A bicycle odometer (which measures distanc4yf me55oj,gp2j gp2u ykre 6:e traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with p5kf yp 2yr5je 4e2m6,gj g:ou24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim havb 61oex6yq(r q3z 5dnce radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear accelera6oczdrq3xb e(1yq56ntion change?

Could a nonrigid body be described by a sing- yn:kjpivr: +le value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a largwb9-j2x 67 dcvbru( zger 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 behinsvvo 6..u:2 t m*:rzurk r:etod your head than when your arms are stretched out in frort2v.ut6u v:k .oo* zre: mrs:nt of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the reataou*3cql-591lp snc;*q r ewr wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprockeou le9*s ncc-5a ;rq*wplt q13t? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend onghj,a7qn r ):qn lcz4- being able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dy n ,jn74 -g):zclhqaqrnamics, explain why this distribution of mass is advantageous.

Why do tightrope walkersbea *am5 wf8r.qru7:f o )h-wg (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zer qx7n3.fr g9dmo, is the net torque also zero? If the net torque on a system is zero, id 97q.mr3n fxgs the net force zero?

Two inclines have the sam9yb4s8bit8/se dk4p q e height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the spee b pky/s9 i8tsebqd844d of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an i5qe 6v y9 -thmxkqeh08ncline. One sphere has twice the radius and twice the mass of theq568 h-0t eqh x9ykvme other. Which reaches 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 theavuk .6c frutumuaj ;n /+((m. same radius and 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 theaumvn;tuck(.u f(m 6ur aj +/. greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular mo dvelk:lck :.4 fj)i.mmentum are conserved. Yet most moving or rotating objects eventually slow down and jv: m :)lcdkfkel4i..stop. Explain.

If there were a great migration o)gh8vx yy7dg5f people toward the Earth’s equator, how would this affeg yyhx5)gv87d ct the length of the day?

Can the diver of Fig. 8–29 do a somersault withia7a d)ylutr-0m0j3 sout having any initial rotation when she le03y7aau0jrd)ilsm t -aves the board?

The moment of inertia of a rotating solid disk about an axis throuym(4d chz,rbop 4m5) rgh its center of mass is ch4 ( zo),5bypdmrr4 m$\frac{1}{2}WR^2$ (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 maw g(13rr z7wys9rj)4h txl,jhss in each outstretched hand. If you suddenly drop the masses, ww9j1h(tyrgzxrh rw 74s3 ,)j lill your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollownyl0sm;x4i,6 1scem8 )lu t cg and the other is solid. Describe an expe8 l s)0,g1m4itnyusemc 6;x lcriment to determine which is which.

The angular velocity of a wheel rotating on a horizo-x-lbzq hsqo k/ 6l:n7ntal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is -n-7zxkso lqq6:/hl b the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large -(;utnyw lxl0; 43c hzimvi/ e) /qkghfreely rotating turntable. What happens if you walk l t)3lm(ix-v g; 0echz/ iw;u4qkhyn/toward the center?

A shortstop may leap into thmq5awtb 6 8es1e air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his sa 8q 6ebm1wt5hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discussy4m e*do0cnvf*w9 8pg why a helicopter must have more than one rotor (or prope c0g *venf8p9 m*w4yodller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angleaonx j a;54 +xv r rijdril5nd/hx/*51s 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 Eartu+mvbj:/qpg ,xyurl 4i(1id 2h because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (ixp/u:bqr i ligy +41vj(md,u 2n 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 Earth89z2. .7xj,po+t prg5w:uwc x z ekvjxygqe-4. The beam diverges at wpg8g rx -5w.42e.j7o z9j+pc,vt yuexq:kxzan angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a re0 z3kp-.)wqgqd-tigate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accele z -g3t0qkg-qewid.)pration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m tpylvb,xte+t3o etccmm 6h. 24i7i):fo another child. If the ball makes 15.0 revolum:eiie, 43l 7vtc2 .t mp6ytc)ofbhx+tions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter l v1kexw.9 5zhtravels 8.0 km. How many revolutions do thxv19wh.e z5 kle wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Caw5;g5;c nd 3h9plogp zlculate its angular vel5 phgwl3zo9p; c;dn g5ocity 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 make 18pqsp2g /u wenez)v(9wab1 es one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the centegs1pp/e2w ue9( bzqa8 env) w1r?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular k t:: cq ozsox 320d3-ltnz4pdvelocity 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 speeli(e2j0:h7v xsq2 zjgd of 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 cm from . 1f./ltxoktm fj 69ck)(eod dthe axis of rotation isl9. t ff6ko.(de tjxm/ odc)k1 to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelnj xp srkxl0.l1;p++ierates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determn0 ix sk+.+lx1r;l pjpine
(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 qy0xd*/mav:9ag + rbq $R_1$ 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, astaf advg4b1*a ,ronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribut1a*4gba,dvf ae 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 rest to 15,000 rpm in 220 s. Through home0 7287suz(nifx qd bw many revolutions did it turn inqis 72m7xd(f uzb n08e this time?    $rev$

  An automobile engine slows down from 4500 rpm to 12009rau8*l cr- on 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 jet,(im69q 9 zw4felk xops in a whirling “human centrifuge,” which takes 1.0 min to t(qox, 9ewm64p f 9ziklurn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly q*n a197sajigfrom 240 rpm to 360 rpm in 6.5 s. How far will a point on theng*j9sa1 7 iqa 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 ,n5q95lm x dyv1500 revolutions befd,x5v 9lq5 nymore 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 cwjzr(9*cqtn-u ip8vdnk 1 9l*aqd,)as the car reduces its speed uniformly from 95k p cc-vn1i,kadd*tz8n (9u 9*jwqq)rlm/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 65 revolutions as the car reduces its speed uniformly t b9 3xmu di9z:09:qp6qhackcq3b :nffrom 95km/cn mhu3:qtcaq9f03ik69bz x: dpbq9: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

  A 55-kg person riding a bike pu3 lfxt j ,j0p)ka fsb 2)(o)g+yqbqxs.ts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of rt)slf ys( x0)gkxf .qj, qa jbo2+)3bpadius 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. Whatvo(0uk1r3x7 ;4uf (fr yqr bsn is the magnitude 310sb frq;ux vfknou 4yr7((rof the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the ,8sx1 c4cv2 et kpqiu7wheel shown in Fig. 8–39. Assume that a friction torque of 0.4vt1c728 pukcex, i 4sq $m \cdot N$ 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 which jjsy)qe. u;-. m4ffmm kvdk85e dl/av8z xe (: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 torj(feq/zu 5ms am8dv)kmf 4k: .;e-8. xdevjylque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque 4j vzkad658map(y9bk pia9w7g21vduof 38 1d7v bd2 4mjv(ya9p u8pagwza69k 5k i$m \cdot N$ 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.d3lb f2j)zxk/ 8-kg sphere of radius 0.648 m when the axis of rotation d/fb3xk) j2zl is through its center.    $kg \cdot m^2$

  Calculate the moment 2,c-;w/ mknxvqg 7pwtg 7 qfven .:am-of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the h /f-wt.xe,qm;mqkn-vgac77v wp 2n: g ub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light r0* 6/ha;oq snadgbcic5ol9-0b6kh meod is rotated in a horizontal circle of radius 1.2 m. Calh o;i6c60qkhg9c sbde0m5 l*/oab n-aculate
(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 wheelxpnu sm;x lhx(lv(/b b4 8zq,1 rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N tot8 mx(pv;z,s(bxnqu4b /1 hllxal.
(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 i.rc4 6ulsay w(/m1j hzn Fig. 8–43 abo1.lycra4js 6/m( h uzwut
(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 oxygen atoms whosen y 3irf//ci)*:xvat h 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 satellitrto,ry.w1 -t pe spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steadyy1 rr wo,tp.t- 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 8.8oty 86: 9mdiny, xi .pypyd3p50 cm and a mass of 0.580 kg. Calculatoip, y9xpmi6pdy: y 38dt.y8ne
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from6khekxor79l(jj( 8xr 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-drive z5jd gari:-4*3kloknn merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglei kz k*5-3lngjoda4r: cting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotatini,) wpd4g;qp g-igy+eg at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.2p-d 4ie+ y,p gw)gg;qi $m \cdot N$ 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 iy+i(omuf)yd05 sva(a os,6lljkx1/ 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 igijsoz 4/8i r+s thrown solely by the action of the forearm, which rotates about th ri+js zg4/8ioe 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 considered a long thin rod, as shown in Fo(* lu yp94vtgig. 8–46.t*upgl9 vo (y4
(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 cong9na jz5bew6;sists 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 thwzd-ma d-..la)wr+6rvd f h ue.gm4. ae hammer from rest within four full turns (revolutions) and releases id)g 6m w-d u.a.zdw. +eamhr4r-. fvalt 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 mommir(r),mh3 qcvs) x-n ent of inertia 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 torq:kyj e9+5rpn h 93p)rhq n28li ltv,cfue of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of majsk1v5 55rllglpph4 - ss 7.3 kg and radius 9.0 cm rolls without slipping down a lanelg-5v jp5hskllr154 p at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun dx06so7lw 2;cd78q prq )bcgyas the sum of two terms;ol6 ) dr 8qcx0q7ypswgb7c 2d,
(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 knvb;2ei05.th mq/ufmass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolutionin mfbuq/te0;52k.hv per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts frsi08ebzjgst *j20t8 q om rest and rolls without slipping down a02ejitq8 zg* sts j0b8 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. It starts to fall akfio 7++a hu8mnd its lower end does nu7+ aif+mok8hot slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210spv kiv t)(p/x1jv/o aoqc );.-kg ball rotating on the end of a thin st1ivoq ajp(o/ ps ckt.v)v;)/x ring in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular mom*yo4j .mpxn l)entum of a 2.8-kg uniform cylindrical grinding wheel of radp )jy*ol.xmn4 ius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotatn)at:asxwgc3wu )10 ying at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, they) sua :gnc)1aww03 tx 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 zt qsg0( cbmmbd);9l/ g6vae9a7exg .in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angulal ;abx 97(m9v 6eme)cq g/0 bz.gadsgtr speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initialf 2l--iv3g se2 phla6i rate of 1.0 rev every 2.0 s to a final rate of 3 623iis2fp-hgllve- a $rev/s$ 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 roj dx hi626uh-k,bq:e6, hzwzuk,ntp (tating around a vertical axis through 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, approximately shaped as a flat disk of radius 8.0 k njp :(zkt h2hzuu6i-6xhb,wq6, ,de 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 mg2stffco6892 4 tq-u cxtq zk luph22*omentum 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 33/ks8 sger4 x1nptx.pyj d0hof 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 .; 2pup3)dukrsa n7mmdropped onto an identical disk ro ;ps) dpa3mu.n 2mkur7tating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsd;z(hate-- b;cm3i8*msxd nv3u eue 7 at 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round pz, zcp2 ve-j:wlatform of,:ezpvcz- 2wj radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity o r0y.uqxu gb(x z3f9l0f 0.8 (.xg0rf3u 9 bzqxlyu0 $rad/s$ 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 eventuallygxn h8nma/q.cao3m /e6w 93v qz5)sfx collapses into a white dwarf, losing about half its mass in the process, and winding up9 /a)83xc3h fsn.zmmq5no 6wxqg/a ev 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 winds in exces ghti 8wq.b m +scp6zv32jpsw0 2-*c0t-marrps 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 w4xd,mc,mi e0i 3v km2$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that cagjm /v )s.up6lf 5zsm1n rotate freely without friction. The moment of inertia of the person 1lvf/m) 6pj. s gmz5usplus 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 d qa(28ijji u/xi2lwf )iameter merry-go-round turntable that is mounted on frictionless bearings and has a mx8j2u/ iwfiq(lij 2)aoment 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 ther2,pp+9pg1+ zjye p lg 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 tly z p+pj9ppg1g+2er,he spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the ab fl(kp24r4, waq 2bw:sreg (Earth. Determine the rb(f2awkg4:2, brwsqr lpea4 (atio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratesq,r5v au6mthp74 u2biqt*jk- +f:rg q from 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 in the shape of a uniform cylinder of radius 0.20 m acquireso7sadk0s r 1a6 a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque del0oaks a1sd 7r6ivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two )*u aqdil7 /amsolid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hul maidq*a)7/ub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the reasw;jv(ptct h 6j.n/ c-r 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.m7 gycmb4 lsj jl7 k+kn91vi0y:i+nize 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 mass in themnig7mvkicy+kj0 i4lb7. sj:ny9 +1l 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 automobil6 ofs+8oi*+vcntwz4 de is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywhzf+ 4sv dnto* +i86owceel 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 s :* ydrfc*pc/$H_2O$ 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 surfacoc: :z-3 bx2 izewvd:9jn b0eqe 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 freelyy-nrguo/anf swze) xi-2pv 9j54. ;ql (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 the rod. Assuruex2-l9fp /sn5jy) 4o v -a;iqnw.zgme 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 t9at/pov opc+x/8lcz.5 eykq -pq+ ujk+j x:/the floor, and we want to exeruxk9oz :p qa+//+kl8 etpqcjy-/ x+cjov p5.tt a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn with al.1rs8ksg j en8 n:si1 radius The forces act s:ie1s1gnkj8lr n8.s ing 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,t7+ /rzvmy :pz lv)rr a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rpr7t:zlvr,/m zy)+ rvest 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 v l / rhcysmx5atc,.pgv4+kexkw 3 )9;8f(tapbody as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then ckk evcrlwp+f)htyga 5 a9.4x (s ;v/,8mt p3xcalculate 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 whi2bfaut:5d*r. tja b9gch consists of two cylindrical plates, of mas f .jr*abg5at d:tu2b9s $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ra71ke xr4* g eyo5qoc)odius r rolls along 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 track? Assume ee7*g 5)oycxork 4oq 1$r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume om g2b/;v0turph dxvvx-j/ -6$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducesryv(.a*o: okq its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m.r (o:kyav. *qo (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