A bicycle odometer (which measures distlm(wo(6lw 0 f9p8empwance traveled) is attached near the wheel hub and is designelo0w( wp98e(6 wm flpmd for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on ts4yjjr8; 1x)o8*kz dzb ptnu:he rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does) 8t r:po8d y*1 zk;4uxnjzjbs 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 akkq- (- *ap)mj0vayxt ngular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a ru:l /ry cp /+8+udecclarger 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 behi ,c/ba-7 gzluqklof+2ys ecp 0tp7+,pcrt (l5nd your head than when your arms are stretched out in front of you? A diagram may,el tyrg-c2p5a+f0p colq ,s(+t7c7 lp/zubk help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the +1* k3i n5xcej9s5fsh vwy8hk pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear s9shk*15k3+jny8 vw ise f x5hcprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower w/ d96in7czmwlegs with flesh and muscle concentrated high, close to dwmc/wz i9n67 the 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) carrycthxe 28/vbe x9(k5le a long, narrow beam?

If the net force on a system is zero, is the net vn.zsd+5ty20wj : pne x-y8vatorque also zero? If the net torque on a system is zero, is pe0 nxn.8z2v-vs yd+:atj 5w ythe net force zero?

Two inclines have the same height but ma z ;*-i2bgs4tnsdu * kei95oayke different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the banygu - ed*ib*oi 2zakt49 ss;5ll at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) d vp5guqjyu-kb +a2a3 8own an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the botuq5 a+k-a8vjbu 2pg y3tom 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 mass. Thevp9xh 6p6qp6d7zr +zaqz1 0lky start from rest at the top of an qz rk6a+0l79pq66z xhpdp1z vincline. 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 i(odp1yplk c. r.k3; lare conserved. Yet most moving or rotating objects( ld r;ky1.plp3c.kio eventually slow down and stop. Explain.

If there were a greafx 2q*,vz8c8cy-zz;vs/tjw jvu; b3w t migration of people toward the Earth’s equator, how would this af2j8jxyw,;t vz szwv8;3 zcq buf*v/ c-fect the length of the day?

Can the diver of Fig. 8–j)jiw- 8mk)d w29 do a somersault without having any initial rotation whwj)-j)k mdi 8wen she leaves the board?

The moment of inertia of a rotating solid disk about an axis thh8 ur7 (eg;9a,grcz etrough its center ;tez,g ru(eg7c r98ahof mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotat c3h5.h )xexz2hfy7p zing stool holding a 2-kg mass in each outstretched hand. If you suddenly dro h75z)f.hyxhzpx2ec3p the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Hoc : yarh k-+ gd.;dl3prt. ux*ewmk80iwever, one is hollow and the other is solid. Describe an expe-h+t pr ;:k gkia.ced8*lmx u0wd3y. rriment to determine which is which.

The angular velocity of a wheel rp(n)ah(p-)t fb x h-aeotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this b p(n)axeh)h a(tpf--point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freelt oxl g3:6, yvianf40nb2 *imn*mcd-wy rotating turntable. What hap g:*6l4d,ocf y b0nnmx*2- iwti3 anmvpens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As he lqxr2u2k8d mm4jrk- 1throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hi1q- juxkl8r m2k2md4rps and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of anguz g t2hx54 .o*rpkbc,3zhw; 4ysnt9kblar momentum, discuss why a helicopter must have more than one ro yg5z;kxk z*.h,snt tp c49b4hbow2r3tor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following g6 7oa ha.zvwcwxx)**angles 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 amafc;2jtl y.s7 dcwcc8;zing coincidence. Calculate, using the information inside the Front Cover, the angular2fwy cd .78tcjsl; c;c 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 from Earth. The wi7 ohmat7 u7d./k,zu beam diverges at a.moudk h7iuzt/ a,77 wn 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 my 87ri,usamga-64ln xotor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slowrsg,a 86-niu4l7 mxay down?    $rad/s^2$

  A child rolls a ball on a level flo: e0ii58 5b9hiw6(toaf brf ruor 3.5 m to another child. If the ball makes ou 8 w5:h69f5ar tifr0ib b(ei15.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter gdy zsb*f91 n)travels 8.0 km. How many revolutions do the wheels many*9zbs) fg1d ke?    $rev$

  (a) A grinding wheel 0.35 m in d f4zo:1j1ags2 wcec7fa25n yviameter rotates at 2500 rpm. Calculate its angular velo 4gn2j1ocawz ev1y aff52s:c7city in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 yrjjf95x05wbfo)e1 r s (Fig. 8–38). (a) What is the linear speed of )y fwjr 05jr5o9xb1fea 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) i2 e+t9fhm ,8liatxsz9n its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a o*gt:a dk47e qpoint
(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 from:j t(ns1w0v tw the axis of rotation is tovtswt0jw 1(:n experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abo wecxt*gnl7lrqj:4 qa 4 w:0l9ut its center from 130 rpm to 280 rpm in 4.0 s. Dete*t:4:4awq9ljq lnwc0x eg 7lrrmine
(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 )/+tvq st3twu $R_1$ 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 M,x (9*icivsi isjd9t4mb e*w0oon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated 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 diameter of (09isc, m** s4i dv9 jebxwiit8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from dj h b,,8xnrptaank7gv: -d:nht8;b )rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this timd8g:ax8;rpn bah)b,7tvjkh:d tnn-,e?    $rev$

  An automobile engine slowsfi:jh cu36- fr*wtew( down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresr: l-k)o aj6yiv+zq z,ses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to tuk y:)z,laz-+6vjiq orrn through 20 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 tm yn/1;z(l3 a(re,d:wtln rwo o 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this tien 1w;l/dyl,orz:w tmra ((3nme?    m

  A cooling fan is turned off when it is running at 850rev/mk6e9n )1b c:ccfpuq-iq)m yv2in It turns 1500 revolutions before i) c:cm2 9ui )y-qvfcep1nbk6q t 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 reduceap6a -jxo e03yj lh52i0zg3hu s its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 ml56 p20yazihhj a3ox-0 3g jeu.
(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 uniformly ktz/up p6,zek0f;k 1hs6 kg7l from 95km/h to 45km/h The tires he06sk6 hkltf7pzk g;1,p/ u zkave 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 cltm/jdy 1 h1i6mimbing a hill. Tm y6h 1jim/dt1he pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a8dkcsd la zacm/7 as:r3kp(,4 door 74 cm wide. What is the magnitude of the torque if the force lsa3mc/ 7k 8:zkr,sad c(d pa4is 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 ab2/f.p9o.te;ini5 3 s+ od kkpp,bqdit out the axle of the wheel shown in Fig. 8–39. Assume that a friction f9tds3e5o.no/ti ,d i;k qi+2k.bppptorque 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 rod v6co o) uc0,kc7pi.5ggj c /pxwhich pivots as shown in Fig. 8–40. Initially the rod is held in the horizontalkocc0ugx/ igj67c. 5 ),cop vp 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 x 1ebucl1 2uph/zh9m. require tightening to a torque of 38 1ep mh192u xubchz.l/$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when the a,x ,qfh vwa*o18yjd* udt-iq7xis of rotation is thro 1w f ux*qd*ti,j,7vd q-ayh8ough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm osz e2tnws0) gur/o)/in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (s/snru t/wzg))eo 02o why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light roai b4 ld2d:-etf,q qi.d is rotated in a horizontal circle of radiui-ddbft2q4:, i e aql.s 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 r7rd4(kt(6t0efx m+ms7hpn t a bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her nx+(6m4t7 7 0ef(tprrskhdtm 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 objects sho;k-bng le9c:wzs -4:j qpx5. gw uu8zown in Fig. 8–43 a8:zcj -5;4:b .g9 lqwupwusgn-kxo ze bout
(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 conso 4dsp r5lt8)her8 6yfists 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 sgdafc .(agv 6tqzs96 *atellite 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 forcv6t.afz (s9*ga 6dcg qe of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass );fag /t,bx u:u2ijhd of 0.580 kg. Calculat:/2 uthb j,ixg;du af)e
(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 s(*ls (z bvel6 /3zvkka bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentiallyz u(*fr)l7 cr mpku9v,n/ c.pf on a small hand-driven merry-go-round and is able to acceleracffu9p7l,m*pn c/ k(u)r.z rvte 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 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 ( 8ewfctx e:d-ba8/tbshut off and is eventually brought uniformly to rest by b:(-8bate /ctfw xd8ea 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 3.4om7xr/j7w ki) hp;4anp6gyi 6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the foreaik1 (chc g8 mq:29rbq )ie0tmx9ysq-xrm, which rotates about the elb8eq)m(0khc ymxis92- 9q:rtg1 qcxbiow joint under the 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 blade can be considered a long thinz vzc- az1:b/y89srhci u- kp3 rod, as shown in Fig. 8–46.v1yh-zsz3ik zrb9c a/cp8-:u
(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 cons43n d4)xi l5ofbj( qptists 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 accelerates the bj*2 pjb rcbnz 6e,h ni3/zk:m8i,uk(ymo /)w hammer from rest within four full turns (revol r,z z*on:yeb,3bimi8m (nw//p)2jkcjk hub6utions) and releases 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 ofs;8 ,(fn1zz u nck6pke8y2squ $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a tob)hq0 lh 32lzxrque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3v q(w2r8o5 vwr kg and radius 9.0 cm rolls without slipping down a lane at 3.3 v ww25(v roq8r$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun agesmn -hb* p2dn (1,nus the sum of two tenenb2pu, m (*hn d-1gsrms,
(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 rh,jzy0 ,yw ae(adius of 7.50 m. How much net work is require h(e jy,wzya,0d to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 2(ijz+t ,rsus,3v lwdt ;;p.se0.0 cm and mass 1.80 kg starts from rest and rolls without slippin,;+ vi,(tspj3tlu e; w srs.zdg 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 verticall(xk 1.(ano oi0nvm z*x:p yqz4y on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hin 0p(n :k vay*iozzx (qox4.m1nt: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thin st;n9p; -qpb s1o j1vl qvo+c*1tstw*tz ring in a circle of rad;vnsq9jp ;stzc l1b-q +*p1tw ovt1 *oius 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 cylq (j gyzg3oh4h b,10du:z0opkindrical grinding wheel of ohopjk q,uyzh4 :0g10dg3b(zradius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is4 km616;kiv3n 5grzrovny yr2 rotating at a rate of 1.3rev/s If he raises hi m6g4563r;rokzy ynv2 1nv irks arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her mo j)4u5mgn)u homent of inertia by a factor of about 3.5 when chj mo4u 5n))ughanging 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 inc06f 6;d6qa;jdlq ic wp.o.lgbrease her spin rotation rate from an initial rate of 1.0 rev0lqp 6j6;wl.giqfddc;. ab6o every 2.0 s to a final 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 centerm9m/xa4r v8mewg8 h4to9f6rx 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 centeratm8e mrhf4w69/ox94 x8mvg r of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure ska0uddx 6nqu)gdlv u)6)04fni6gi7 f gcter 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 m8:4 rmez*vwghe Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an identij y2f vtxyuie(a1r(7, cal yi ,tvre f72ya((1u xjdisk 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 2.4h8 /3u oymym sz6z09rr $rev/s$ 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 )x9s4*3ea0lnyqht ewrotating merry-go-round platform of radiuh0x9 ew*ay)q4s l3nets 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 ig1d j 4qy9cyq(,e:c dis rotating freely with an angular velocity of 0. dji 9g yd1yc,ce4:(qq8 $rad/s$ 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 dwarf, losing about ky 7k)np.mqw +half its mass in the process, and winding up with a radius 1.0% of its existing rad.y nkwq m7k+p)ius. 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 exces )ne i if)29;ylh5rjgls 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 )u nafbwa0.l(ctt .jbh, a8x ;$ 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 rotate freely withou5) zrfv,krh,xa u;mgql3 ss+)t friction. The moment of inertia of the person plus the platformxq, a)s)hur,l3gr5fv ;k+szm 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 -/ad2(g4j dk qlxsh/tn ;f 5lccy2r3 oedge of a 6.5-m diameter merry-go-round turntabler3adcl/sk 2y45qn c td f2(h;o/jl xg- that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with theapn4z4qx3:+bt,t ye(xlu / zrrh5 / al 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 5z4/plt3er r:(u4 /nat+zxahyxqb,lwithout 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 side always faces the Earthg,t8eab dzraw1xppi9-) ,v( v. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular m p91da(g, ba)xw pvie,8 rztv-omentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate n 8lel9olo7*x 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 ojp2m)8do cb +bf radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by jo)d bbc+mp82 the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindy32j+5*aiu pt v 2b gtb 2k6ja0dfii-rrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical h*v-p6tjdabyraui2 gt 50kf i b+23j i2ub 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 82s **piwcr t 1da2asuis the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as ,o s fngby3zg8v6z h.5great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mas6g fbyvg3.sozz h5,8ns 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 use enero:6q6u z8z1 sp 9yz6v5csx plggy stored in a heavy rotatingzzppovx c5 yu6q: 66l 9ssg1z8 flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “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 al p x kfd-wuq8(e+rj:qw mx2x:+h;rx+n $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v=3.3 07w v xte26k y9i+eiebic -av+$m/s$ 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 frictio2c; yr4uk r9jwn) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At th ;jrc2yrk49u we 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 v+spsqfdi4ya;f7j+) 9 liq 2q /p7dkg-tpv vv,ertically 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 (Fig. 8–55). The step has height h, wherq) k j+ppi4t v lf 9 sv/7,-d2svagiqqypd;+f7e h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn w3spm5,ocuz(jhl 3kgdgu 9 ;x4ith a radius Th ,co 4zs3d3xu9u;lg( gh5 mpjke 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 ak+d01de q u2gd 0.50-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 from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does thek0e2 dgq1udd + torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, maki.,q wdc xlf)6dng ,.d )f wx6dclqreasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consi+0(vmijj j(w5xl.aw qd3me adi 77l*hsts of two cylindrical plates, of mass .i3(5 emjma d 0wd jhil+aq*lv w7(xj7$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 m 5agb6xr8d;o looped rough track of Fig. 8–58. What is the minimm5g8;r 6daxo bum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume 2kcu0r4 fbp f1ujx.*v $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the +nne ja7qyq+c )l/sqd0. d db4car reduces its speed uniformly from 90km/h to 60km/h The tires have a di0 4desdan +ldyc )b/njq+qq.7ameter 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