A bicycle odometer (which measures distance traveled) is attached n1ub:n7:5gqzmk) 9x gac crq a,ear the wheel hub and is designed for 27-inch wheels. What happens if 7z k mgx1a:c)nrgac,5:b9 uqq you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim 2xnibg wrtu2q8 6f8vgfx*6e .have radial and/or taux88 e i26gg v*2wx.r fbnt6qfngential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single va71uj ln1 u+quvlue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater t qdg yf2cx;;*sorque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your hesqb/ r:uen-q. mx52r ead than when your arms are stretched out in front of you? A diagram may help you to answ mxesn beqr.5r2u:- /qer this.

A 21-speed bicycle has seven3)vd cx;(odpd, umzc8 sprockets 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 sprocketxvp)u co cd,dz38d ;(m or a large front sprocket? Why?

Mammals that depend on being able to run fast have slen ; z hu3szy6v, 9sptys.je),qader lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distrib3q)aytzysuj,z6 eh s.s , ;pv9ution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrowt7-lt1.v ucn bl-gv)e beam?

If the net force on a system is zero, hfuja0hw 9nb;e2 oi-kw.x-o * is the net torque also zero? If the net torque on a system isb*on9 o2e0k. a- -u;w fhihxjw zero, is the net force zero?

Two inclines have the same height but make different angles with the xn,;4z x6rai,7lbqhy horizontal. The same steel ball is rolled down each incline. On which incline will thi6 ,x,z;a4 n ql7hxbyre speed of the ball at the bottom be greater? Explain.

Two solid spheres sim+ ugp*a ;m+1uo4e;9ow/byrqg fznom2 ultaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches themygo91;;* z rqao++4upumbew/ 2gfon 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 radius and the sameaw z cch6,uym*u, a*y1 mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom6*h,ya ,cm1u azw ycu*? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved8c3:zs d3h 5qy2 qdp7+itlkdq. Yet most moving or rotating objects eventually slow down and stoh5+8dcddt7y2 :k q3 qszpli3q p. Explain.

If there were a greath3rw +lhu7 zq;g s;i2k migration of people toward the Earth’s equator, how would this affect the lqsulh32;;z7i+ gh k rwength of the day?

Can the diver of Fig. 8–29 do a siu q w51ptb5,vomersault without having any initial rotation when she leaves the bobwp5,i qvut51ard?

The moment of inertia of a rotating solid disk about an axis throughmstmxqh6)j eyz9ujy.i (9rs 8a 5u-9x its center of mass is-mjs.usm ury txe)z9j99y8a(5 ihqx 6 $\frac{1}{2}WR^2$ (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 hl3ca syny/3(a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, deh n3 ly/a3cs(ycrease, or stay the same? Explain.

Two spheres look identical and have the sameo4rvy3m5d y3bpr*-ch 6q :xcu mass. However, one is hollow and the other is solid. Describe an experimentqo3*- rymr6 3d 5ub:yxc4c hvp to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pointxxm3t7 h+wf.z ,0(cq e qs.syms 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 +z , qefcqs0x .xt(wm.m3h sy7linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely g2na+, ,llusj3d*s s protating turntable. What happens if you walk toward the alsj *lgud sp,,3n2s+center?

A shortstop may leap into the air to catch a ball and throw it quickly. As hebuu yipu6ym2+p (.;uxva sj,. throws the ball, the upper part of his body rotates. If you look quicpvua 2+6up.b(x,; m.siyjuy ukly 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 ang6,qecg*udra ./ w-9wqu+lb yjular momentum, discuss why a helicopter must have more than aewuy6.9 d-rqjug , b+c/wql* one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anglesa abzn r8u/5 m8*spv(; 5c8zjeos qf-s 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 coinci da/xb9e4wimqj50 / zwdence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun andx/ jbw09a m ze5q/wi4d the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directedyzp /*.en2uns at the Moon, 380,000 km from Earth. The beam diverges at an angle/e.npn z2y* us $\theta$ (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 )( fyb(yzipb 46q5kkhthe motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the y f46bqzk)i(hy5 pb(k blades slow down?    $rad/s^2$

  A child rolls a ball on r44,po aav (t:ym22sbpga9bea level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diameterbpe,aarmt4 2:obs p2g 49a(vy?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutionf1,mem d7o9les do the wheels make?lf9d m1ee 7o,m    $rev$

  (a) A grinding wheel 0.35 w cgr5u-bkj+,js(,av m in diameter rotates at 2500 rpm. Calculate its angular velocity inwjbr,s5+(gjk ,- uavc $rad/s$ $\omega$ =    $rad/sec$
(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 s (Fig. 8–38). (ji,pd *c-td; kg1sm. ha) What is the linear speed of a child seated 1.2 m from the center?jt *.sdgh-;p1imc,dk    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Eag (7 iwsv1fxv;rth (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 pointqy5q /tb(lv pce4j52 o
(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 th6anepc 8f57)z*mot yre axis of m7 e5pofr)ya6 tz8n*crotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acc+mh4 gz -;;*hds rf7tk oibvzm)y0bj(elerates uniformly about its center from 130 rpm to 280 rpgzm(bfz ;hhm0+r-b ikydvo;*s) j74 t m 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 radiusih-x cke58okl34.i) mttzua 7 $R_1$ 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 spaceg k6 k,zh9wyqn0qwr-(craft put themselves into a slow rotat -wnw0kq,q(gkyh z6 9rion 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 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 re.pq0 )ozjvi j:z )xf)ist to 15,000 rpm in 220 s. Through how many revolutions did it turn qov0iz f j:x)iz)j. p)in this time?    $rev$

  An automobile engine slows down from 4500 rpm x:sq ck k k;z;:2+o)gnl;d wklto 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 jets in a whirlingrjbad8 av 7*4t “human centrifvb*a478 rjat duge,” which takes 1.0 min to turn 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 acceleweatf7 2oftlxy(k873 ix-dlkg 5e,4arates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a poino-k7li ged284xtayf t7( f53e, wlk xat 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 turns 1500 r45a-2ztit 5 js s.(nmwt uqkn2evolutions before it comes to ztqusi t25nstj5n(. w2ak -4ma 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 qt c 4qj7tcvf4wdj c1,45e2prthe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m 2 eqtc54q4wpf1, t cdjvc47rj.
(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 majp ;wzr*5ll+ u-bx ot xf*po(:ke 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a dipxo:t (x*u*f +-rl p ob;l5wjzameter 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 hbmvzb rmeba ;m:+i 96,er weight on each pedal when climbing a hill. The pedals rotate in a ci6ve mm9rbi b+mz,a:b;rcle 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 74 cm wide. Whati)zk)z7 kb g6z is the magnitude of the torque if the force is exe)g)i76zzbk zk rted
(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 p 7qy2 dk2m6/hk:.dw4argi +ofstvr/ about the axle of the wheel shown in Fig. 8–39. Assume that a76:d+/4fgaok2id prq m s2tr.y hvw /k 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 masslesvl2ze oht+l3r.s +3qis rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnit z2 rstelq+3vioh3.+l ude and direction of the net torque on this system.

  The bolts on the cylinder head of, fq8et):gy/t*fa uzx an engine require tightening to a torque of 38 gfz t: ,qt/feyu*a8x)$m \cdot N$ 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-k(z(,yc h, pwscg sphere of radius 0.648 m when the axis of rotation izy (pc ,hw,sc(s through its center.    $kg \cdot m^2$

  Calculate the moment of iv,o7yd) 4efd f*mu1mqrz+1 *efl 5auinertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combinem 5yqal,4uedoi*d er+1*fmuf1zvf7 ) d mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end y*yukau /z64 qloejk 4 95x9upof a thin, light rod is rotated in a horizontal c4yxelu9u* p/ozq j4u6k95kayircle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angu.7dxxe+1 )mfk 5vizo ilar speed (Fig. 8–42). The friction force between her hmf.x 1x5+z k)v7odiieands 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 shh 3kpwas 4iyos2 .g/t3bg e8x6own in Fig. 8–43 o4 s3 gbyk3e 8hisat.6pg/x 2wabout
(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 co;: s6yuelbd3-n9 rggunsists 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 sat9nh l4lg8qll +ellite 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 a8+l4ln9h ql lgnd 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 os/ t)o;v0xulg1uq; n wf 8.50 cm and a mass of 0.580 kg. Calcut1n vsgl/u0 o;uq ;xw)late
(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, accele(5tto ibmm,r1 rating 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-np4qa1 ln 2*/e 6rdxxwdriven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (epn l*rax2 x qd614enw/ach with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut b/vj;tb qkx+oqs0 oxkn9.*cn w go3/0off and is eventually brought uniformly to rwc/go tvqn 9 /0no.j *k 0o+sbxqk3bx;est by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45;vzv ;b(al f ma3lwt-+b z,d9t accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown b wi2b;yam08.v(snh u0yqfi0solely by the action of the forearm, which w bnyf8a 0qm(i vh0;b02siuy.rotates about the elbow 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 consideredeq1: bxah/l8x a long thin rod, as shown in Fig. 8–46lxeh:x q81/ab .
(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 consistsvny+;.a 5d;vk4bun3( wubc y r 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 four3rd 6m(6:hqsb kzgcu+m-p t0x full turns (revolutions) and releasesm0 bkcpdxh u:3(- m qt+z66gsr 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 inefw (a +cve.vq2ve0; jirtia 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 torquev:y7djqz4(4k1qimye0 3i i z f 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 -,pcvl l te65ns0z iqqc ,r66qkg and radius 9.0 cm rolls without slipping down a lane at 3.3vl6nlcziq5 e60s, cqr 6t q,p- $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of tcny6yltv.x x2n0ew ** wo termswl.2*xny 0tv xc*n6ye,
(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 radius oa dqb p250zla6f 7.50 m. How much net work is required to accelerate it from rest to a rotation ratal65 db2zpaq0 e of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass :-c rf e* phqq zsft5+md:o(3a1.80 kg starts from rest and rolls without slipsh:fe*cq 3r p:(at-z+5q dm ofping 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 balance )msh+s:l0/ n1rgfvkbd 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 befo ms sh1kvn+/r b0:lf)gre it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.21vwn; ds a21y uwy* m8(we/sb)q0-kg ball rotating on the end of a thin string in a circleybsw2*wy)s u8;a qn(wdem/v1 of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum+n,7rdox km(fwru (,zt2/ xi;dzoto 8 of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at krz(d (t/7u+no,tw ro xoxid, z; m82f1500 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 yb ,8r ulig5b8platform that is rotating at a rate of 1.3rev/s If he raises his arms to a gr8lb85 b,i yuhorizontal 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 Fig1 m.- :+roe14g6 dz aq pvz;ywwpjz8rg. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speegyoz e-wvd1w z;1gr4mz+8jr q: .p6pad ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spiha13vhsd; s:3 fo7w2 v/vnhjxn rotation rate from an initial rate of 1.0 rev every 2.0 o3aj:hvwx3n vf21 vs 7sd/h;h 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 arod:(qj 0 wc04ea a0zzusund a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5ze0sa(azd0 :u0q jwc4.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinninyj9yhi5 iq6z) 8i hxf3g 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 0np ;/z.kmqapof the 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 dr2 iu m :n;mf.m6,rhooyopped onto an identicalnoyh.mm6muf or ,;2i: 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 mmrug)l * q6s-d6vq5b lub.y2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merr0 p+ta *xx9nu4 cdmfw-y-go-round platform of radius 3.0 m and momenpuf+-mc 9dt*ax0xw4n t 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 rotatinp7krm e:t 1d 3ecqm*v.g freely with an angular velocity of 0.8m m1 ptde.*c7qr:ek v3 $rad/s$ 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 eventuallyl3vwxpyyz/;+yt8i 0:gu6 iv:b 4z hkl collapses into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing rul/ziiwl x: g:t kvvypz68+h ;03byy 4adius. 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 rk9xcnw.:e l7 winds 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 ))bnbv p lhel36k8k6 uuz9e9h$ 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, that4dggcty h5z; r.np q; l/k: setral4//; elmt1 can rotate freely without friction. The moment of inertia /a 4t; q15;lerzcn.dhmk/gt: gts;p4yl l/reof 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 diameter merry-go3+uc d dzgb76kh8.eo 8+xsiea-round turntable that is mounted od+exh ze6 cbkg8d. 7ius3ao+8n 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 b(bjh(ssag5z v v84,sh +et w)the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of e v(h(g5sw 8s,+vas4b)jbh z tthe 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 of mass move?

  The Moon orbits the Earth such that the same side always faces thec r bt2cas,dum9jzh /yj 03;2xvr zz8: Earth. Determine the ratio of the Moon’s spin angular momentum (aboubh rjv; :ur zx,c 09zy8mjt/zc22da3st 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 a r t4tnaeiab;k58 fq32 w wewf,5ate 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 cylindec8nrb5gfk3z8mfn 38 5mur7df r of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration3f f8g km75nfu5 d8nr8mrz cb3. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical8 zsn79g.-nrsbst6c f 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 calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is releas6n nz9b c. t-srg8s7fsed from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear4ri g0u-t;m wr wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were ,fcj;0hfz l*5x0twyu:,gzxc 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 mass in the process, what would its rotation speed be? Assume tha*w c:u0ghz0jyfxz5 f, c;t ,xlt 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 storkxo5 b 9yey4y1ed in a heavy rotating flywheel. Suppose such a car has a total eo x1y yb9yk45mass 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 an g7aqa* jd7a.hr r) v*4pkdh)x$H_2O$ 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. h+smn2o ,lmm/gas2 ys5 ;*ral9athw surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e.,)rv*wliio d3 + 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 ofl3do *viwi+r) the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and we ue:g+vdk) 3uq want to exert a horizontal force F at its axle so that it will climb a step agains3u vqugked: )+t which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn jnlzz 5m y3v17with a radius Thvzn jm75 y31zle 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 length7dsdr kn8*yw; 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120nsw7 r; k*ydd8 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms a uv g-7e/br,eas thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tight be,g-a7vue /rly against her body.   

  You are designing a clutch assembly which consists of two cycd4hzhc+mk-yq-yv ; vs )(dnc:xg g ;7lindrical plates, of mhczch+- ;:4dg(y yqdv -xg; csvm)nk7ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loopedk+tp -(np e)rf+mhru 7c 8lu7v 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 r(l7m7hpf++ e-uukpt v)8rncr each 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 nov +f;vly(1pekr4)s(wf v fj(dt assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutionset4 6m:car+p z as the car reduces its speed uniformly from 90kmpcm: 6rz 4te+a/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