A bicycle odometer (which measures distance traveled) is attached net7ue0kj ud/.f ar the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheeuu .j/d0e tfk7ls?

Suppose a disk rotates at constant angular vly b5z n56pqf*hc+ o-yelocity. Does a point on the 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 whi+hy-pozyf65 lbn c5q*ch cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a slw -cn0y0t/qaaa ko;( ingle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater tos(ve40qc hp*frque 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 thant0+(z s;ijn jjrn3h2u when your arms are stretched out in front of you? A diagram may hel0s+ uj(r3jz hj itn2n;p you to answer this.

A 21-speed bicycle has seven sprockets x2)n+ftn0uidj698: - xjn e dhgq ab7yat the rear wheel and three at the pedal cranks. In which gear is it harder to peh dxj62q0:7gn u9n+)fbn -x8jiyda tedal, 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 3yc o,tbe+i:t.pxbfy y 4u :f(have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of roc:y:+bp4 3.f bfo,exiyty ut(tational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narr 5v 3jxpx(e0hgi- n/aea;jfo+ow beam?

If the net force on a system is zero, iyeeik04 3ll1p s the net torque also zero? If the net torque on a system is3 yi0klp1e el4 zero, is the net force zero?

Two inclines have the same height but make diffe a qjm)cbvr:uqn0 o+9/rent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of)9r0q mq /ocvnju:ba+ the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. o1n tkp9/)ux gj 2dp+sOne 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? Which hauo k 9t1/p)+nx2gdjs ps the greater total kinetic energy at the bottom?

A sphere and a cylinder have the samt g+6t2p,;/ wwux h*wnt-bwyve radius and the same mass. They start from rest at the topxh- 6wn t2wpgww ,y*t/tu+v ;b of an incline. Which reaches the bottom 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 conservib:sj +5m aj (plrd7kc2mh7b6ed. Yet most moving or rotating objects eventually slow down and stop7da+ 2h5j(bm rmk 6spij7bl: c. Explain.

If there were a great migratz,m-gtvb -1id ion of people toward the Earth’s equator, how would this afdv 1,i-g zbtm-fect the length of the day?

Can the diver of Fig. 8–29 do a ah4lj(,qb0 ) gksb-rgsomersault without having any initial rotation wjga gbbs0, 4-) hklr(qhen she leaves the board?

The moment of inertia of a rotating solid disk about an axi*ewo ( g/j7rr cy2n+lqs through its center of mas7+/y*2 lgc (roewn jrqs 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 std) 9banzmmo. a+uk(,sool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Edzo a )msbua,(n 9k+m.xplain.

Two spheres look idenzele 4k-(a 3kp)2 -8ga djqcghtical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whichpqel24kjega3 a- 8 kdg(z )h-c is which.

The angular velocity of a wheel rotating on a horizontal axle po x5:9s;d lu4h3imfj nkints 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 increash;js 5i4l3 9x: mdkufning or decreasing?

Suppose you are standing on the edge of 6.w / s1lfi ingg1jh/oa large freely rotating turntable. What happens if you walk toward the centen./oj6 ihw/ f 11ilsggr?

A shortstop may leap intk.: l,4zs/plyl*xscf mz5m*as)b 0 d/n d/y cfo the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotated/l4fl.pm:0, bzy/5 ds s*k yn clf)s*xam /zc in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conser*f l4/;xi u:b5rwt qpxvation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propelri xut;l/* w5:fpx4bqler can operate to keep the helicopter stable.

  Express the following angles hg, ggfs7a.1p in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Eartb6gysnuzy94 l ph1b *1h because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in 1bnsl yu1b hy6z9p 4*gradians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the ;yo t)m;f0lpw Moon, 380,000 km from Earth. The beam diverges at an ant;ofwpl; m0)ygle $\theta$ (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 a rate of 6500 r9aci7 c;e0qd ipm. When the motor is turned off during operation, the blades slow to rest in 3.07e0cc9 iq;i da 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 makev3u+aqn6-kumt 7h7/uc9zwkka jpa15 s 15.0 revolutions, what is its dia7 q6v-wmnka9a tapkk 1uz+uu c/35j h7meter?    m

  A bicycle with tires 68 cm g+2ps qx4w-ao4vzwe;r. l c1kin diameter travels 8.0 km. How many revolutions do the wheels egl v;ps.4ax2 c owrqz+-1wk4 make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angulekswx0 *fy1khi89 ) kn 2ft.asssftxn w0 h1 y.kfi8a)9e2kk*ar velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolutiontpq x 0)q2j6bz in 4.0 s (Fig. 8–38). (a) What is the lineapx) tq2zjq0b 6r speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in 6q ;tesgi*m0e,pmp; sits orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a jg mf(ow.8v5u7n blho2 qc;e:;, cqrv 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 rota0miji x3.-vm25 dguf9+axr gxte if a particle 7.0 cm from the axis of rotation is to exj0i x2vd+uxr mg-ig.fmx 53a 9perience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to rjhl3 / qcib5w5v+m-l280 rpm in 4.0 s/ j wql+ mc5-3i5vhrbl. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius q. 8qjljy/py;v oo ;/g$R_1$ 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,jo6;/7l sazkom -u x8w astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated fr7 a8; -zuksx/l jwm6ooom no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Thr* g))wky8bx yxough how many revolutions did it turnxkw*)ygy)x 8 b in this time?    $rev$

  An automobile engine sl up *0et*vgm:a3x xat0pmt3; )n;squaows 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 thcm 4k n aohjfx5t3n0.:e stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fic0h anfxj.t n4:mo5 k3nal 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 accehutkptz-6;.hip43ui q8 8 ejzlerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in tiuqi6h3p4;kz u.e hp88jzt -this time?    m

  A cooling fan is turned off when it is ru w 79i exn04m87mtbibzzmrl0)nning at 850rev/min It turns 1500 revolutions before it comes z9x n0)4mtei 7milz7 bmrw0b8to 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 reduces its s 3dki/d+i of(ypeed uniformly from 95km/h to 45km/h The tires have a dia f+ky(i3 /diodmeter 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 reducvz+v8p jjhl9sen/l: 5es its speed uniformly from 95km/h to 45km/h The tires have a diamejs/ zl8n +:hl5p9jvveter 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 cli;eay *2 l8 .-ujbrxce7gh wj5pmbing a hill. The pedals rotac7r8eaj-euj 5*bx. gywp l 2h;te 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 n*7lcqrfm 7t a*tu3a455 N on the end of a door 74 cm wide. What is the magnitude of thltc*77 f 4 anma*3tqure torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque g/tj 4lbkisdeh 94 kwe 67p-e-about the axle of the wheel shown in Fig. 8–39. Assume that a f4tdel 7b9ih4ew -epsgk-/j 6 kriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are - .:ypmlz5p4gi /ogl m/e9vjx attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initi/z 4 le/.:-9m vjiogpxg p5mlyally the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening tog:y2zq kk9u im;(z li*045i.jamrzvh a torque of 38zaqglzr:z u*;0 95mi 24h.k i j(kmivy $m \cdot N$ 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 in mmt)d00n5 uls8glam1p :xje+ertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is throml5s0x elp)g+d8 n1am0mj :t uugh its center.    $kg \cdot m^2$

  Calculate the moment -0c.sl5r b7.q jsogb4s, *7nvfiuqqyof inertia of a bicycle wheel 66.7 cm in diameter. The rim aj 0c*y7s.,q.iqq5sf 7 nboslub 4v r-gnd tire 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 t kwu)76p h1f elvyk;tv)l+v+rod is rotated in a horizontal circle of radius 1.2 m. lf+ 6;wu)v k)yvhpv 7+ tekl1tCalculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’k 3fq2e q0yymt3 y)j/ns wheel rotating at constant angular speed (Fig. 8–42). The frictk q3f/njt0 )yye23 mqyion force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of adwf *,*:j bj 2xlo)k 0i xv7gsln0,dapoint objects shown in Fig. 8–43l0fvj x,kj2 a*nl o0*)a b:wx7gd, isd about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose tog-jv qwnx9+, wiwvu53 tal 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 rd9v e )60nnlmqaa6v+n ate, 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 satellite is to m+qlda n0vna9)n v6e6 reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radf k7/rp b *xsjdtrwn:o*0e.-m ius of 8.50 cm and a mass of 0.580 kg. Cao*s0rj der p7-k.x:tw* /nf bmlculate
(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, acceleo*xq ;nr(: z: imexd(hh0im y7rating 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-drivenu5prif3 qfr :/ ,xo;tg 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 p5ix/3orgqutfr ,;: fmass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eve98 y 7op5e0fgzth)phqntually brought uniformly to rest by a frictional torque of 1.t9hpy o)70f zpg58hqe2 $m \cdot N$ 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 *b4hp sob /k6ta4 b5iyaccelerates 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 8 f41bh-hbhhxball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 1b8f1hxbh 4h h-0 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as showu24d bvur a(if56st6wn in Fig. 8–4ru i6ta64bvuw25fs (d6.
(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 dq9bo/1t 9pkr grxp)lik*g 91consists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accele k6 -ufubd4 )mm2v 1xba9(jcsrrates the hammer from rest within four full turns (revolutions) and relea-smkx9m6vru1)j uf (bdac42bses it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inert1ul.4tz 1;p rgr9f7v6wn*ch e/enkcoia 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 dea gxe60v4sqb e ,cqk23velops 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 maq a7,2no:wfzer5 4(+jp3dk6znsls qrss 7.3 kg and radius 9.0 cm rolls without slipping down a lane at 3.3 n+nsp zdj(so z 2q6fwkal4:7 r 3r,5qe$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with res q.qufle.)th 8pect to the Sun as the sum of tftel.8 qu.q)hwo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a g5q78htk+k gc)aw/dgmass of 1640 kg and a radius of 7.50 m. How much net work is re5tgkg+8q hca)7 dkw/gquired to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg staraw; jrdyz19ex5c ksls1:t4( ky3k1up ts from rest and rolls without slipping down a 30yj k 1k x14kzp9a:syw scre5l; 1t3(ud.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to favi9v :8j wzorl1u gf+2ll and its ljl v wfz:2 8ivgr1o9u+ower 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-kqbhk-5vtt2d2 haa3a /)tvbonmq9 ,b 8g ball rotating on the end of a thin string in a circle of radiutbmo 3 kba)h d-n22a8b5 v/a,th9 qvqts 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 cylindrica6t t6 swy-p.vwuh)0t kl grinding wheel of ra-uwtp )6yh t0k.vs6wt 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 platfor 32udemgco4.bt) wm) um that is rotating at a rate of 1.3rev/s If he r u 2ug4db))tco e.3mmwaises his arms 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 iv6)6tu sqs )cpn Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck 6)cvus )tsq6pposition. 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 rd5 (fzz y.5cgjotation rate from an initial rate of 1.0 rev every 2.0 s to a final ratc zzgdf5y (5j.e 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 rotati i08. ahm8,ozpr 2e-huvb 5bidng around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be consider ohr0bd5vi 88pm z .ueh-a,i2bed a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5 3 o n6b8.6xeiieek6 cx$rev/s$ 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 momentu/kuv1u:*x :p64s)o gl4m ktzasug l4nm 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 mm kj3x.2fxg3q oment of inertia I is dropped onto an identical disk rotating at angular spe. kx2g3x mqfj3ed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2cr6jw5z,t9q m.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 rotating merry-go-round8i pmlkh)*+a ciq)*nkwc6 l2r platform of radius 3.0 m a l +qic )pl8c*w2inkam)h6*krnd 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 f jxu yq ,kh.+9a-g*nbis rotating freely with an angular velocity of 0.8 -ghb q+ akyfj*u,9x. n$rad/s$ 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 intoe * ny.cakom+sj 6mw;3 a white dwarf, losing about half its mass in the process, and windincy3w me;.m+on6j sa* kg 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 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 inmcn uwhmg;;v5.e 1 /hx 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 tz7zt:x8)f yfp,r p i4$ 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 plk)c-sc r/ 4hvx)nojo/t(,haz atform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus txh ,a-cc/z4k/o)svohn( jtr) he 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 k,7m y4(ddo8af 4r 5znryil9l6.5-m diameter merry-go-round turntable that is zay 4odnl45k r (8l,ymrf9d7i mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the enc +r4b8ez yivi.apxhbk4:y n-vp -7 u(d of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rop 4c-( b7ai.vye-yzp rukpv:xb8h4in+ e unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the ;4 /wo+xwrulf0 wp 1ynw, nu-bsame side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about it /lf1bnuwpw;o xy4,+r0 wu nw-s 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 frifek g:g b*uk2mcl2e8 73qc il22z5prom 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 acquit g) r riiamylx30c-96res a rotational rate of from rest over a 6.0-s interval at constant angul-lc0 rmit ri36ya9x)gar acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid 0*erz i37i3j2dbl e gtcylindrical 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 calculate03 t3ezdib7 gil*e2r j the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how iqv0gxomh 27 xp2x(fd,s the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rot11r- jgt0 fy xf9avv3hating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no ang1yv3 -1afht vx jg0f9rular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobiol ap) zu:8s3f,ug.wd tr0sq/ n;p3pule 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 needing a flywheel “sp0;lrzg3uf)p 3p .qw nu8osds:a, ut/pinup.”
(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 au hg m3 oceub44 1t.p:z)cvme(n $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed ;wv )kzhc6mljkh/ s +3hnd e )*i8toy3v=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 free 6 xrcid2wqdt6 5i7(ubly (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) 5rbq6wi 7(idxt6dc u2 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. ).5 rwd j+qxigab8x-vIt is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that itx -ar 8 bgj+qxdwv.i5) 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 road is making a turn w -ev mv8/r ,t qfchi*du3g1k)vith a radius The forces acting on the cyclist and cycle are the nv k/18gc et3rvfm h-vdqi,u)*ormal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m6lmi,3 s g4awbfn gg2-;f6svq and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this n -f,i;g6ws l2 6a3mqbg4gsfvfeat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder anjc(n,qdy.vywl0 yg pcb 3*-9bk0t7 wrd her arms as thin rods, making reasonap0dgcnqy yb(k w07-3vj * br,cwyt l.9ble estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch ass2wd u6kh2 ;ykaembly which consists of two cylindrical plates, of ma 6akdky;h2uw2 ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of ao.+5gv: p ril u:g9aiFig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of thou5l+iiapr:g . vga:9 e loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume f b96:j(kj:bznpfq 2z$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduk6ft* q0obw6j8 owe+lctr f;c+dn :e7ces its speed uniformly from 90km/h to 60km/h The tiedw fr86*nq6cej 7tw0o+ o ctkb+lf:;res 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