A bicycle odometer (which measures distance tranj2szvx2*b3 x7+ h ipnveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it 22z+sn h*ix3pbj7n x von a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on s nwmbzm0 r*+5 kpy82nthe rim have radial 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 magnnwr5y+8m2zs b0nm*kp itude of either component of linear acceleration change?

Could a nonrigid body be desck adk s k-7q3qqcx043pribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert osof+vtme9 sh2 (u,1ia greater 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 beht zyc gkb5 qy76vp)fz)*05cycind your head than when your arms are stretched out in front of you? A diagram may help cyzk6 *)z tv)5fygqc7p0 c b5yyou to answer this.

A 21-speed bicycle has seven sprockets at the rj8bf) 7ufj5za 3 y ;d:do9z hdtx)vd7qear 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 geaojq8bzhd zy3dv f7 j))9:a7d5duf;txr 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 l1ummlj,)z n2q as tcs(0fav fno2/b*) ower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explal 0()v221co)s* jsbzmftq ,n auamn /fin why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam7-w*xttw *hre yre3d9?

If the net force on a system is zero, is the net torque also zero? If the nelacm5q s;a( r3t torque on a system is z3c5ralma ;q(s ero, is the net force zero?

Two inclines have the same height but make different angles with the horizon;f:vhhk q3s ,gfymp z2z+i /4ytal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom beh 42mi p:,fvzh;3k /zgyqyfs+ greater? Explain.

Two solid spheres simultaneously staoz ;emz+8n 4pl+bu(b :v(ti3hpfi g (mrt 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 has the greater speed there?zo4zemi + hb( bngi;p(v+tp8l(m:uf 3 Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They stargo3p3+2al2r2 d -fzxoii dj: yt from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at thrd zdi:2+f 322o3xa ypliogj-e bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or rozbpwp8 7t .(2n-mqx vztating objects eventually slow down and stop. Ez b( wvxn-2ppt87 .mqzxplain.

If there were a great migration of peof ux j0:,xaj:aple toward the Earth’s equator, how would a ju:f xx0j,a:this affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initialpmg t0;3sz.iqe6 :b:xdi,rh o rotation when sm g.i,p 3ex q:dzh;trb0o is6:he leaves the board?

The moment of inertia of a rotating solid dis 9)- gtn1 dafrdu5labu 32fnw1k about an axis through its center of u1dtb gf3adf59wnl1 ura2-)n 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 holding a 2-kg mass in each uvmety2y p2j 8odf/+*+ hqee2outstretched hand. If you suddenlyhu +/t*v2 jm8qeo2pe yd 2f+ey drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look idect w0+f wr+w28 j*hsr(m hbvc7ntical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine wh(h 0bcfw 8 htj sc2v++rw*m7rwich is which.

The angular velocity of a wheel robn2kj2cw i9mi j(vlarb68.7 xtating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is thw2.j vxn86rcb (i i9mj ka72ble angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating tuklr/(iuyfho1/p* q gfsw5, -n 0+ vosfrntable. What happens if you wu 5f, /hffqlvw0/ rs1n-gsi+*op(o ykalk toward the center?

A shortstop may leap into the air to catch a s mw eab0sfkw0::.l ;xball and throw it quickly. As he throws f;wx:b0l. wm:sk0sa e 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. 8–36). Explain.

On the basis of the law of conservation of angular m3 4 d-if3rdinjomentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or mf 3iir4n dj3-dore ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in6*u mvwrg 8n5i8tv l4j 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 begq t2ukf:7jhe24 vmo (cause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as sfqhv7 g2u k2: joemt(4een on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beamgh26 3,mm rg v9zsg56rvu5dec diverges at an dm,zg5v9r63rs 26h eugc5g mv 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 lcf43nh1aaf5l,1jbjgie;:t 3;hzga i q/1jt a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is ,a jgjn;fl/3izj5 1cat4 baf1:3l qghehti 1;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 m2jyhuj.i*.xyg/wub l+yy( ; fakes 15.0 revolutionsi/y.*wu 2yy+f;y j(gbux lj.h, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do .6w7si if 56c8e0g cxmngl.ye th c e .6m68iw5ie0fng7ylcx.gse wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 h 2)inu 1t2zns-jh1vhrpm. Calculate its angular v22nnv-hih 1z1u sj)thelocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s ew,xc8: ,bdcw(Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from thwx8,bcw:, cde e center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around s;:)sedhznemq 63t q7 the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed t3uphc oc z.bq/lh0c)(9q2z eof a 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 rotalb p ,fonu*a1 .)ayv-cy+zr g8te if a particle 7.0 cm from the axis of rotation is to experience anag.yu,bylnracz vo*+) -fp81 acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its cf5k 9ouw4eer31t5qzq enter from 130 rpm to 280 rpm in 4.0 s. Determi4 q zt5q3e95ewrf uok1ne
(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 radiukf e--u)hvyob0 1e )wj03zfrps $R_1$ 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 th*z8b v oz( 0nl3rczm9ge Apollo spacecraft put themselves into a slow rotation 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-g(ncl 9zro3v m*08 zzbmin 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 15,000 rpm in 220 s. Throughw1+y7k: k w 5iblpzj:z1kb)x5:ky s rt how many revolutions did it turn iwzj::5+kkt5kx )w:k 1yiyzblb ps7r1 n this time?    $rev$

  An automobile engine sa ogz;0v +cr5qhgu y86lows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying v84b rxes 2*k f0qlpl-highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 completv skfb-r0l *x48 eq2lpe 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 un5om(b;var:x21 qg +nfvfww8 hiformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travele v b:frg(xv2w+nwh 1;8 oqf5amd in this time?    m

  A cooling fan is tur6wwtr;veyi v(isc6 f,ds:r y a,+g y6.ned off when it is running at 850rev/min It turns 1500 revolutions before it comes to a stop.fd,yye(srwv+;.:sy t wc,a6gri6v 6i
(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 63w z7x 8cecyy15 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.807cxec3zy8yw 1 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 sp kcnpi;iqg-gpty)9. 9k 2/uyq p/m5zmeed uniformly from 95km/h to 45km/h The tires have a i.pgc qq-iy/u5/ g 9tnp92m mkz p)ky;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 x x-nyk,jdbq: ksm:hqd70zqr/j+4i/all her weight on each pedal when climbing a hill. The pedals rotate in a circle + dq :-dims/bj7:z /qyh4j 0q xknx,krof 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 forcefdt (x2-v9woz of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the x-(2f9voz t dwforce 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 the wheel shown in Fig. 8–3q w4z9pg2q, on9. Assume that a friction torque of 0.p4nwgq9qzo ,24 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, areg :gf2m,am 3r1 nnitm/ attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is hemm a/gir3 2nm1:t,fg nld in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightenq8pzs,/7gfx7 h o*s*k bipu5 ping to a torque of 38 87zo5 *qkuip/ss*xppg f7,bh$m \cdot N$ 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 radius 0.648 m when the 8k /4w*ebtw saaxis of rotation ise8wa/ 4 kwb*ts through its center.    $kg \cdot m^2$

  Calculate the momentkc*lvmph*8:x( aue9 m of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have aclp(vxhk a9m :u*me8 * 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 r e dqz/sad5n*0:db dbz775x tis rotated in a horizontal circle of radius 1.2 m. Calz 0xden 7zrbd5da:td5bq7 /* sculate
(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, ea ,alq)rv*e7x/rhf a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands ar*7/)f,qv, ree haxl 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 point objecwk68rjx2o-bi ts shown in Fig. 8–432o8xir6j- kwb about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two h(h gsh7fa3f*sfla4 54kz/bc 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 the correct rate, eng h7/q.qk,i0oggw x8o zineers 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 stead/k 8,i g0g7owozq.hxq y force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 5zs4z6h1a0z.m ok a pn0.580 kma.a5oz ns1 zp4zh6k 0g. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player sw9ykd7xuh ,,bnings a bat, 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-driv5468w s;c wohp frwh)oen 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 is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two child)o 6hwrw5 w;fcho8p4sren (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventfx1xz lkqwxw5 dq)39 4ually brought fxw5qdk lwx31 zq49)xuniformly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 p5f5)h+ iqn 6zh sml+kaccelerates 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 actio (6 bwkrtbky71n of the forearm, which rotates about the elbow joint under the abb(7r6 ytwkk1ction of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered;r rii r/k4p7n a long thin rod, as shown in Fig. 8–46.n 4rrr /ii;pk7
(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,*-u /ukkuq mn-s*/l odsuor* - $m_1$ 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 accel45 dk3msuc:jsog: y b+erates the hammer from rest within four full turns (revolutions) and releases it :s+: 43km jys5u dgbcoat 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 inerti0 0c. lb8o1ipf fe3qu;ibt8xv a 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 3zni1(.hr6x ohky um /(wd sz/develops 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 mas 6(jcdi7 epoo2s 7.3 kg and radius 9.0 cm rolls without slipping down a lane od j6e po27(ciat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the oh 9s *bmj33yaSun as the sum of two terms, * yabm39j so3h
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.4(t ;ps*euuv u50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.0* eust4uu pv(;0 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts f5bc ulnfs b*3r-h2*jv rom rest and rolls without slipping down aflc bj-**5 vrnu s2b3h 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts t3gc wfh :e+1ydo fall and its lower end does not slip. What will be the speed of the uppehe3dgf1y +:wcr end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin c cw sf*ghb(v/oe 8m+u ))ivepoxwc+eht/57 /string in a circle of radius 1.10 m at an angular speed of 10.4 c+ im/xo)/s o * 8vute7hge f/ehp5cwvb+(wc) $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of ag6g fay9x:z2gw( zl:b 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rw(gz : 29fg6b ayzg:lxpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands ad) jw9 b9fn,pt:cl7sy 4b5dfht his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a honp )9c7,bbdj f 4lwyd9: st5fhrizontal 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 zv)88t3sty,d dxodz(–29) can reduce 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 positdzt8x, vys t38d()zd oion, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incri/oejd (a1 zqp-us+ 3wease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3p q ow+ezu(a ji/31s-d $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center atca.f86* ccozik-0l bxs sz0)p a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it? csko.pca6 f0 i* c-)lx0bz8zs    $rev/s$

  (a) What is the angular momentum of a fi2mchqzqi4yr8p5l n8+fkhi9 gc*a1.rgure 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 mome5 *e m42vkjvljntum 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 inerty-tvkd9 u6)t:cjoo j3 ia I is dropped onto an identical disk rotating at -o6ju)o :ct jkvd 9yt3angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 29u2 :pcnhou/6z;u v ph.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 q/ i1g6z5bi;twek lye* k s8v*rotating merry-go-round platform ofq*l1ks/k5b t8wevg* eyz ii6; radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rot rk .ua4j7+x+gefd4hn ating freely with an angular velocity of 0.x7eg4u + ahdfrn+ 4kj.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 collapses into a white dweerb.e+z; b 2xt5mm smm m/;b5arf, 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 would the Sun’s new rotatio2mt ;m+ 5er./m b; zsbmmxee5bn 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 excestcq-+ 9 l/w : jgwx,p+e)qsadcs 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 (zar*acl mf- ,$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that xv(yotbcog yh *87hkht48pl6 iw+ 0sgurz160 can rotate freely without friction. The moment of inertia of the688i(ch1x* 0hgpzw07hrsl4o v yub 6otytg+ k 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 diamet -sey9u af1+gser merry-go-round turntable that is moa e1yss +u9f-gunted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rollse ;rjewgz,: 8l on the ground with the end of the rope lying on the top edge of the spool. A person grjle:we rzg ;8,abs 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 Eart99 ;w gohrb)btgvcq8v 0c +t+rh such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum.w9c8o q )h+;r9g cv tgrbt+v0b (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratess,07da cf 4dfk6s8m.5od8kdsm5nlt9omi 9 od 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 radsz7+t h(z7tigius 0.20 m acquires a rotational rate of frz7 i(tg7szth+om 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 disx,3w/ofyp 94d iz 2(ov:r0 ljpq c4rabks, 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 splix japo (c fyd2vbw0r3z 4op/,4q9 r: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 th s+uv3* q xi45cm)9qgebjjtjyla:x j1ckz2;, e 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 )7 bbtlylbv0r;w l: 1iour Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would: vlli;wlytbbbr1) 0 7 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 is for it to use enul bn)qt 3q*rb)d:oqg.sg wr+m0.1(kuh fm 8nergy 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 withou.tb f):0g s3q(drq1*mqku+gr 8l hnmnbw) o.ut 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 illustratesb 9rik31+zf4lde gg/u an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizo8shd gc2* yxx+ntal 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 igq 5(2 w.ixzxe sv0dl7ma0*k6ofpz7ncnore friction) aboun z7cqolmx* 5p0.wze7a (0ks2d6ix fvt 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 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 on the floor, 6+ll f9.ui f3pzmvk-gand we want to exert a horiz gf6mvfiu-zlpl+9k 3.ontal 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 be24g jf;ew 6mv=4.2m/s on a flat road is making a turn with a radi fgj26;4mbe weus The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rockjw2lhk u kwj)9. uv40bv tu ht(r/eg.8 into a sling of length 1.5 m and begins whirling the rock in a nearly hori. 9h.vjhvkl e rgu)b0ku4j/t(wt8wu2 zontal circle 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 armnxvh zj x2f6ox 3m+6d2s as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, xdj+ofnz3 6vxhxm262and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindr/ 1mja*0v jwx ;gf1zoyical plates, ofj01a/1wjv gmx*f z y;o 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 rolls along the /80pdy6 qdoiwk, y(bblooped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble muw 0poydiqd ybk(68b/,st 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 f *:2 jknbk,uuzsv z9wjj (s:-assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car f7w45e *s bbpbqui5 .rzw-rt(reduces its speed uniformly from 90km/h to 60km.5u(be*-54wftpr q i s wbzbr7/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