A bicycle odometer (which g)w. g2o :z/x4 qspfyk/o9v utmeasures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What s9vyxo :f//.w4ouk 2qgp)gzt happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim hav4nce2 i8 6ia5s)go fyye radial and/or tangential acceleration? If the disk’s angular velocity 8)a5g oy sc4ifyi26neincreases 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 value of the alzg:n a3jx h/4ngular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a jf rdd,ttkj (:u+v*xu4./y p ilarger 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 ul 1 b,u+;j,3*qvshiq+pllg7 ycu( zrsit-up with your hands behind your head than when your arms are stretched out in front of you? A d1,lcquls;b g+i7uhzyv*j ,qp+r(l3u iagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the8 dy.i0fjhh xqbb)1r( pedal cranks. In which gear is it harder to pedal, a small rear sprocke) ( ifq0hrbbxy1.hj8dt or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs wit*p 4ulps3( vjc(l v3xxh flesh and muscle 3xpu( vjc3(l4pvl*xs concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry aohu 4 +kxhz28.e)e apd long, narrow beam?

If the net force on a system lyi t*dl-8xqg,53a nwis zero, is the net torque also zero? If the net torque on a system is zero, is the net forc-yin xq 5l*wadt8l3, ge zero?

Two inclines have the same height but make different angles with thy pu/0geg79 9a6p btjze horizontal. The same steel ball is rolled d6 9z9ye0/abjpgp7 ugtown each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneousrj. 1-8focjl(ytzq8 lly start rolling (from rest) down an incline. One sphere has twice the radius -c(jrf8. jyqzolt8l1 and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and t( ka.i,k--:/93k axa upswb:xf s ush,vb9i nvhe same mass. They start from rest at the top of an incline. Which re3,ua v:iukakhnk.(:x9b,bass9f/x s - wv- ip aches 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 angul;+: p( ,qkcflefjqq j:ar momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Explain.lffqj; j+: :(c,qekqp

If there were a great migration;3dvby1e+ w jse010+eunmdik of people toward the Earth’s equator, how would th;w 0mkd+eu 0b +1e 3sejdynv1iis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotapmr x:r: 7byh+qd c7p0tion when7c rx:pqm 0dbp: yh+7r she leaves the board?

The moment of inertia of a row* 6oxe(o/ja qr chn(aqmph2w6w7 59l tating solid disk about an axis through its center qp5w qw(rn6(ocj2*w69m7 h/xhoaa e lof 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 sbl7 v+;o.zgn2p /0o jqf bi9artool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your qbl9;. frp+v ogoaz2i bn/0j7 angular velocity increase, decrease, or stay the same? Explain.

Two spheres look ide/er*4x vhax5 jg2 px,a0sn ik0ntical and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is whiik 4/v xx2hej0*xnrsp5a ag,0ch.

The angular velocity of a wheel rotating on 0 s1q56jk2fdukf f.hwa horizontal axle points west. In what direction is the linear velocity of a point on the top of the wskfukfj5h. q0fw162 d heel? 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 of qu8gual1u i;gs,h,(dq 95y:5 ex otno2y7t vb a large freely rotating turntable. What happenqe9s5dg gy(nyqu8 7tot:uu h,v b,o52laix1;s if you walk toward the center?

A shortstop may leap il4v4sd4z q(1y he- vyyvnx9b,nto the 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 hips and legs rotathqy4x1 (vy v4y sblvn94-,z ede in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of cons*o qci9-xktn )ervation of angular momentum, discuss why a helicopter mu *-tni )x9okcqst have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in rk:aww8p:,x wgxzmd0 :5 bi c3gadians: (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 amazi.2- gbwsrq jl1 xy u88 bonpfc7+7*bssng coincidence. Calculate, using the information inside the Front Cover, the angular dia2b1sj7-cs g p * fyw+sloxrbqn u.87b8meters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed axbu9g 8+mglvqi x j ;t*jol/-8t the Moon, 380,000 km from Earth. The beam diverges at an anglg lmoj;t u+bi8xv* j/qg-x9l8 e $\theta$ (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 ohxjk, ffoe t3x2 )(j.ko c/r0af 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration aefj.ht k/3 rj(f o,ox 2x0a)cks the blades slow down?    $rad/s^2$

  A child rolls a ball on a levez;3izt8:t:i .qc ze9ke5cs mal floor 3.5 m to another child. If the ball makes 15.0 revolutions, what ist;3:zazezticic: 9q.5mes8 k its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0kschn gp7ad)n9 i,/o ; km. How many revolutions do the wheels make 9nakp7h),noc isd/ g;?    $rev$

  (a) A grinding wheel 0.35 m in diameter r -3iyh3r;;vj+prsfd f otates at 2500 rpm. Calculate its angular velocitys;v- j3h +prrd;fi fy3 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 covrd;sb hm;69m (m b a3pxk*j4umplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a px9ka b6*u 3bv; hr;jmms (dm4child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in iesy(17o 08zibvn5 c .f- ztkco v9jp(its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear syxnp.w0n q2utl/kw ;e*n2z 6ipeed 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 frykjnuv6v34 j6 e ko**com the axis of rotation is to experience an acceleration of 1 c u4vo*k6ke jn3*6vyj00,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelera gk,)jh1lq2l vtes uniformly about its center from 130 rpm to 280 rljh qg) 2vk1l,pm 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 radius.0k n3p 7:(b.gunpasrmsj : rh $R_1$ 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 ab; awd)t,e. l,)crfj1nk :tboz oard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of thn;,btz ):o rwc)f1jkel.d ,ateir 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. Throug z7hkb)sfd9h9;e:a vxh how many revolutions did it turn in t h)fz79:aedx b v9k;hshis time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm ini;dka,9oaf ) 1strwd, 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 flyincvv)n, 2vco ;wg highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to vw 2v c,vnco;)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 diame6rk ro5vng-/w ter accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the v/-gk n56rorw edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when oz :thrnuh8s(;2a 7euit is running at 850rev/min It turns 1500 revolutions before it comes to azn7 u8uto :se2h;rah( 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 reduces is1 ;( t5(il)hjndo wt;f cpw)wts speed uniformly from 95km/h to 45km/h The tires have a diametw n1lw;j(td o(c f5w)i;sp)hter 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 revoljo.mfob dhy *q0xn9dx 7q4j++kj-zn5x jd-n,utions as the car reduces its speed uniformly from 95km/h to 45kmnj d7-xk5o d +fh0onb+.9-zq*4 yj ,qnjm xxjd/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 puts gh4o ni h*2qf7 umucj;upa, :0all her weight on each pedal when climbing a hill. The pedals rotate0:muoigfuqcjh 2 7,anp4u;* h in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N z ccvzs0btr 1henbuv3cc3(+7fo 08 v/on the end of a door 74 cm wide. What is the magnitude of the torque ifz 10cc+8cber 3nbfs tvh0(cov/7 z vu3 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 whee 9vd( vz,vhzsd,2ayot5 rr*r3*)*gdcp7dxp yl shown in Fig. 8–39. Assume that a friction grd*d5 zxt,p c 2yzsy dvv,9)(r3*rh o*av7pdtorque 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 af0swo(h)/of rod which pivots as shown in Fig. 8–40. Initially the rod is helha f0wos /)(ofd in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engin8 g:tkqcfzw yk 11*s4be require tightening to a torque of 38t*:1gb 1 zkkqcw84sfy $m \cdot N$ 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 inerti xhu:i+a 7 dl6adk 24r7 ,ajnad3a3rmla of a 10.8-kg sphere of radius 0.648 m when the axis of rotatiol7drkm,36r n 3i ad+24 7x:lhaauajdan is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel,zjc3qh3vu v 2 66.7 cm in diameter. The rim and tire2,3hv vucqz j3 have a combined 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 of a thin, lightg us euqqjd)805zo,rum +n2y / rod is rotated in a horizontal circle of radi yng) ,q do05 r8sujum+zuq2e/us 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 ang5g09a ei( y2iis j*.cprncl/ kular speed (j2 sl/gncyr0ic*59pki a e.i(Fig. 8–42). The friction force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of k nvt,tnz9 / gnam(q0xk33/ gxpoint objects shown in Fig. 8–43n a3n/tqgz0mktk/x39xgv (n , about
(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 whose total mas/mulka4 0 f l+abimisv+h96:pev5 lf.s 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+e( zqfd r5k7b spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm i fkr+d75ze(bq n 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder wfxfwracqr x4 ng)1xv,z c5;4.ith a radius of 8.50 cm and a mass of 0.580 kg. Calc4) zgax5fqfw;nv,rrxxc .41 c ulate
(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, acceleratingawfdg0 *hg 9mfwc9gkx 1t7,49nr.j r a 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 merrysx7p 76nbg/9 ado gksr p:51hj-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 unj ns7hk 5rbsxgpdo69a/g1 7 :piform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is evenctliu 7x- 63bptually brought uniformly to rest by a frictional torque o ict6p37bl -uxf 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 abr2,i2la em j8ccelerates 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 solely by the actioqe78hx 6s; vl azy)2xkn of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45; y8l6)kzhx2ve qax s7. 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 szv8dcn - oq:v0hown in Fig. 8–46d08 c:vv nqoz-.
(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 consists of 7pmxb 7 :.ryv:p5 euyytwo 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 fourj)42r biewd u;6k vf(o full turns (revolutiono2 4efi );b(6wdjkvu rs) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a j8r(+ 7:hvxx ecrzsn* moment 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 torque of 2806: k hlc5rla/x $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg a+-6dmpqgamje 6bl9d / nd radius 9.0 cm rolls without slipping down a lane ap jd/e6mqgld+-96bm at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to xho,l.f hdxt1+ir 5/ hthe Sun as the sum of two term,xt1f d/rh xl5io h+h.s,
(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 mam qs5*d 2soe0ipjse.d+w i02 css 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 revolution per 8.00 s? Assume it is a sol0psjs2e*qc i.wd+0s deim52oid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from r1*zh2k2hfrdx 4 n*ezgest and rolls without slipping downd eg r*n2x *k24fzzhh1 a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It /iafs 5+ kffg0starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole j i0+ffsak5/gf ust before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating* ccpojz4cn79 on the end of a thin string in a circl9pj4ncc7*zo ce of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grin /uji-w-j ,yv5dn gjs7ding wheel of radius 18 cm when rotating at 1500 rpmi w /jnu5v7,-d -jgjsy?    $kg \cdot m^2$
(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 rotating0tf e4go8x8 ds at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotat0etos xf4 88dgion decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inertia ;zp pbj5 kz:e)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 angu)jzp5b p:; zkelar speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an+-h0,d 9y 3f0twn7chbclj amw initial rate of 1.0 rev every 2.0 s to a final rat d0hb0 +w7hm3fct-w,j cln y9ae of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at ax +m m xr04gulh9mqy3. 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 cu4xm.gr my+q9 m 0x3hllay, 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 moment m*0ijp0ic (vqijw8bl1vq*v/ud 6(xwum 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 ofa7x* k37ucij p 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 momenvo-xuoai. 7*a 3 dd9hat of inertia I is dropped onto an identical disk rotating at aox .73a*-oda dhviua9 ngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns aa)hd(ux hl(zyt30/emd fdz j e,y,s84t 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 rotax( kt hmiq:*6)1auf6m ts rrz9hm+,xvting merry-go-round platform of radius16 (9ux+,immrxh k6trvsq:tm)*zf ah 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 fr rs(b,m:ho+ a0 5tdskreely with an angular velocity of 0.8 5(tk dhsrmb,:a r0 so+$rad/s$ 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 ik) fph*sy2(e+jl 5e7lvh/mc k nto a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carriesl mjehky+phesf*5vl/ 2k )c(7 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 exces3c mxug;fgs1pwl/ks 7 .7 hh5rs 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 vfijij 07,o* xbe3;ue$ 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, ic.ewc eg7f9-ksp p + q,nt8ok:nitially at rest, that can rotate freely without friction. The momentq w sknk87 pe+p,-cf9o:ge c.t of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m dijs5p9w h5,i+mc0xpiz;q8 ydf ameter merry-go-round turntable that is mounted on frictionlesw9fc5jmqpid, 8py5x0is z+ h ;s bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the groundshs2 rwfy2ww7q 3a4, y with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. ws73y2r wfs24ywqa, h 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 the Earw+ 0qjmky+l-1udx1 dd th. Determine the ratio of the Mooydxd10+1j -d+uml qkwn’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 accelerates ffa/sss-x.) lq jkl3gslv2p )(rom 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 c:h, di9*nzb4yoo1 ila uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torqo9,z*:y4l o1hi ibnc due delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two soliu*4aq il 3fg/ad cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass l*g 4i ufa/qa30.0050 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 spee .wt*,9ub9p8pljf eh xd of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but 3o7 9 ewadp,cvwith 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 the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that t,wc av 97pod3ehe lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy /mxlv i rok0azb9,mt1yp6w34zeb. ,jstored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km witr6 l bt a1mpbize4j,3v9yk,m/0w.zo x hout 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 illustratekm( *w f896/b.sjfr w:sdr e*zxpeuj*s 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)z5m4 bpwh.p:kz 9u2h b is rolling on a horizontal 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.elxu0c;rx/*pc 8 rbl0 o., 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 re/rc l p;obrl0*x 8cu0xlease, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It isg1j/1yh7p 9uty i-x tw standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step againstygu hyt7j1itw9 1/x-p which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.*dstq p p8ypdk*ga1rmec-*+7(78ixe -ud es v2m/s on a flat road is making a turn with a radius The fork8( r8ee d uimapdx +y7ts*vp-e*-pscq* 17gd ces 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 whirubpb)z1e s5c (ling the rock in a nearly horizontal circle above his head, acceler(sp u)ebz15 cbating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid c*up diy)yb2asg20+ *aaawpa1ylinder and her arms as thin rods, making reasonable estimates f21g sp ibdy*2aaawya*u0)+ paor the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, of8p-i7osab 8jwyincybxxo :mn 6-spj, 3m 7 64w ns sw b7m7x4i -op8mbjx i -a jp3ow866c:y,nymass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped rough track of Fig. lr;z. yzo n+b;qg67iw8–58. 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? Aolqig .yb6+ n z;zr7;wssume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bz opr5n5x6wv,lce 6-v v1v2vjut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniformly cc utgvw1zarq1;t j/6 w9 42/rzao7mwfrom 90km/h to 60km/h The tires have a diameter of 0.90 cuz1o2v1cgr tw4 7 ;6 a /mwwrajt9zq/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