A bicycle odometer (which measurvy, .e8xl*db ac38euaes distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you useaecd8.v l bu xa*,8y3e it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the ri .5futw,zwab*-)cggpm have radial and/or tangential acceleration? If ) u,5cwptgg. *fabwz-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 whh;c29zphv) value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a large4dy)(3kjuhhh tpr5 d,r 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 thaly-tn:rz c n+4kwh/h .n when your arms are streykhr.-+ 4n/ tl :chznwtched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at t,an0;hr2lny n. d( iygf3a4bbvd*i8 lhe rear wheel and three at the pedal cranks. In which gear is it haai8ynagr ilvl;y.f4n bb,0d(3 dh* 2n rder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run 0c oa,vtn8hzil 151s /olt6onfast have slender lower legs with flesh and muscle concentrated high, close to thlnln o /6c85s1ao it oz1h,t0ve body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry cos rs2y;qn)0-(zmx f a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the nzdumx7w 1,od ezg m66,et torque on a system is ze,66uzmxgddm17z ,ow ero, is the net force zero?

Two inclines have the same height but0kel(36no*m,zn lbyh make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be grea 6(knb,zlhe 0l*mon 3yter? Explain.

Two solid spheres simultaneougz1io4fa 2qvs tnp5t/w (2l2d sly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic qf vtidlg/a42t25snz o2(w 1penergy at the bottom?

A sphere and a cylinder have the same xb 7nj(sofd(ce8f 9v+radius and the same mass. They start from rest at the top of an bv x8((fj9s n7od+fecincline. 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 conserved. Yet most moving-n4rsl8 t ki9;ij 6hcc or rotating objects eventually slow down sht4i86nji- r;9 ck cland stop. Explain.

If there were a great migration of people toward tab +czt c:m/,f (8/yypb,rslxhe Earth’s equator, how would this affect the length of :f+,c(b, a/sp rcytlxym/ 8bzthe day?

Can the diver of Figdj lrrx ()zb045wr+l a. 8–29 do a somersault without having any initial rotation when she leaves the4j5zr l lb)ra+(0r wxd board?

The moment of inertia ot eheg1b 4xes04*fyq2f a rotating solid disk about an axis through its center of 4t4e g*1e2ebqy f0hsxmass 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 mae, -z1y0xcgo.qth ;p yss in each outstretched hand. If you suddenly drop the masses, will your ax1. zyot-yq0;e ,c hpgngular velocity increase, decrease, or stay the same? Explain.

Two spheres look identica.yw xbr* 9dfx9l and have the same mass. However, one is hollow and the other is d y 9*xrbwfx.9solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizont qui l(d*-gy-l4,d.zlxko jz9al 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-izlu4q dz.9(- x k,gyojll d* the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freeb b99tuat-b1(fh/e wuly rotating turntable. What happens if you walk toward the cenu b(f-u9/ethw9ba1 btter?

A shortstop may leap into the air to catch a ball and thr).j2w,rqkk5-gi8xxc0 a p slq ow 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 ro5l g2qk, .s0 j8 ax)kiwcrqp-xtate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentugvm54:opdvy : 8rqp d4m, discuss why a helicopter must have more than one rotomdg q:dvr54p 4 y:8pvor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles5ec sdvv4 aw/1 (0pqmzuh1 5xl 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 Earth because of an amazing coincidence. Calcu (nc0 7x7caehnlate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the 0ne7chan 7(cxMoon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bea :xr8smlbc(7i/wp 8qrm diverges at an anglb7mx:(rqws /licpr8 8e $\theta$ (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 65qvh9lbhr7t4k i)i9*q5 t7.n z y1bpt0ab7vxj00 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow downv41qp i. vat bz b7)ix7 9lkq5hrttb90*jny7 h?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 mu0k a 4yf2)7bjlavth4 f-np5 e to another child. If the ball makes 15.0 revolu4v5 0 pe4at nbkffaj) 7h2y-lutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.6*0tj)e nv5(mi wdesv0 km. How many revolutions do the d0w mje*6 i)t e5vsvn(wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rota8(dn suvbmv + 95fh)kbtes at 2500 rpm. Calculate its angular velocitysu(bv)m+hvn b f8d5k9 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 cok 4 -eje,x+iel7ptx1y mplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear s ,7k4-1pejxlyie+ex t peed 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 its orbio xmsa .ia/4,ft around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poix 9l-gsmioz3h2w mg3fkl e0-5 nn.rj4 nt
(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 r+ r7a3mh3fjddpp9y74j or+r.3ju1rvw sg v(a otate if a particle 7.0 cm from the axis of+ .9(vry4mwjgd rap7ar +sjhv7 3u3p fjr3d1o rotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center fie3ix(h-jg r/ l94whurom 130 rpm to 280 rpm in 4.0 s. Determi-x 3e h9iihj/lrugw(4 ne
(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:h6ov9bbuxq5dwy v8ph8lx5+ $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put thems. zu-k9 5wuuflelves 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 cylinder with a diame-w5z9ulu ukf.ter 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 u+kjlv1h u2q6 q fnxo7snh.)k.niformly from rest to 15,000 rpm in 220 s. Through how many revolutionlok 12nqf.jv7quh x.s6+h k)ns did it turn in this time?    $rev$

  An automobile engine slows down from 4500 +8ldp/ k gdt av548guhrpm 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 highsq(h+4dz r)lw+by6 2 xq u )cjfh(ezq3g1p7m dypeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 2bh(c +wxzd e7ud)qlpm yjhgz 4)3+6q12(fryq 0 complete 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 uniformly from 240 rpm to wei19 0,.3 hanvdspjshgl(z) 360 rpm in 6.5 s. How far will a point on the edge of the wheel phl9,e wg1vn id.0)jzs(3ash have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turmf79 lboaif ph0 -,ik;ns 1500 revolutions before it cof alb m-fi,0k7p;h9i omes 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 maejw/j9/0ag (wg2wg -q mx,nggke 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameterqj/29gww ,(nwgxm- a/gjge 0 g of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unifor/ mo ksyw-kfh ipcn-2:6isz v/*)u 2nhmly from 95km/h to 45km/h T hp nwk*-z:2yf vc si6s ok2/)m/nhiu-he 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

  A 55-kg person riding a bike puts ar )fzg /pwr.e.w :jvl+ll her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 c)ww.gf r j/.r:v l+pzem.
(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 w a-*:mb6 zepk 3wd/zwaide. What is the magnit d/*z pwk wezm:aa-b36ude of the 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 about the axle of the wheel shown in Fig. 8–39. Assume owr-+qs(; fmo mq sorof-+w;(that 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 of a massless-hp b5l;9quxz rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the mh 5 l9-zup;xqbagnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requri(qxt:sn4/ge cbc3 1 / carb9ire tightening to a torque of 38r/qb(sxn cbc/r3ci 1 4t:gae9 $m \cdot N$ 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 t*1 kjbo4lvk;od;- * vwognb)she axis of rotatiol*wsbdo*o- vj) bg;;v4kk1onn is through its center.    $kg \cdot m^2$

  Calculate the moment of ins ,+7piwho, sfw(d1fo uf9es 7ertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have wdo7,,s(i9p s+fews1o7f u fh a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rqv/+ n/ cemx;totated in a horizontal circle of radius 1.2 m/etnq/c+ ;mvx . 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 rotatineuvma.*i3 zrz5x/*2a vak1lhg at constant angular speed (Fig. 8–42)/*ha32z l arez5a.k vi*u1xm v. The friction 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 point objeoc 7iru ubsr-/0i 6uvk4 fy2r/cts shown in Fig. 8–43fb-/ 6u4r0k2y vruuoic 7sr i/ 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 tota t0 ,30uccm/ kkhtacbgln+ w3(l 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 cylindrica nl7zki.z uujxd1*rprl(:;0 j l satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of eacnr710:*u kj lp;z.ri(u zxld jh 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 unif6 vs*i3w)h i1uixxse;mqq 9n)-fy:u p orm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculate;uyu vsi6i)*-wi 19 f)qxmpexq: hs n3
(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 restfxi+v2us 7mw+ 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 9:9 mtigamfm4ulx,l (*-yv g ubgwg *8merry-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,i:yvgbma8lx*,u- ml4mg9(g wf*t 9g u 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 ofxjtq; +h 1jq6 ta)tje3f and is eventually brought uniformly to rest by atjq j +1ahq3jx e;t6)t 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 acckgh)iac:*bdft tn*3 ,elerates 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 t6; zby uzmsv,k57 ioq*s ) 6c3k(ezpmmhe action of the forearm, which rotates about the elbow joint under the action of the triceps musc5u)pzqkv 3y7iomszb ,6m z6m* ;k(ecsle, 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 a long thin rod, as sho5as+xyes)7u0d h9 6a2maiduo1thu,dwn in Fig. 8–46u1u h a2s7adxtedi, soma9 0d uh6)+y5.
(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 masi4yk pa80 t/xsses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer :d c 99ts(hc.fwb b jq1uck8n( from rest within four full turns (revolutions) and releases it at a c s8wt(dbk.c 9j qn9 h(:1bfcuspeed 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 oia;1 7i aejjs6f inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine yu:tk:wy owi3m php 0(a:4+yedevelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm roll hxh6*w-qi./ lzitu4b s without slipping down a lane a.-*hib/wt4i q6l huzxt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the 1sw-pn8+oia v b3 k:msSun as the sum of two terv3pkni1s wamsbo+:8-ms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 164q7 l r./9jagwig 05unn0 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolqrg /g nanwu07j i59l.ution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from res),wdx kf enz898.xxlwqw *wo)b1+3 jc lajq(ct and rolls without slipping dc81.xww,98) d bewawljn+*kj(zoq x)lq3xc fown 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 arbd630 s)qxhm9aoj c;nd its lower en9c 3baomxdj ) ;r6qsh0d 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.+m:z.d( eakcu/ (- z g 98ld:x)hbnidkrqtp; n210-kg ball rotating on the end of a thin string in a circle:n-+gz nd/(.mbhaueqp8z);rkdkdtxc( :9 li of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinditqv 8+q:l6xi*,u jtig ng wheel of radius 18 cm whx vt,qj ltig+*iu:q68en rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating atkch -s )c+0rct)z)uxcv.o k/h a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed o0tcz)ohk)cv - . kus+rxh cc)/f rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her h +kmlb 7ki+7kmoment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotatiok+ibhkm7kl7 + ns in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial yat,zr7g ld54q7 z -bki5.r merate of 1.0 rev every 2.0 s to a finakrz . ,4l5trdgai-z5y7qb me7 l rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a e.:yq lpt5xjez-+ mu0k p+ g)ifrequency of 1.5rev/s The wheel canu-g)y p.mtk+ :+0epjz qe5lxi 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?    $rev/s$

  (a) What is the angular momentum obwr1 da rg)b:x7e7aw0f 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 t jb zyo,rwgm)(bnmxvw6u )986he 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 cylindo bjr8(gb m3,jrical disk of moment of inertia I is dropped onto an identical disk rotat (,g8m3 rbjjobing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 6fv43ix e/fo a-c( ttjat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round plabglha*065 f tut7 4fe.a 4tr3tqodn1s tform ofa0b*fqu6ftdtrt.h 4ae 1 547t3gosnl 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 rotating freely with an angular velocity of c8.2gkb+ li.h su+awh 0.8lhsbua+2hi+cw. g. k8 $rad/s$ 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 dwarfcbc)e y:n ns98*l1xwc , 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 Sun1l)*9cwcn ycebx8n s: ’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 ofshht y 8z;lbuzf2xjq19 +04lq 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 6ucj4;*wcpf5z4dwc. fy wxj;$ 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, initiall-vy ya( a41lbcy at rest, that can rotate freely without friction. The moment of inertia of the person plus ( y1-bayla4 vcthe 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 ,k6k6ram3eix t k9)wdthe edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment o i dm)kw,k kt3ra6ex96f 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 smt.0 p(nm *9h2qz (cmbqai3f the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a dmpa.(z *mimsqq09h 3t(nc2f b istance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same sinw-od tie2 *f.de 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 Moon as a pa ofe.ni*wt-d2rticle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from r,1cm um tyzawzul:)5 /est 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 ox *e5b 3h60gcsfhqq-) +kktp pf radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at tx qb 6+c)3s pfh* qk-h5pkge0constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylifasx),cair v()3/ -v p3 ra q+zlehel+ndrical disks, each of mass 0.050 kg and diameter 0.0q+,h/3xevz)eaial -lrf sv r+ pa3)c( 75 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long 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 angular spebbh6eoghd*. ,ai) fhu2x*pc0 ed 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 rfb e3 8z/cqra3vcn1z0 otating 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 itsn3/ z a38z1eb0crqfvc 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 usf84w:u+0o3kkzacb )gcw s;yue energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cyw;yf+:g bsu zk4 wkcuca0 )o38lindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates a hd1//) emsizjn $H_2O$ 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 ab5r3a6bkz i kri2 b(4nq i78bw horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore fzqm3 ojn .;l 8nb36fnfriction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of releasn 8fb. ;jf noqnmz363le, 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 v3 1levqz:: mq rlip-*vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Figq:evzm3illv- r q1*p :. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is makin s,f(imww3is6g a turn with a radius The forces acting on the cyclist and cycle are the normal force s ,mf(w6isi3w $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 m and begins whirl0y ,7yihwpkd53r ne +m0fblj0ing the rock in a nearly horizontal circle above his head, accelerating it fkmwhd ,l0ne00jy+y f 5ip7b3 rrom 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 cylinde)b8 3hwzfdshkd. y qsnq, *3cz28f:pkr and her arms as thin rods, making reasonable 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 2z3qfz.qpwhd *3snf8c:bsk8dykh),.   

  You are designing a clutch assembly which consists of two cylindrical plates, ofy.px9 4tnyvf/ /yvxtpyf.4n 9mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Firhw5o(bh2u 91hea x:vg. 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 leaving th 9bwu avh5:o( x12hrhee track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu p7bue7kj5vx 0me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifou h:1*s/we r . rgy9+6:ojfj,fvrxfhhg.zly 6rmly from 90km/h to 60km/h The tires havoe/*6hwzrysygu:xfgl1.f+ .rh9 jh6 rjf ,:ve 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