A bicycle odometer (which measures distance traveled) is attached near t 7tm5rh-+udn v0zt* rehe wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle withm*5r0z- ettdv nrh u+7 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the riaw xhqu5b9 n-)m have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration cha -9h qxn5abw)unge?

Could a nonrigid body be described by a v9f2eg l:lunoz:num41 ,oo3 qsingle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explaiw .gqie5uti .pj wa9r2q4x1/ vr:jm q.n.

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 thagv9+x9 5rixr4i mqai 5n when your arms are st9i5xv 95ixm+q 4rarigretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rea;ui l+ i3p 5(szkiy)dkr wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocke)kk; ii(u lisd3pzy+5t? Why?

Mammals that depend on being able to run fast have slender lower legs with fler7ap dr) y5s89k:ov sysh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass8 yrso95ka ysdr7):vp is advantageous.

Why do tightrope walkers (Fig. 8–35) cazs2+u 5je3lpv2drwa9 tp , in(rry a long, narrow beam?

If the net force on a system is zero, is the net torque alstx3m; xc z:dpt1+k.nf o zero? If the net torque on a systkxd:f+n3txtzmc1 .;pem is zero, is the net force zero?

Two inclines have the same zsiy:1.jc4 zm height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the bal.z:s 1c y4imjzl at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an ih:1ljub5 qid n-f7k j.ncline. 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 spe:b- i7j1f .lnjqk5h uded there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the sam2 y(shv. a5jt d7fyal.e radius and the same mass. They start from rest at the top of an incline. Which a5ft d(27jasv.y. lhyreaches 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 or r4 s/aunzt .- 0cvl3aixj e 41:17fobikvg6 ifnotating objects eventually slow d.t z3agi4 eis bn:0-f1v/n cuki1o7vlfa6 4jx own and stop. Explain.

If there were a great migration of people kv hzhu3t2s/ob8 8vc3 toward the Earth’s equator, how would th 3hbtso/8 2 kvzu8vc3his affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any 2h,l: f6uzstf*h9 2* shorvlu/w8ylfinitial rotation when sh,h lf/u8*fs2lw yr:fl 9h o2ushzv6*te leaves the board?

The moment of inertia of a rotating solid dis,6xq;9tiqtj7s*jg5m zy(i bs k about an axis through its center of mi(y* q 6;9m jig,tbsst5xj7qz ass 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 rotau *4(8 dxruyaqting stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the sameq u4*dr(8 xuay? Explain.

Two spheres look identical andz:n2 mfb iqe)2 have the same mass. However, one is hollow and th 2 bnm:ize)fq2e other is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a hokfgtt+5(kzf l (zc hw52 gz)q,rizontal 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 thisctzkgq+ kzz (w f55l(h,2f)gt point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of qw1 35dz97jg e)*qbkwaeh i .la large freely rotating turntable. What happens if you walk tow17aw3zwdqhiekb j.l q)e9g5*ard the center?

A shortstop may leap px.r3izp3;7 c*k qulointo the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his bo. q;l7xizcuo* rk p33pdy rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular m0oq)s0w*i gzb omentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicoptez* wgq00o)s ibr stable.

  Express the following angles in rbwu4 a, 8 qui2vp8owu.adians: (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 coini2/w7,xcn 99uz7 7h;pasy 7doqyf huwcidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Ear2y7hq axp7,7;/cw i f7z 9ndwyhu sou9th.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed a gbl b7dc tl.lp6k8)l3:vb3iut the Moon, 380,000 km from Earth. The beam diverges a7cgp3.lu lv 8lkb3 tdb6)il:bt an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor jgxm632;r x9gp b2s*n qe8briis turned off during operation, the blades slow to rest in 3.0 s. What isrm b6qj 28ixp9;neg23bg x r*s 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 t- i ki:mg1q05du1pkjghe ball makes 15.0 revolutions, what is its diametuq:g1pd01- jimikk5ger?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. Hojbeo,xg,5l2 p w many revolutions do the2, el ,ogjb5px wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angaw-mr 9l(byo .6tnmimhy84b 7,fwm i hp8 i.t;ular velocity w9ib a8h, ptm rh8-.n w6mfiyyoim7(4lt;b.min $rad/s$ $\omega$ =    $rad/sec$
(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 m+(ji9 oe /l+ wstiulz8akes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear spez u jwiel9i/ 8+o(lts+ed 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 orbit around / 7fy fjwbefs2,os(i v(q.s,i ,spe8tthe Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of dx9+m* 6bw ct17 9oube c(wqwda point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm fr7uu)m i13 -oz0 kuxtjlom the axis of rotation is to eo)j t30 kluz7m1xu-iu xperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates u+(ikg2p+a s(s/vsu -0yof q ty3gh,rmniformly about its center from 130 rpm to 280 rpm in 4.0 s. D(,ssvs0 g r2 ihaymk+/tq-puyo+gf3( etermine
(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 radiuse38 5qtqwqs /i $R_1$ 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 theyq3f)s(6zs t nswc*u1*pud(d mselves 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 revoluti1yus d zdwf**)qu(s3p(6n tsc on 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 uniforgf3g* f)ulqc9mly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn 9)c f*3glqfugin this time?    $rev$

  An automobile engine slows down from 4500 rpm to 13z39qagodf;w x 7zy (lqxg5z7 snrc.8200 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 highspeed jetshk: a 1vku keu(s;8b-k in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its e-ak;uk( u1kvks: b8 hfinal 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 .k5;lrn ticu)accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on rn5k;.i u tc)lthe edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 rev4*yqj/ z)hih1xg y3 ddolutions befo 4* jdg)3hi/xyqy h1zdre 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 revolutions as the car reducelji4e6 .9 dny 3z ye6siwg2q6u8 at7uzs its speed uniformly from 95km/h to 45i2q6l4y9z3 gw.8 yujt une7szd e6i6 akm/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 65 k mx+a)d,+t o)ujpd- irevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires tp+ okd+m-xudia ),)j have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all heb27 ++d hh w*g7uculwdr weight on each pedal when climbing a hill. The pedals rouc+ +*7 uhdlh7wd 2bgwtate 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 forc y212;k.i+ekf yv6w/e xyrzxue of 55 N on the end of a door 74 cm wide. What is the magnitude ofui wv2yx.k2eyr+f ;/k xez1 y6 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 i nj;sfgj,; p28,wecf the wheel shown in Fig. 8–39. Assume that a friction torque of 0.4 c,gn p;jw2j8 sf;f, ie$m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massles 5t229l vjy6jef:kl;:8cf tde ixsb1e s rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this syste8ef 2j1 5 ;sjbli v9:2:kctldy6efxtem.

  The bolts on the cylinder head of an engine renm: f.d*i( ns:lgz2ahui /fp 8quire tightening to a torque of 38 g8u:*.ahzsfl mpn/ :2 ini (fd$m \cdot N$ 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 1ts79jv9 1l ehi0.8-kg sphere of radius 0.648 m when the axis ovlt9e9hi s1j 7f rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.fef4:n b4pi t07 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The ma :i fbfet0n4p4ss of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lyst .ael du+h6 gd2l ,bsdg(jmi*r (-4ight rod is rotated in a horizontal circle o2hst+l( abdsdgm*gl (-u6ry. ,d e4 jif 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 angula.,yke k:x08zsm8hmne sg 7- xar speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N totka0nxk-s,m87 x. hgs e z8ey:mal.
(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 o:jhkubbi lf 13 /-x pq(s1r,aibjects shown in Fig. 8–43 l-/fkq,hbji1xi1p u: (3ba srabout
(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 oxo4b5za2 hv8zj ygen 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 cylin.r:(6 aipxy whmfv0 t9drical 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, wmxf6h:. pvy0twa9ir( hat 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 andcuwe-t jgbzn:5 /; e1a a mass of 0.580 zu;tg/1n-b5ec:weaj kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it kxb8xtf,4)g u p yx2zbzumm0 6c6t.,d 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 oeddxw1-/ kv/h i.;u ntn a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edgh//d e1 dwv- uxnkt;.ie. 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 /pxp9s b06p e.vm/043y yh kadhijq+vand is eventually brought uniformly to rest bavph +49epy3v d/ 6bph0jq.s0 k /yimxy a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg2ulx6h k g.so6zeaw 3: ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action ofbj2ecac1j3k/ aps, ma) ba 4ric (8xn* the forearm, which rotates about the elbow joint under the action of the tricepskiac)*1apcsr3xbn(j,acjm8 2e b /4 a muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can beqa (3phua mxie) /+gmf ym3*y8 considered a long thin rod, as shown in Fig. 8–43peg myma )xfq y+/8m 3(h*iua6.
(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 :p gzp.md/.s itwo 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 accelerates the hammer from ,ytum4,d smy;7 )(9ef-wnnc xn4teif rest within four full turns (revolutions) and ifu7n fy ye;44 tn,(wdmt-9ns),cxm ereleases 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 ofg1ldq.)c y6raqm t 07b $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of,: cmo0 9eqjpv 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 rolls x 94t1zbxfjkn,8 yu4n without slipping down a lan8jn1 y4fk9tzb 4xxun,e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energdka/ up) i5v 1oc3u-uvy of the Earth with respect to the Sun as the sum of two t5u vc ua/13kv dpu)-ioerms,
(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 x1i+sbvm.b+ xv12mn f, sxen7 kg and a radius of 7.50 m. How much net work is required to accelerate it frnbv+, bms+.1 17v 2sixnfem xxom 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 kgs+8:xys xky +h starts from rest and rolls without s8s:+ h+kyx ysxlipping 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 tipsbwkos,vzl 4p+q *7j(. It starts to fall and its lower end does not slip. What will be the speed of the upper end of b4j s+wk7po*zvlqs,( the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on0+e;56z 9 zoy 3ze gxjbq)mfpx the end of a thin string in a 3zq 0x)fz e6zyoe jbgp+;95mx circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheeib8p . j;:yty3vjy-furqx7c+ :dxa 8 wl of radius 18 cm when rotating at 1500 rpm? .tv j8 iyawx-3 cq+:yd x7p: j;8yubrf    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his d)d:fd l/h) tsside, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal posidtds: d)/f) hltion, 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 o p18 tta ;:x+5n kyyp8wsgh*o6io+yahne shown in 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 position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her ni* y5+ 8ha :+ot ahkx6spgy;yo8pwt 1angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increq3axzn2ii/sm3pz;* ;aj8xuvq- b - zpase her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of;*pzv -;z mn2/8aqjpbxxsaq -33zuii 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 j/h-zeu vi7a wl0ci,/ center at a freqv7il e/i0u-czj/ a,whuency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum nmb geh1 6qtz*w/ q8le:ex /b(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 9ed5g0gn8 saj.prukeh c:2v6Earth
(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 o6 q *e8ggok5cef moment of inertia I is dropped onto an identical disk rotatin e65ogq* g8ckeg at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns j.g93 pndz p5nat 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 nkt3xi d3v )v,.cgsagw5-kyn7y 4gs4of a rotating merry-go-round platform of radius 3.0 m and moment of i v5y,)kt-vng wk3can.44 sg7yxg id3s nertia 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 0 wakvf/+lf;t:b xft+/caq- dof 0.8 ++:bfcf/f aaw k x-;0/tldvtq$rad/s$ 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 collapss idf.f4vq( z41mb/ zjes into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new ro( 4v4 sf1/.zjdimqzbftation 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 exces vcdrzo+(uu-;)/bgk ns 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 es0ch -: iac6l$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotg8c *0 a9l/yxp2uptu)ofe 1gpate freely without friction. The9u y2g xecf 8ltgp* /oau10)pp moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5ln8o 3fd77 b(fy gz.iz-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1700 bd.l 8yg3zf 7z7i on(f$kg \cdot m^2$ 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 thez,0vsk /c ovre1 +6tbe end 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 rope unwinds from the spool? How faz 01/v,tev+ker6so cbr does the spool’s center of mass move?

  The Moon orbits the Earth sucf3 uh1aur7) ifh 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 Moon as a particleiahuf31) f 7ru orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ra-u.(a pbxcj.g z 6vu2v.v+ts.c;vzi mte 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 uniformhc7r* hqk.q1/x h:kji l0v. us cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the*:q u1hqskil xc..0v/r7h k jh torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical du1ut l:p j6.mamd f)*lisks, 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 end of its 1.0-m-long string, if it is rm.uf up)dlja6:m l t*1eleased from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed3hcsp0lyt f9 )2y2wfl 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 w )bbe)0:k y0uv2 jlhhrotating at a speed of 1.0 revolution every 12 days. If it werh)j0 v0y2kebb l)wu:he 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 angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to uq w;+,x;zg cqxse energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 wgq x zc,;+q;xkg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an t(k.u paq61 q:l0pptf$H_2O$ 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 speect 0miv6 ic5j+-;x2y-zuout qd 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 piv8psbk8obrz3w gvi3 22bd./, itragq) ot freely (i.e., we ignore friction) about a hinge attached to a wall)agt8 porbrz2 i k.38 ,wqigdb3svb 2/, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and we wyht; 22hk:r aqsgc ,q( tz.d)hant to exert a horiz;qsdtkhhy,h c2tqga( 2z).:r ontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a k+,(ib ok-c nhturn with a radius The forces acting on the cyclist ando-i+ k,(bc knh cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and bh g,, gfpoz80gegins 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 feat, and where does o8f ,hp z,gg0gthe torque come from?    $m \cdot N$

  Model a figure skater’s bodyu8: *g ksuvc4y as a solid cylinder and her arms as thin rods, making reasonable estimates focsgy48v *k u:ur 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 assembly which consnxuyz-b. g3ga nzaf3gp:*v); ists of two cylindrical plates, of massg3n)3 zgy -pav*b:; nzagfux. $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 Fig. 8–58.eocy ad5efj 8/p744qo What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point f4 yoa c8q5eje4o7d/p of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, b3 qxw s7ik1jf-ut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the cpg :j t.umx6tlj,b5y+)gt5tp ar reduces its speed uniformly from 90km/h to 60km/h The tires have a.+j ,l mg5 :tbt)y5tpuj6gp tx 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