A bicycle odometer (which measuue2u.eh9x h1 iemaa 5+res distance traveled) is attached near the wheel hub and is designed for 27-inch wh2m 15.eu eh9i ueaah+xeels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angularqw 1liqk)8kusd:b(g 8 velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of links 8b 8qq(kiwlg)1:duear acceleration change?

Could a nonrigid body be described b3r4wi zrm/a;p-c*7om1vp/t vl z4zmvy a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger fo0qud .qd- .if*ck3 *bbyd lyr;rce? 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 thavjq*h;d6 bp.e+1ylko n when your ; qb+ *epklh.ojvdy61 arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wh61sg*w1j lrd meel 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 fron6 rd 1wsg*jl1mt sprocket? Why?

Mammals that depend on being able to run fast 3l; segh /e y1cl*b3plhave slender lower legs with flesh and muscle ecb3 plse3 yg/l1*h l;concentrated high, close to 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) carry 3ykl l7v1+fuanv4 1 obu;b *ura long, narrow beam?

If the net force on a system is zero, iez 1v6-yr5 05oxp1nz op-fe58zs wwrls the net torque also zero? If the net torque on a system is zero, is z8e v-rw10xz6 l 51z-ops5wyorf ne5pthe net force zero?

Two inclines have the same heig sdx312jsp qz-ht but make different angles with the horizontal. The same steel ball is rolled down each incline. On which s1 x3jspq2z-d incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One6zp: dc/; dbqayw+x *blzy +jd -o5rp6 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 energd+w6 odz5 a *+/pjb-z6:dx yplb c;yrqy at the bottom?

A sphere and a cylinder have the same radius h3ag.+.a9s )zqsq yc8uv c)ozand the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic eneycvoz9 .gsa+8 zuq)q c h.a)s3rgy at the bottom? Which has the greater rotational KE?

We claim that momentum and a3ks /j ;k7( nvv.jipqhngular momentum are conserved. Yet most moving or rotating objectsj.v pkvns 7i;hk (q3j/ eventually slow down and stop. Explain.

If there were a great migr hdh(keqz+5s 1sgxlrg8i6tkaj 8(.( hation of people toward the Earth’s equator, how would this affec(8(+a t .rz(k6ex85sjihhhg1qg ds klt the length of the day?

Can the diver of Fig. 8–29 do a somersault without having z3iftup k mt7p.g1-w0s0 3p sdany initial rotation when she leaves the board fmsp3.0p7s1zk 0d-w ttugp3i ?

The moment of inertia of a rotatii5 tewt;t .t-0bqy,sik6 pm )sng solid disk about an axis through its center of mass;qtm tpistbsew 6, 0.ky)-i5t is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outst6 45rn58cwvnf u pvp:e,xn4vmretched hand. If you suddenly drop the masses, will 5e v p mvv4 :nn4x58curf6,pwnyour angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Ho u-xv:czhq86owever, one is hollow and the otheruzx:choq8 v- 6 is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. Inzo8 yw++t xa;)ah5j1 cp9v vdl what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreas)td; xv5l+ ja1 coz89+a ypwvhing?

Suppose you are standi0 vd5 *q, qxlkc d :u15j*jjy,kxl6zyfh5w0wdng on the edge of a large freely rotating turntable. What happensk5q6j h1,*dfy q* vxj:yjlcwd uwzldx5 k, 005 if you walk toward the center?

A shortstop may leap into the air to catch a baemu 2dht7 t4/ill and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you wi hmtued74/ 2till notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the 3g6vvga2rod bdx-an;kl 6g1-law of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discusg-o a6 6v2db -3k;rnv1xagl gds one or more ways the second propeller can operate to keep the helicopter stable.

  Express the followingg137cqix j * /zj cy5tcvy53cj 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 Ea1yvh57;j(mas d7xd8-n f imjerth because of an amazing coincidence. Calculate, using the inmxjfa8(-ni7d ms 1 5;ehj7vdyformation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The bgywz2xu( b3a3;z rx88* tkdzfeam diverges at an az;3 (2kxtgfrb8zd w3a u yxz8*ngle $\theta$ (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. Whs x6:f;,ig di7qga+ua-,cix ven the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration xq6 , -gaxidag+vcs7i: ,fi;uas the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the bardq z a.neln(-n5*1 zyll makes 15.0 l (*y-aq5rnz1nzn .ed revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How yew8+r7cpr4 q., l lrrmany revolutions do the wheels ma+r4 rrley8.wql7c r,p ke?    $rev$

  (a) A grinding wheel 0.35 m in diamjg2l z (;1etfw4cgk3ueter rotates at 2500 rpm. Calculate its angular velocity ke ul4(jwc213g fg zt;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 lya)*rjl(a k2 in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the center? yak(ll*a) j2r   $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angularc:x 0);)otr dczb y0zz ff0hf7 velocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a xq8. e*h dbtl tj6z,j;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 centrif/g 0 yow0,zmbbuge rotate if a particle 7.0 cm from the axis of rotation gyobwb z0m,/0is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 287o48n)(5e )3hrkzrmzcpiz yf 0 rpm in 4.0 s. De()r nzk 4735hizmcy zpero 8f)termine
(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 3m4vsd) :k;oqzgysrg2j) :we $R_1$ 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 , axgn7xav6f:themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation g,6xavn:x7 afto 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,00a h-i* 8gu+bqd0 rpm in 220 s. Through how many revolutions did it turn in this timh*g- 8+udb qiae?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpmk* r27mev(zbwchkd: 35x n4hk in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets ine( g/c7z3/yyzzy/nl4 ulbpo7 a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete cyzlpn77zz3by ge4/u loy// (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 diameterh /1auo t7pr31 eictu. accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? e c a.p 7r1utui1/o3th   m

  A cooling fan is turned off when it is running mytjufpwg7 xsovkw;1/b4d/) 4o( j;f at 850rev/min It turns 1500 revolutioo(wj/14sjf/7 fu x vpd;4btk;ow) myg ns before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as vm/pn p8xkxd10an( 5b 1 262itqt ujhvthe car reduces its speed uniformly from 95kmvjvn nd(2 k 2u8x1ip0q5/m61p hatxtb/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65z*x-n8v7 )jpjq 0napx revolutions as the car reduces its speed uniformly from 95km/h to 45km/h jx0pnz* np7xv8 - jq)aThe 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 all obb ri /e.-q0mnkgc 66her weight on each pedal when climbing a hill. The pedals rotate in a circl b-ok6qi06e cm g.b/nre 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 a door5 zlb8xz2hu1 jp58(ekbsec s2 74 cm wide. What is the magnitude of the hz5lx bseu j1c p(8 k85ez22sbtorque 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 sutg3)p4c fess 6( *rbl)dye.phown in Fig. 8–39. Assume that ab )egyr)(p.l s 6psfce3*dt4 u 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 to2/q bqtm *)ehhe ends of a massless 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 systeh)*qob2m/qt em.

  The bolts on the cylinder head of t p7z*s xnu68ean engine require tightening to a torque of 38 pens86x 7*tuz$m \cdot N$ 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.kalmr9-m 3 04ub).b7pf wz0vi )ayxen648 m when the axis of rotatioruyp akew n0mxm)03v) b baf74l9z-.i n is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in ds,b t8nbx3i9)uj wl4n bsvs19 iameter. The rim and tire have a combined mass of 1.25 kg. Tbvl981n 4tw3 ,xjs9n)sb ibushe mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on dg.xls w*bhokk1 ,c* 7the end of a thin, light rod is rotated in a horizontal circle of radius o*w d*hkx,bls.c7k 1g 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 angulartctdv s/*wuk3qb(6y; speed (Fig. 8–42). The friction force betwee;ktd (uq/36bw*cts vyn 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 in2bf ksxjrber 8 oq;nj6(tdo g74b./(vertia of the array of point objects shown in Fig. 8–43 abo boj6r8jv27s(kno ;4 erbtgx (f/qdb .ut
(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 consi42 flvct19 fbysts 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 cylind0 j,omnn ;fx of/7rzn hyp1i09rical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satejomnhor00 9nzf/fip x;7 1,yn llite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to 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 an re)qv+ /u. +y:wegs+uiyjz6ed a mass of 0.se+juy +g6ziv:uqry/. +ee w)580 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 , zo:pd rk9fv/odswxi lwp.w)h0/ 83h it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand9c uyqlg.b-jezxr8tk.w;b d st:5:-lwlui87 -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 kgu:t-qkrl: w5c88d9-i;g l wbj tzulyesb.. 7 x, 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 p4tgf f4)w0r gat 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.4f)g fgr0tw 4p2 $m \cdot N$ 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 accsr1zr/p2* hvysvgxgs- 4ty;u7* u x+pelerates 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 bai158tcr gqc- xumxgki(u 6l;39zwk)vw0;i mwll is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly tr )iiqwzim6wc m9g(0g;- kx31k; ux5 u8vcwlfrom 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 shown i.qkla( j ig59zdcn*r;x43 rfbn Fig. 8–469 (z*r;b4f5aqxdlr 3 . ickjng.
(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 consi.lz zx)2ms ,q b4q(nvists 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 hammer from rest within four w1 vkuk9;e f*/ z w(gsue:1lqjfull turns (revolutions) and releases i/z uwk;s v*g9u1:ke e1f( wjlqt 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 inertvt0wgzbu-*ua 6syz, i,t8a 7mia 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 develops a torql 4bim2brocyg- u( k28ue 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 rolls without slii1vah9 djw+3m pping down a lane at 33mvi a+dh19jw.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with 1 nrv6:ml*t d7vxny ,rrespect to the Sun as the sum of two n6tr7*xrylv:v1n,dm terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radg-vr zs11*ckbe u4ikl o /0k.aius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revoluti ksl.-r z*b 1/c10ka4eu koigvon 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 resm oku zc6ga(;dt; m26xt and rolls without slipping2gcd ; a 6k;ou(m6xtmz down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. jdqut m(,qc9li5 h;b9 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? [Hint: Use conservation of energy hdqbu9;ml(i,tj59 qc.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating 2l)zx;t r dq/hm.6cjdon the end of a thin string in a circle of radius 1.10 m at an ajcdd6t.h rl)zxm2 /; qngular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylind 9i*e z+/r es1lo/il,ulif l8frical grinding wheel of radius 18 cm when rotating at 1500 r/el8ul+,rf*z/lfilis 9 1 ei opm?    $kg \cdot m^2$
(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 abt396ep 7ce)eqyl:ax 4) cxr platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Frx3cel7bq) pe6)49ct ayx a:e ig. 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 s*f3ikdrl:+l0 di4d sr2v n4kreduce her moment of inertia by a factor of about 3d 0vd ills+kisrk:r243d*fn4 .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 angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotatio qk2h u,e *5tg6qdy4ion rate from an initial rate of 1.0 u2 q*oqeg,ki 5 ydt6h4rev 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 center a gon gf-v92e hf*c3;cft a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diamvfe3f ;2gcg9 cnf o*h-eter 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 momenv1vd2x a7 p*bttum 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 Eartheiq sdc 1l;myf*ey8.ru- w7t 9
(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 otm7an,o 95l wvf moment of inertia I is dropped onto an identical disk rotating at a,na 5 vtl7w9mongular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2vct +aiz(1azkns , m8,.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 kr zk k3sc )fhyom1h;5(g stands at the center of a rotating merry-go-round platform of radius 3.0 m and k hz(h m r)3kyo15f;csmoment 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 angulsip ma /1m)ya1ar velocity of 0./iamm1 a)sp 1y8 $rad/s$ 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 half.gsyb.z/10c e8nfg rx 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 rotation ran/cgg0r8s zyb1e. x.fte 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 of 1 9(gir7)nboys 20 $km/h$ 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 bt/ zepz;0 gb 0(tre,y$ 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, ini im2eo4mose r n 399ci d:phrux4f/l+)tially at rest, that can rotate freely without friction. The moment of ie + ud/i24r9ol 4smhnm:irx)oc9 e 3fpnertia 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 6.5-m) jm+a61jfxn r diameter merry-go-round turntable that is mou)r 1 jxan6fj+mnted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end *4yue3;+ hb1txrvbo fof 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 ropehter b ;b1x34+yf*u vo unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the sa 3zhntx.1 kphw*qq1o:me side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital anguhznqqh k 3 :*poxw.1t1lar momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates frommk51 2;hz( fgq qh)vve rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in2x/lzf5 9.n:6 *b- ag haqp7 fnrpnjxx*vr c,s the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.7xlbpvffxa nxj.gn :* - zs*n5 rq/ra,h26 9cp0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylinda (8mgzh n1i3k4dq6m.i tmrqvkh e198rical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to cazmt 1ia.mi4h h6gqmk8 v3 n( r1d9kq8elculate 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 speed o/emq m +a1anm1aha oq9:sl o1(f 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 si cdoj/vvp-ara rv( ;ns*8(kr- ze of our Sun, but with mass 8.0 times as great, 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 mar v*djvs(opr v;c8-k- /ar(nass 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 energy stored in p - n;0 g0jiptapr,5lxumlc+. a heavy rotating flywheel. Suppose sn. 0x- m;glta,+jr5pl 0cpuipuch 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 a7 g7q(+af xid ku(v9m/u 5(w(brpqpsfn $H_2O$ 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 l, i+5h dnc/bsvg+q0d/vvet7at 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 ignd1jdtc;a( rs.z ;+mb kore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of masr;tm;k +(s . jcadb1zds 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 wez d1ph akv43n6h c-qt) want to exert a horizontal force F at its axle so that it will climb a step against which it v3h-c t qd)4nk1z6pha rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/sfutq z 2()r;hi on a flat road is making a turn with a radius The forcertz(if2u) qh;s acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-wmli2- 4c,g1jb :dgs*a( dc ljkg rock into a sling of length 1.5 m and begins whirling the rock in a nearly hol *:,g-g d(iwl s1j2db c4acmjrizontal 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 the torque come from?    $m \cdot N$

  Model a figure skater’s bod5* f(an/z v+wd vf/wvdy as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio o(fav /z 5dvww+ *vn/fdf the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly wpwj0xb4b ra l6y.a48a hich consists of two cylindrical plates, of mw0pa4bx 4j8y. arla6 bass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 /nv /jrfp* .bvthe looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving tvr./p*v fjnb /he track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but doq k3o r0+fl-ivto)uf*xa5x* s not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniforwp; mg0umfenpg tal(mb. 10+4mly from 90km/h to 60km/h The tires have a diameter of 0.90 m. gnlfm ;. ptm0mawpe +bg1(u04(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