A bicycle odometer (which measures distance tc,l qkzgpkloof/kv nt 7;,9)- r4 ;jxqraveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens ig,;o ,qkk/k otj9xncfl) vp; ql-r4z 7f you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point okds-i.yw c y;-c+xli3.c6gp en the rim have radial and/or tang cxl ci+s.iey cpgd 3.6-k-w;yential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velocitejri/jp68 kqib2d(m ;y $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? E -ziue.8 lk 5atki+tt6xplain.

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 hadwzb6 -+fm rtpre2g6)nds behind your head than when your arms are stretz6p6gmr)dfr 2-wte+bched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thrj-n .dzz3iv 9h;.t aviee at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocke.zti9v zvd ai-3h.jn; t or a large front sprocket? Why?

Mammals that depend on being able to run fast have mf wro c(m lm*rw31y(,slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distrio*1r3clmyfm(, m wrw( bution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a lo1jjv vk uz1 mdon a7;y+mp5d7*ng, narrow beam?

If the net force on a system .)minm9d 0 erais zero, is the net torque also zero? If the net torque on a system is zero, is the net force zdan.r 9m m0ei)ero?

Two inclines have the same height but make different angles 8kr 1rh)d rh+hwith the horizontal. The sahrhkh 18 rd)+rme steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (ykyhp,keac +r7gi 5di*). :ag from rest) down an incline. One sph,.kydrey: +ihag7gki* ac)p 5ere 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 has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same massjtcfnl2r.oat) /; cg3. They start from rest at the top of an incline. Which reaches the bottom first;trof 2/ntj )lc.gac3 ? 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 m*7mw 2 fku qbrf (d1(nkiau57uost moving or rotating object7(5k fikbudn am uf2rq*71u( ws eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how waf:w dxrjv;k/y* .u.qould this affect the lengqj.d:uk/ .y v wx;fa*rth of the day?

Can the diver of Fig. 8–2c4ej:43dcy5 dn lgc p2zd2up2 9 do a somersault without having any initial rotation whzc:d yj2c4p 5gn2pcud 4de23l en she leaves the board?

The moment of inertia of a rotating solidk0v mmy 7,(d0nba/kbk disk about an axis through its center of mam bv0y d ka,(k/k0mn7bss 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 outstre2 xhl1ihb)uc; iy2z6wtched hand. If you suddenly drop the masses, will your angular velocity increase,hiz2 whxub6 ci1); l2y decrease, or stay the same? Explain.

Two spheres look identmebm0ohgdjm6ldh1we+ 5 , a3-ical and have the same mass. However, one is hollow and the other is solid. Descrimm+-e bhe doj 0h,63g5 1adwlmbe an experiment to determine which is which.

The angular velocity of a wheel rotating o.l:qv (y4 f )3 kpgfuzh8k7svkn 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 tokpk :(q4f svuzlg. f)vh8ky73p of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotatb p1 2 arm.wl46d9uxaling turntable. What happens if you walk toxl62 b1l.dm u a4apwr9ward the center?

A shortstop may leap ij lmym7(g/bqzeo 0o ,j*r-h0 knto the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you looo-z/rh ejy7l k m0*0o(, mbjqgk quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss+* g7)qisg spdz: :n 0ms/gcvc why a helicopter must have more than one rotor (osvg :/ni*)+0gqcdm gp:z s7sc r propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (ahm-p ,+sdiz:6i v:sr )(omgu8fpqsa-) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amnle/u v6kk i 6p w82xcc4um6j4azing coincidence. Calculate, using the inp 6wuic6k/vlm 6u24xcjn4k8eformation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km frk 6r njzfmi*81om Earth. The beam diverges at amnfzik6 1j8*r n 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 a rate of /ve+x/zlvn89 /ai gq j6500 rpm. When the motor is turned off during operation, the blades slow to res va/jg+ /8 xizn9/lvqet in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball t q*qp-0jm .hdon a level floor 3.5 m to another child. If the ball makes 1pmjdq -.q0h*t 5.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travv ;a8zquuwz 9*)vl2kzblh)0nels 8.0 km. How many revolutions do the wheels man8l)0hq) *vb; 2zl wvuz9a zkuke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 3a+g; .4 hwuiasuy1vf . 7 anzkjhol6/rpm. Calculate its angular velocity in ujhznfk;. u 4/ga713a.owh ai6+v syl$rad/s$ $\omega$ =    $rad/sec$
(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 makerc u6x f1m28(6fsl0: xaunccb s one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a chi61fsf06cxm2a u:l8bn(ucxr c ld 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 its orbit around tp /y4vv g8henf;9.wlz he Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed c0j1* r(ks 1 ujqph9flof 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 centrg5tsfdv 6h*x:v. jwe +ifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an v hg*je6txs:+ dvf5w.acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its ce8(2bw y .uyqm7awyxr 1nter from 130 rpm to 28yuaq ym w.br71( 8xwy20 rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiuwq/ n-f*octq9s $R_1$ 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 Apols.92 lr w53q mr5xcbvslo 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-min time interval. The spacecraft can be thought of as a cylin5rlsmbw. 5c r3svx 92qder 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 fvrx6j bfyf ,ix7e080 wrom rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this r6y0wj0exivxb,8ff7 time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpmd mf66c)71xvg,0kaqy 6 dgdq w 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 highspeed jets in a whirling “hugp p0/w05oncvn h: a;hman centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fhv :pgh 050 noa;wnpc/inal 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 diametd3b;;mi la0n643c aj5hh nrvuer accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of nbirn ju5vc;;h a3 hl43da6m0the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 2+kfnjqrxj0pyd- hiy0*o ) l /850rev/min It turns 1500 revolutionsnl o/q-dkh yy +0f*rj0)pxji2 before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutip*2 n l8 wkt+5atstyi4ons as the car reduces its speed uniformly from 95kmtp tli+4ty85 w2na* sk/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 6g i. y-xv7(3z vwqg*: zbmo:9vj4f ebo5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hag9* . wjbiq b4z3-:(vgovf y zx:om7veve 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 clif(gkmwz5t 4 ubf:l/. tmbing a hill. The pedals rotate in a circle of radius 1(b lwkuf5:t.fg4tm/ z 7 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wv9 aybjj o/ -(uip:o4gide. What is the magnitude of the torque if the force is exeby uajo 94p: /vjgio-(rted
(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 v .hrjicie qo3:;;9klbe d23m–39. Assume that e;b9mci ro3 iq.k23e h;dljv:a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends/akc xswh h2tp9;r6efkyq ( 3- of a massless rod which pivots as shown in Fig. 8–40. Initially thwh2 ehcq9ft 3; x k/y-a6(prske 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 to a torque i+ukht*;kbnzr v*g2 n5d ;x8b of 38 x k+ 8u2;k nzthrg ;n*ivb5b*d$m \cdot N$ 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 mfc p *1m-gg.puau8dvuo4 k s)2 when the axis of rotation is through its centem8)ad2-kgpf4 s uuvg u c1po*.r.    $kg \cdot m^2$

  Calculate the moment of inertia 0miusyk q6w(/ of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignoredi 0uyqs k/6mw( (why?).    $kg \cdot m^2$

  A small 650-gram ball on the en4+ g-ykmevzc- d of a thin, light rod is rotated in a horizontal circl e zvgk--4y+mce of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular st00g)b;0pr +n pic(ks rubo z5peed (Fig. 8–42). The friction force between her hands and the cla0 rp(k)s5bcorp0i0+tznu g b ;y 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 objects shown in Fig mo(7;e.r f d(daoqg.n. 8–43 .rqo d7dmn (ao(e.;fgabout
(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 c o fx2uf9:jf7qx;l0 pjonsists of two 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 corre+ 1bvgrmwo 27lct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a lb7vgrm1 wo+2radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mao5:wqi-,t ff5. cdy jlss of 0.580 kg. Calc cwl.,tqy o-i:j dff55ulate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from regoev1c+k ov.e+m 1y 1rst 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-r9ygstl1.xn 2*tl 26f ylz2t muound and is able to accelerate it from rest to a frequency of 15 rpm in 10 *gy2yxstmt 1 lf ll29uz26tn..0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and -)x shj5:-il.f9+qwaisvsug8ud e8l is eventually brought uniformly to restgq-8 +i5i jw. v s8ussd9:hfe -lul)ax 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–-nylg lax)4 h145 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;k9.vl:g sfe f ;dlzhju t1,b+ solely by the action of the forearm, which rotates about the elbow joint under the 1hzl ,ff9. skbuge;j:vt dl+; 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 blfh7 2vc5 n.ojpade can be considered a long thin rod, as shown in Fig. 8–4cp7 5j.v2no fh6.
(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 8 q-vn+gs:w2xaz1qm econsists 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 accg4h8 n ago;owrhr/64ielerates the hammer from rest within four full turns (revolutions) and releagrgo 4;6w/oi4nra h8hses 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 inertia r9z( f( zzpamnp:m7p k0*x0wqof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine developsw/11 w 6jnbcqsf-tn7y a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 c(dp aw+e;mt.c-br1j) u v0n gem rolls without slipping down a lane a (tew+pvm)n bc0u ;d. 1-regjat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ojqqa)0x3 3 feff two xqa0e j)ff33qterms,
(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 )axdh -cfk -3)p0 hhfcsm2w 3j7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 0)2hxcf3j-wd h ap -ckhsm)3 f8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and i4z* x1zd lv gift5z wm,:v23emass 1.80 kg starts from rest and rolls without slipew,* v4d5z 3z1il2i mg :zvxtfping 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 tip. It starts to fall awh4/v 2xiox do(*wr ,lnd its lower eri4xwx, /lod 2(vwh* ond 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 5 fdw 1 belwzzu/ p,:pf.hw.1:sir9 ngball rotating on the end of a thin strns .5 ww9z/zh if, rd.l:pup:w1bfe1 ging in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momei)r(j2l4cx bqntum of a 2.8-kg uniform cylindrical grinding wheel of radius 1x )42(lqbj rci8 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 tfi e 3-9twzd*i)7e+ 5s;czzucj+jrr rhat is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positizzwcrj;+*rft jc 53ze+d - 97i )uersion, 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 shownjo:(gd/441el iezy bf in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when cozildee 14yjg/b(:f4 hanging 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 rokx+v1 ,oy (zbttation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3 y(1ob+ xkt, vz$rev/s$ 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 yrp knt5rw+gs j1-q+6s,.ifskr1.vnyti1 k 0its 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 radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clrtn61s n1sry kpyq5.f.srtk0vj++- ,ii1k gway sticks to it?    $rev/s$

  (a) What is the angular 1gub0k(ep/ik* vpbq9fm16xdk kd-t( qm7 qd. momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eart6+qfi 1)i0xb(xe mqxvh
(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 cylindric-j o98tphdrj320ppvm qlom v4 8s u-6kal disk of moment of inertia I is dropped onto an identical divtqphlm jo30j8vm- prop4su2 d6- 9 8ksk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2xpmydbjnz-srf;)mp e, 6 d2;0.4 $rev/s$ 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 sta qmm0f7uu4u:rb) zc zf:-ka0 jnds at the center of a rotating merry-go-round platform of radius 3.0 m and moment of :)mcbzj:rf0zq4- mu7u 0uafkinertia 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-s1if w -2qti,cgo-round is rotating freely with an angular velocity of 0.1-2c, tiswiqf8 $rad/s$ 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 co5/ dzvr4hoj(illapses into a white dwarf, losing about half its mass in 4zho(rvijd 5/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 rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess o: an+7u5e.p.i +xg5z9hm rr wu hyjy2jf 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 y9zp0wks7;jl x p/m,t6boqh +$ 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 r u,ppz/i 6sm+ *w3ang2xhayv 5est, that can rotate freely without friction. The moment of inertia of the person plus the p+pva/3 56* zimyw xugs,n2hpalatform 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 diameter mek3b0 rxn.fu+ty2 qra8q2d . hirry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 170buy3t 22 kf. ir+8dx0aqrq.nh0 $kg \cdot m^2$ 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 ofzqs9 1;f3 6r ruqhpef ;7bc,zo 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, Fzouc,brq ffqz7 ;9 r1;ps 6e3hig. 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*) n3pg/ppps a)1mb1 w shav ns(:p8gm 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. (In the latter case, treat the M38 n:pnhwg1s/mpsppv( 1 )ma*g apbs)oon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleraterdf+ro/-b 8 x+ (yqozhs 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 5gvazd6)d 2bc radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque del)dv cbzg6d a52ivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cbvf-*g5q; bihylindrical 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 speed of the yo-yo when it reaches the enb iq5gvh;f- *bd 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 the aaywpu*f yz v:y/hms fj*)54 )bngular 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 k:ecn 7uj2z.o 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-quartezjo:uec.kn2 7 rs 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 azd hn/* lm(,fcw*m v1 )g4v cayvvic7: low-pollution automobile 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 dia: vazmwfdc 4nym,i/lc 7(cvv*g 1v*h)meter 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 vywyx(f bv g;2,8j :qirv*m/kan $H_2O$ 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 rollig:d+* ga nhd,lu :lk4vng 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 le9;odj,k tc svwf s8l;;ngth L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hintlk,f;;cd jvts o9 sw;8: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing verticall 0b5 c: 7/o,hc0xklgmt i akmaedi7c(8y on the floor, and we want to exert a horizontal force F at its axle so that it will climbx0i8ko,l m(itgc hka ac/ :770m ced5b a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.zqqy /l;c55uf2m/s on a flat road is making a turn with a c5uqfq; lyz5 /radius 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 wkvg(e/ zi w*40.50-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it fro4k(wv*/ieg z wm 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 d7cfc 7til-dl*b1 ;p esolid cylinder and her arms as thin rods, making reasonable estimates for the dici 1lep 7d*bl; cftd7-mensions. 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 assembly which consists of two cy vb;z vq obba+ri9k0k o*v8(p4lindrical plates, of mar+k zav4kbq(*o9vo;8ivbb0p 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 raditjmwzt/loc/u m 0avt2m ;l5) 7us r rolls 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 it is to reach the highest point of the loop without leavin /)tc/ maltm2 ;u jlo5tw7z0mvg the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do f3 2necbhs)/x*mdu h2not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduc53 6lxb.hr8th9b2u3e zkwbqr es its speed uniformly from 90km/h to 60km/h The tires have a diwb83r 3rubzq 9h.5b2h6xk elt ameter 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