kgclj 4tm42o 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 m32mymfone416n 5vzruass. They start from rest at the top of an incline. Which reaches the bo15frovz6 uem432yn n mttom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving : so(4qov),cacb u1sqor rota(soo)cq:c4v ,q b1su ating objects eventually slow down and stop. Explain.

If there were a great migration of peopth:yxo ev(v4nir-wm th3 is67aax:vg.ty46 )le toward the Earth’s equator, how would this affect the length of the dh-otnx3644 ivtthe76.v:)ax gs ry miwva (y:ay?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation (ziekv cp* /g-when she leaves the boa( * pkg/zcvi-erd?

The moment of inertia of a rotating solid disk +5mcw2 oolj(utndn*tibe. 1b8v 0ul :about an axis through its center of massb:*j wou(ln02cevi8.+ 5uo mtdt1bnl 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 holding a 2-kg mass in +hb*8z;mdbd o each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, domzdb ;8 hdb+*ecrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, owe+w fr17x+yk ne is hollow and the other is solidxww7+ fk+1r ey. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal .7u ;un* bzvexaxle 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 increasing7 evb;*nuu z.x or decreasing?

Suppose you are standing on the edge of a largerja rq,4+(k4li5t b wr freely rotating turntable. What happens if yowqtaki ,b r+4j5lr (4ru walk toward the center?

A shortstop may leap intoq0(: 6e pk r fdq8xk*uxtzno*5 the air to catch a ball and throw it quickly. As he throws the ball, thx:oudt6pqk 8r0(*z e n*5kfqxe upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular moment rlbt:, j:*chkl..d bpum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or morj.d r, *hcl:t k.lbpb:e ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) )addgi;-u4 c2p78p+qva ib sv30 $^{\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 amwf.m6:vrovih6 zn l eswf )ds ld:9602im:5czazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of) zmiw6:he6mnoid v29z:0.6lcv:ws frl 5dfs 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 divergesnq u rv147kkd1 ak47r kuq1dn1vt 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 r 4r .t.juwe9 ixgojbo;e8- 9ppotate at a rate of 6500 rpm. When the motor is turned oxoet.wj;rie489 jo- 9pbp.u gff during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to an23.glg n dtjv7other child. If the ball makes 15.0 revolutions, what ist37g v2n.jd gl its diameter?    m

  A bicycle with tires 68 cmoe d5dy 64pn;3mz6 gmf in diameter travels 8.0 km. How many revolutions do the wheeedygz6f n mp6 o35;m4dls make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500k,t ruh v.pa wrk6 j5prw7f+8) rpm. Calculate its angular velocity kpk w+ trv6),a.8rw5hfru 7jp 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 make h ,.vcvq e9q24ag-jx99cwpuy s one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child sea4cuqa9q g.9yv9j 2ehpwvc-,xted 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 (n,b 8-,wph6e gs7crf2svx 7uoywy y77a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of 5x9(cl g(6jzj( p b2jm)uw ncra 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 th:hwj ;mc gg3*re axis of rotation is to experience anw3c jhg:m *r;g acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel ac1 qk2l vi3.lrbcelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Deterl.bqr 1li k23vmine
(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 radiup6z+. qhy-8y n tyh6tls $R_1$ 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 spk7t *to9ukdg 0acecraft put themselves into a slow rotation totokk 0*7du9tg 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 uniforcfz bk.h2s29p mly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time? 2 9hkp.csf bz2   $rev$

  An automobile engine slows mtgzxzb-x98g5f g te903ads5(q om 9kyc/ 9hp 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 stren34; 0topmcf(nu kigo 4,ehm:sses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 comple3cfi(th,u negm04;n4op:omk te revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniford(erl;qcq/m3 r un 9c.mly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time?mu3 l.d rq9;r/ce ncq(    m

  A cooling fan is turnes*hk1x dnl0;ld 08 svod off when it is running at 850rev/min It turns 1500 revolutions before it comes to a stop. od; nssxllh8k0*d v10
(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 reduces its s/7b u bajj(zc(peed uniformly from 95km/h to 45km/ ab/(z7bc u(jjh 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 bem7 z-h.hf+mi7 oa) euniformly from 95km/h to 45km/h The toize h-.7fe7+ m amhb)ires 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 pedal when hq t* j25cxqj7a;mln(climbing a hill.h(7qtnx*;cj qm5jl2a The pedals 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 cmik6h 2/a vlx,+rw ig2hewp--alyl f/ . wide. What is the magnitude of the torque if the +rfx/-w6l hi-e 2ai,klwvl./agphy2force 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 torque7tr.msh1a t:0gnxw)-m7ii a5 irogt8 about the axle of the wheel shown in Fig. 8–39. Assume that a friction to7-ti0: imri 1ga rx) ntwshm5a8 .go7trque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a+ lzzaku2g tx9i d73;3hzkna 7 massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positt3;kdz3ia +kx29n7al zh7z guion 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 tightening t .cbiv i(43w/vgcybq:o a torque of 38 q/icb.ci4v yb( :wv3 g$m \cdot N$ 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 frtuq9k r3nwd; m9j:juf8)2xre of radius 0.648 m when the axis of rotation is throughjumr9k8d q 23t r;jwxf: nf9u) its center.    $kg \cdot m^2$

  Calculate the moment of inertia vuutm9 bw541ya 3)ajuof a bicycle wheel 66.7 cm in diameter. The rim and wm49vu 5u)bau1 3jytatire have 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 is rot)yzw9*hapxh(p iowfzw n.5 1ze:w3 jdo9y: v)ated in a horizontal circle of radiup59)o9d3xaj) ewih *wnzzw1: y( p v: yfz.hwos 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potterwsk .tz+gw5f+ ’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N t+g kz5fw .sw+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 iner520m wluwhyl3 rj3p;2usud ,itia of the array of point objects shown in Fig. 8–43 about2l m5 ,urylu3jdwphwu2;s 30i
(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 twokjsu;mcxo. o u uy/91; 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 satellite1s4ee 2czz yl+b d3/psi5)qxv spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is ledc 52v+s4i)ybsqz3zp /x1e 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 n,-(h) qzwbmza radius of 8.50 cm and a mass of 0.580 kg. Czmhnbw-,() z qalculate
(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, acce7qad /sh h+5wxlerating 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 kjx3sx6wxb xtl: 863fis 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. Calcula8xslxbjfxkt6 336: x wte the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut n8q,2 e00qe8 qnzg ezroff and is eventually brought uniformly to rest q8 20n eq,8zrg0 ezneqby 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 04o q,/ llo4e,aslrdwb,1 mrs accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whi4g *froyddo* :v5+s a/tcbej- ch rotates about odce*d+5y-j /4tv s agro* b:fthe 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 ctbyd1rbd b jvde6.92 eeqj -k(4o9if5onsidered a long thin rod, as shown in Fig. 8–4ded- jk.jb9e 65bo qt1b(fd vi92ey 4r6.
(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 ma(l)eik hpi m):sses, $m_1$ 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 aqzie7 c 86(vjturns (revolutions) and releases it atjz8e6qic v7( a 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 momenc/,e gxwfth )/t of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque gi 9n4u,,i;dcedn; qjof 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 cm8 xdg jx2 dy*- y8kd3ev5gnsj: rolls without slipping down a lane at 38d dgv:jkx gdj*se 2n3xyy5-8.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to thee2v f:fp34yz0 zn7 m1b en: ;ypmyrea ;js0ul8 Sun as the sum of two terms, ur3p 2mbf e:an e;e1vy7 yj;m8fz:z 4y ns0pl0
(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 7bls/j6gk bvjexy ( c +e638;bu.50 m. How much net work is required to accelerate it from rest to y;b6b8ju(cgve/ x6je 3lk+bs 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 1.80 kg starts from rest and rolls with--gt dt:*b1 ss/nsbsjout sl*tsjb:-gs bs1 td/s n-ipping 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 lk9bu(46ryetq. ff e0 tip. It starts to fall and its low6 9ty0 lub(f4e.kfrqeer 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 s15zovbut a+ :rotating on the end of a thin string in a ci1 bs+avu :o5tzrcle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding* :j:a:hrauzhvik4 1 d wheel of rad*jahr iu:zhav4 :1k :dius 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 th9pb9/ onqbtkx8hk +5wat is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position,9bob h8q t5wpnkkx9 +/ 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 thelsuz:;/ip :xu 3 nz2h at,gt3a one shown in Fig. 8–29) can reduce her moment of inertia by a factor of axhtzg2u : s3ilzup:at/a ;3,n bout 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 increase her spin rotation rate from an initialfmjb3 o ; 7 cv7+ 7aq 96-sd7qymowmvx)2pxazq rate of 1.0 rev every 2.0 s to a final rate x7b9)+6y zo-p3m7svxc mqav2mqd7jwa7 q;foof 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 rotaljvk6nev h*i ddr77:: ting around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radi 6vvk:le7n*i7 :jhrd dus 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 mome5 q j0v aykov-jy0 gxge4/d/o*ntum 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 ov 5pr*emmtw3 z++oojm8c n-z.f 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 dis +d/mdbyl /7frk of moment of inertia I is dropped onto an identical disk rotating at angular speed rfl7d//mbdy+ $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns atek5jhgrw+ wvg7,wpfo- idw:+x /or 7a5w7y/s 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 et, r 0cnppwgmcym:/ 3w-++43 z zvtwjof a rotating merry-go-round platform of radius 3.0 m and moment ofm-+z0jz:+cg wwp e w/ tp3rc4m,tvn3y 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-ro:u6ekdyxg7(k1yiyp ,f 3 9e bhund is rotating freely with an angular velocity of 0.,9:(kyepi3 fd67gy ku1h xyeb8 $rad/s$ 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, lositz)o5 okea0y *3az zo7ng 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 would the Sun’o05zo*t3 ykaao e)zz 7s 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 winy0qm4s hg, m z44zft,uds 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 - gt- :hkki.gr$ 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 pvi tvs fkr4;4p1x0z f7r*j2ooo1-ur clatform, initially at rest, that can rotate freely without friction. The moment of incpzr 7 o*4rvvt jrof1s4-xo;1ui kf 20ertia 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 edge of a 6.5-m diametzdps v+i;3oynbymi3) **bc 3 eer merry-go-round turntable that is mounted on frictio3odzv*pb*ic+3 ) ynes; y mib3nless 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 rope lying 9d1d gdlybwxghjnf(2:+ r) 9non the top edge of the s)d d9 gn1dbj(fh:+y2glx nrw9pool. 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 samubhx q; :+nsm13s/et se side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the l1qssnx s /b;+hu 3:tmeatter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratep*bm afw31znh;,ho 1j s from 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 radidv vupoza/jd:b v 4d)z5,t :ki6i)fg,us 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque deliveredo db ,u)z:v6/f)p5dv, 4zdvtga:jiki by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindri (tiep.n:c (cucal 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 energy to calculate the linear spuc :(. epictn(eed 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 theg3j249ek au d:swcy9+t:bn jy 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 withjut*bincq7l,. xih)cu ( e( -jtj1 4ssrc;2ml mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo )xj .siu mjl qctl*ejs4 c(2;ib17ntc( ,h-ur 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 no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution a/jqk *wjl5hy: utomobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car ykjq*h jw/l5: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 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 anbv ggk(7f)9h fht9mlza5 8j:u $H_2O$ 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 roll()at+t;kvgl jing 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 (izjjwa6 14vm4p.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 the rod. Assume thpj 6 ja4w4zm1vat the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor,k+ j8 3co7n:izz4hsmajq7i j9 and we want to exert a horjji3iq7 n+a z9zm:c8ko7hs j4 izontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat ro++cda* b6jd,pf:d xvyq u.xg(ad is making a turn with a radius The forces acting on v+ x ,xbpq.d +g6*f(c:dujyad the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into ao 06 ezu4+ dmwaq5)lt oziub0*cs8 +ji sling of length 1.5 m and begins whirling the rock in a nearly horizontal ciq os0u*8 i0j)a +mz+5uc6lwzobidet 4 rcle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her a yn8o1nc*j,t var(26mj q/sjorms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular ,ajjc(6 *n v2r8n mjoyo/1tsqspeeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a ae,a*rnmf ht: iv30:dclutch assembly which consists of two cylindrical plates, of ih 0*nme :afrdav3,t: mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 */au7 krt0us(b p: mfurolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if i pmrsbuua:t* (u/f 7k0t 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*mlja 0a73sfsh f9k t7 not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifb6w,;fwjcg;ja) k z- iormly from 90km/h to 60km/h The t)wiw zfc k,jg;bj- 6;aires 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