A bicycle odometer (which measures distance traveled) iw eu3mz u2. r/0qca4xrs attached near the wheel hub and is designed for 27/racu3uw 0zmx q4r.e2-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity 9lp+jwl:ehv+9x c+bp . Does a point on the rim have radial and/or tangential acceleration? If tl + xp9 b+vcphw+:e9jlhe disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be descxyew1:,*c c/g ay2:bg/ xsnuf ribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force8zsetc at b(+*? 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-up229b- ydh+xrnwo;o op with your hands behind your head than when your arms are stretched out yb+o- 9 ;on2xoh2dwp rin front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven spr.a ,*isfvj6 xas/op*hockets at the rear 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 o.a,6poh s vx/jsa *fi*r a large front sprocket? Why?

Mammals that depend on being able to run fast havexofx5)cs4a4v*qt 1qm m1 o y5p6n0ymr slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain 4 xym mp611mr)*t45n0ocq y sq5xvfoawhy this distribution of mass is advantageous.

Why do tightrope walkerskk-,9v2tg*o/ 9z le (ml odknr (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also z/d/ vez/ pcj/n1k z/sjero? If the net torque on a syste /necjzzj /ps1vk/d//m is zero, is the net force zero?

Two inclines have the same height but make different angleg0 4(vxjst/fjys 17vxh . y/kqs with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gxyf(4k7vxjhg1 0ytj s/.s/q vreater? Explain.

Two solid spheres simultaneously start r,ifcy(ho 8 ba (hn7q3polling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reachpbq ay ,hh(fc3 n(i8o7es the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius3s;95dz x fpkq d+mjj(yujs.7 and the same mass. They start from rest j 7ud5m3z9+jfy(qx ; . pssjdkat the top of an incline. 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 pv. ;a6u .oajecs1bv (cur8k ,angular momentum are conserved. Yet most moving or rotating objects even;a8 eo suc.v(,cbvp1 6.urjka tually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how 0yf br.o5e3u.fcu r z)co;.apwould this affect the ure5roufczby) a. p..co 0;f3 length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initiol.4 g2jt //hx-qyndl al rotation whg 2xn q.4-lo jtlhyd//en she leaves the board?

The moment of inertia of a rotayg5y ap04,o0 p :a3qxx.5xou7 uajntoting solid disk about an axis through its center of ,yqa0nau 4.p507xp yjgot3oaxu:x 5 o 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 rotating stool holding a 2-kg mass in ea5irn4axky0 k jh er4kmf0 y183ch outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? E5 01r48hkk4yym0f3ijaenr xkxplain.

Two spheres look identical and have the/z9560p lx:md bey ebzph5 p)m same mass. However, one is hollow and the other is solid. Describe x 50yb6pdmm:eb 5z h9lzp/)p ean experiment to determine which is which.

The angular velocity of a wheel rotatin f3os9 75vixdwg on a horizontal axle points west. In what direction is the 9 v5fiswod 7x3linear 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 decreasing?

Suppose you are standing on the edge .(83) usnm ws2 s wt :rdls:mpnf5is*wof a large freely rotating turntable. What happens if you walk towarddns5*2p ts:f3 s(nwu8sm rsil m:w.w) the center?

A shortstop may leap into t9z4 b*-indim4h(h drh he air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotate4nz- ( rhh4d9ihb idm*s. 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 momentum10rli/vem vg(c, tb +f, 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 hemc+( 0vib/fgvet ,rl 1licopter stable.

  Express the following anumb+4b+0v yiwxigk 46gles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, using: p weqniaw.q.vkx skzzbu9.v +:(*r) the information inside the Front Cover, the angular diameters (in radians.kax qqvk *p(sv9+) z. .ze wi:n:wubr) 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 beam dive0 xl:vj- vantju s(i8(rges at an ang s0u-jal(xj t: 8ivnv(le $\theta$ (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 is turned w :nl5l w(a8(mwafz :soff during operation, the blades slow to rest in 3.0 s. What is the angulwnzl 5 :(a8:a mwwf(slar 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 the ball x0i 3zkvxy5zn9 d0 ce1r,j/slmakes 15.0 revolutions, whi5c9zkn djs,xre 0 vzl0 31x/yat is its diameter?    m

  A bicycle with tires 68 cm u 9nb1gb,7bw rin diameter travels 8.0 km. How many revolutions do the wheels mn rwb7u,b91 bgake?    $rev$

  (a) A grinding wheel 0.35 m in diameter ro hiyf). ;arhka5zoi:0tates at 2500 rpm. Calculate its angular velocii: yhkz5h )0;io.ra faty 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 rev26mr f 33wyetfolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m 3ym r26wf ef3tfrom the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular i lcdse406x5bs w,+zmvelocity 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 okq e*lel g;;(ef a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 )qatx ebc. x/wi-8tg;cm from the axis of rotation is to experiencea-/ twx eci8b ;.)xtgq an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center yld )e iy sij;4tc8)bwln-/4v from 130 rpm to 280 rv/c)wdit84 jn4y y e)-ls;bilpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiuaz9/ij )yha:ps $R_1$ 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 themselv sw50wcvx74sz es 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 z7v0 4sscw5wxcan 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 uniformlybwxmn 6m(h+wk (2 d0nd from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in thibd(kx+mnw(w2mh n06 d s time?    $rev$

  An automobile engine sl ). uzmk,m0l /abfm+hlows 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 stresses of flying highspeed d ;g asmii4 f/c.6cf9vjets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete /f gf csm64i9.di;vac 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 diamet a3 q i7xniq,r)+lliatxz2(r9er accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How i9l,a)qi27 i (x3 qzlr+arnxtfar will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It tu:2/ie x5a:r zzd0lzonrns 1500 revolutions befo5iod/ 2zzn : x:0arezlre 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 reducesppw 2nu lt3 71zpb)7hr its speed uniformly from 95km/h to 45km/h The tires have a diameter of 72 bu3 lzr7) hpnptwp10.80 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 revoywte/5 ;3 b6bti uwri-lutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hau-tbiebw63y 5 irwt; /ve 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 pum y qs/a14rwg)ts all her weight on each pedal when climbing a hill. The pedals rotate in /1w m)g4asqyr 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 a door 74e p+-89k ; lk,c 68gczfoeuwby cm wide. What is the magnitude of the torque if the force 6 ky,cep-g of8z c9u;+ek l8wbis 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 shownipp3 5q2 gb;okin. ( rei/ )2vfwaizo3 in Fig. 8–39. Assume t 3wef ;i /iq)np2ik52( orvzbpgo3ia.hat a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod whi; sbs nvsqeo zs)nkeqg(-3(n ,cp ;9f7ch pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the m;nqes7-ss(v;3c,)keg qbpnfzso 9 n(agnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to cx h.u4tswlp/;;2e,y m hnf9yyu. h )wa torque of 38 )wh;h4fewth/yxcus n pu ;yy. ,2.9lm$m \cdot N$ 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 radiu8y. l3z wx-yvidx,6u vs 0.648 m when the axis of r3xxzyw ,8vy i6dv l.u-otation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bik2 .6gyouwh9n a8/ ;l 4muriricycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?). l/a9hmi;r ikouryg n.68 2u4 w   $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lf s0d 2n+uibv:ight rod is rotated in a horizontal circle of radius 1.2 m. Calculatefuvs+ib:0d n 2
(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 angu23se kszg (6(bkwaq 1vlar speed (Fig. 8–42). The friction force between her hande(( 2kb3s zgv6qska 1ws 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 shown in Fig. 8–4el-v z if7r(c:jm:dw2jx pn:.3 am jierz::cvlwj7-x :n(2d.pfbout
(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 oxyu v9ro26wk. e91 cjnwjj 9(aqngen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, engi.)qbskty.y+4dldp(x neers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius oslx ky+y4dt)q.db .p (f 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of 0zqebc3 w rc231.58 c1erq2wz3bc3 0 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, accelerati /p5w;mxk+ gwqng 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 hand-driven merryk qbw 5*.l/ack+ ;f,ymj +iqdbj+t/ia-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 lit/+ia kk+f*q,/jjbcm5d .yw + ;qabof 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 io oxky9p;cfg mc d(*71s shut off and is eventually brought uniformly to rest by a frictional torqxp1okco c7(;*g 9fmy due 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-kg ball a ynd;9xhry* s8z;ny+a t 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 ilu.cm,k6a*pslq1mx / /- zzfes 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 accelerat 1mu c,zz*q p.- 6amllsxf//eked 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 bl)6o; zntfna c.ade can be considered a long thin rod, as shown in Fig. 8–46 zn;fo6n tc.a).
(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 ca q/ v3cybd7v.sq*bbbr3k5 +* 1wu oxzonsists 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 n1voxk e pp539four full turns (revolutions) andnopve5 k3px1 9 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 y mp:8qurktr)wgm;y ee37 uw x(2 a,/linertia 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 torque of asy)l3vq,xm l(2mzjws3yn5 7280 $m \cdot N$ 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 witx acm a9;-,aithout slipping down a lanai,9;- xcaa mte at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum o*-t ka (sxhsf9o x6ce) (jrt:tf twor*x-as6fo:tjk9 xs the(()ct 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 am00yw8ihg:b wxkh 0 j m/vs)dy9c9+qj radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a0kyb8/y smxdij99c:) +mv wh 0gwjq0h solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg sta0zhv0lbb-44pq y /f. hz hmf:trts from rest and rolls without slipping down a 3fptzfl z-b0y v4.: hqh/0mbh40.0 $^{\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 balanc*z5/;tn z;pf ;qmte d 9wbzcx 05tc-aked vertically 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? z n0tz5/xac;qc9m fkpt ;et;b*z-5wd [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end fo hbgvh:iyb7/te0d ymq c)a 9, d:w4+of a thin string in a circle of radius 1.10 m at an angular s0ema+ 7o w:cg bfdq)d hhbv 9,y/4i:ytpeed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.: 1lbqjq s:sd28-kg uniform cylindrical grinding wheel of radius 18 cm dq sl qb2s1j::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 is rotating at a rate ox, 7da5jbhv b8f 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation dec57bxa, 8j hdvbreases 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 moment of inertia ff3ts4 j0lno -by a factor of about 3.5 when changing from the straight position to the tuck position. If s-o4fftj0n3 slhe 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 rotation rate fbvc zon,. b-0grom an initial rate of 1.0 rev every 2.0 s to a finalbb-, 0cg no.zv 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 t pnbpov8g -e-(hrough its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approx8 go(p-pve -nbimately 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 of a figure skater spinning at - w64qvfv1e-l7cb/ ptm.va x z3.5 $rev/s$ 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 tllop 7 zhx*s4gp,rt(/he 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 cylindri+ ,1ey ef veas9szl fi/j25+kycal disk of moment of inertia I is dropped onto an identici5,s2f1+ ya9e y e+svlfjkze/ al disk 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 2.4 1py d5ej8eq+0;yyqvf$rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round platforu0vp8x2 (ww tly blxb9y5)im s j1h)3am of radius 3.0 m a8p1ys9b2)tvah b lu5w3j w ix)l0ym(xnd moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an 8:l.js,hg,gn gpp h;aangular velocity of 0.8 h8; gh jgls,,g: pp.na$rad/s$ 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 y7;s: /2 dcjqzxrym 9l5zb4os a white dwarf, losing about half its ma9:5/zzjsy7yqo bmds; 42 cr xlss 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 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 wia+ktbe4 wgf/v rkf4g9ae a), .o-/so ands in excess 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 b8tat8j/t9e p$ 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 platforwlc t 7ndb)p-.m, initially at rest, that can rotate freely without friction. The moment of inertia of the per c)7t-n pdbw.lson 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 :b;ri 4s7,byj. d9szs(vwouns y ut9; a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings ab7;sdv u ;s j.,os(9 y y9bu4zwstn:irnd 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 of t +lp9zy8nzt 1zm:hve.f6eay jh:e.,vhe 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 far does the spool’s center :1lna .mh 9 veh:6+zeevf ,yyzt.8 pzjof mass move?

  The Moon orbits the Ear xr s/o 2;sbgez,i(bk0btro. t5q4 tc9us dk-.th such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (a5itb /trbosrg.qc9.k s- dkxe(z4t ; bso ,u20bout its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a0447i rpek agb rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape /n *j )3vopbhzfe ak1,of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intep*eakhf 3o j)vb/nz1,rval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of t /grr :nv c/koeak.0n.wo solid cylindrical 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 drkcank /no./e.rvg0 :iameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed ofx)ze-:c kii 4m 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 time t3:bczxr)6 rmwtf20xs as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to mx:t6r wf xzrt0)c2b3undergo 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 use energstr v6/ewzbt.v* z /4qs8 hw1hy stored in a heavy rotating flywheel. Suppose such a car has a total maw v/*4weq s.1h rz8h6/vtszbt ss 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 illustra(7nmp(se2 ufh tes an $H_2O$ 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 s tewn8: t74z02di8 y-afsedhegc* kr; peed 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 pivotl3h 2,icu0ibz5xsf .cn/ /yvj freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of tlc i cu fyi2b,3vh/0n 5/sjx.zhe 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 v1ur1 owt i1h2aertically on the floor, and we want to exert a horizontal force F at its axle so that it 1 at2rw1u1iohwill climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with s0s1izgdn 54 3kqnb k59rrk fx,peed v=4.2m/s on a flat road is making a turn with a radius T0 19r5n zdxb kskrn,k5 4g3qifhe forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins whirliv(qd 2m(ilrv :ng 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 (qivr v2(:dm ldoes the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rods, mbd8 66syw)+p c5pz kqqzn.v,z aking reasonable estimates for the di6b+zz q5k,d)z.vq8s w 6cpp nymensions. 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 we3 mw ; sq39t-wo2jboehich consists of two cylindrical plates, of mass 3swq b3;eemjtoo29 -w$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 along2a.9sb bldpu; 6xwtt* the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the trb2x t9pwlu;b t das.6*ack? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but d.w7x 7dx wi qplk5spi0d1wzy3 e- db+0u4,hk do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformlyswl30:0ht9hduk te7p8 0b f mt from0lh8e7930 htpw:ku 0tbmd sft 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s