A bicycle odometer (which measusl (+ jy w)w u6gzpgbt.j +,2 378d/xlunemhtxres distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you u,yup z+nt8wsxl.muw gj g2 (+e/dt6jxl7b 3h)se it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim hav8jujzc i-b27 me 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 acceleraji-mjb7 czu82 tion change?

Could a nonrigid body be described by a single value of the angular velocit uzwgu-p u( q.,pntyw6-hgn2y19( kjfy $\omega$ Explain.

Can a small force ever exert a greater3((riguwa .auj 5kwv* torque 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 y )z3knri8tvh lqh8 +5uz hr6b;7qh2phour head than when your arms are stretched out in front of you? A dkbzh6hz3h i8 )ut872h rp ;5vnh+rqq liagram may help you to answer this.

A 21-speed bicycle has seven sb d,:a c:xe0vsprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large fron:,a e:db0c vsxt sprocket? Why?

Mammals that depend onp w,,9 ny,a05yqudwrk being able to run fast have slender lower legs with flesh and 05uydknpw,wq ya r,,9 muscle 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.dh5 :7njgnbc z6v,ox–35) carry a long, narrow beam?

If the net force on a system is ze/8dvsg2o.+uz+ aw jb 4 qpck7hw8:vt ,rt ybb2ro, is the net torque also zero? If the net torque on a system is zero, is b v psz+acdwb2tkh tub:,wyo8 .q4 g2j+/ 8rv7the net force zero?

Two inclines have the same height but make difb1( juu)ld:dh ) gbu*rferent angles with the horizontal. The same steel ball is rolled down each incline. On whichuj ldb1*u(:r) gbd u)h incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simu4dfasnyv,jd7k6j4 1 vltaneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom fdavk6n4jj1dy s4, 7v?

A sphere and a cylinder have the same radius and the same mass. They startw7i6(afdo k.an0 zh/(w2 rrak from rest at the top of an incline. Which reaches the bottom first? Which ha.0w in rdkaazaor(f76 hk /2w(s 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 angular momentum l*z w, *xb bgp:ee5gr9are conserved. Yet most moving or rotating objects eventually *z5 g9,grbexewbl*p : slow down and stop. Explain.

If there were a great migiyf fe- hh(g5s3l 9b/vration of people toward the Earth’s equator, how would this ab9lh5- /3yh( f gvefsiffect the length of the day?

Can the diver of Fig. 8–. nobnpgq.d8rtd5 , 0w29 do a somersault without having any initial rotation when she lea58dprtwb n, o. .gqnd0ves the board?

The moment of inertia of a rotating solid disk about an axis through ivfi1dl1k2g n6qqut1 *ts center 11v 1qg kd6*intlf uq2of 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 rots h9 etrpbz-;,ating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity incrz;- brhs9,et pease, decrease, or stay the same? Explain.

Two spheres look identical and . 3bw1fp ;xpauhave the same mass. However, one is hollow and the other is solid. Describe an experiment to .p3f1 a;ub xwpdetermine which is which.

The angular velocity of a wheel rotating on a horizontal ax:cd-; p 4 gwfnw4pzv9dle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angulaw-ndfzp pw 4;v4 :cd9gr 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 standingdkeff6 1pka ow,y6 0t2) yb8am on the edge of a large freely rotating turntable. What happens if y),ya y810pofe66kdf2tamb k wou walk toward the center?

A shortstop may leap into the air to catch a ball -3r-7/nf iqpcf rz.dfoui e3+ 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 rotate in the opposite direction (Fig. urnoei.ic-3 /rzqp +-f7f3fd8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a heli (*4/ zmcuwvldcopter must have more than one rotor (or p w/4*mczv(lu dropeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in yt4bnrvp )9 1qnih;(tb(9iby 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 amazin.qho pzpm2* h j,o5ge8g coincidence. Calculate, using the information inhq.o2eh *ojm pz8p5,gside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges rdau2jeq63dqj 7g7 e:at ae6u27j7edag 3 qj:qdr n 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 rate of 6500 rpm. When the motor is tuns3mtdu )*i :8swm9;k okdf:jrned off during operation, the blades slow to rest in 3.0 s. What is the angular accele8m *;fdmidkk: 93wssjto: ) nuration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If th d3vvi2w2g,us e ball makes 15.0 revolutions, what is its diameter? 3wgvs,v22d iu    m

  A bicycle with tires 68 cm in diameter travey 6sfjn coa 2 j,o1.20jsmpt)vls 8.0 km. How many revolutions do the wheels22j .m0)jy,sfno 6joa 1pcvts make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm*cu6y b( *wd.u.jgn+rhlfo 0s. Calculate its angular velf(luygd0.w.s* u6ron b*h cj+ocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolb, v(y8no,u)a+u c4: vz2vqa rbxk cy7ution in 4.0 s (Fig. 8–38). (a) What is the libu za4bro,vca8ky )c:v q(vx y72 ,+nunear speed of a child 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 its orbit wbxkk(rt, +4 haround the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear s2c 3jk+(qc tdspeed 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 par lwc,:4sbaz 82x2qdpo ticle 7.0 cm from the axis of rotation is to 28w2szbc,aqp:o d l4x experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniform u ;c-rc1r3kw 3ixruf3ly about its center from 130 rpm to 280 r- f1w3 r3u ;xiu3rccrkpm 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 radiu9,-lke(u qkp cs $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put tm6l9143ytimx uz:f sg hemselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no:s64mt9i1xgful3z ym 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(qef,xnk 06d6 h) 7suu: kjukn7a(lmv how many revolud0k7k h7(f6v,nem:(uul k6ujn q) xastions did it turn in this time?    $rev$

  An automobile engined2m j 9*0lp zuzexby5* slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “hudv h ;h lfp;-sv:l4pa0man centrifuge,” which takes 1.0 min to turn through 20 complete revolutions befores-:;vhdv ap f;0hll4p 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 from 240 rpm to 360 rpm in 6.cdojj5j in;i(jin+)u79nir ef2o0 : n 5 s. How far will a point on the edge of the wheel oj;7 cod n5f :nj)un9i2rj n+ii(jei0have traveled in this time?    m

  A cooling fan is turned off when it i afh gt:f8-gd x4ph06ms running at 850rev/min It turns 1500 revolution4xm:a-h tg8hfpdf6g0 s before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly fkeg-evg 1;gn56 a*zuc rom 95km/h to6*1 5ggagee-uvcz k;n 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 spee5nlyvlt5., y vy l:8qbd uniformly from 95km/h to 45km/hl8l:vyv5y b,. lnt yq5 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 all her weight on eawikcsc5y 4av z6; s;7 idt7vs5ch pedal when climbing a hill;i; yscvt54wviz 7 6as75dsck . The pedals rotate 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 on the end of a door 74 cm s (:acmn0) cdrk5w -(gyjltg ct4r0k4wide. What is the magnitude of the torque if the force is exerted 5sa:jkkc0-4m g c wn(yc4 (0ldrrt)gt
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig.b i/gyn6)a+t2dn xw:x 8–39. Assume that a2 x+ nia/ y:dgw)btn6x 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 n47ggw+oy peadubv s1m3(/ ;pattached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnituw yo1b gpm4up/ag+es(d73v n;de and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to-h,hwmi r,llk1;nw 8 *kcdil6q4d5j o a torque of 38 liml jw,h 5o* 1d6 nrw8,hkk4 dc;ql-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 10.8-kg sphere of radius 0.648 m when the uqcavd5i 0mb,ci,/ y+ axis of rotation is thr 5bdv/u,,q0mcci y ia+ough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wh +)r05 ofap3lvfg0n ipeel 66.7 cm in diameter. The rim and tire hav pofrvp igl30+f5n)a0e 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 thiyqodf6zaw6pa); w) x3 tx+:47y brlacn, light rod is rotated in a horizontal circle of radiusw wdo)rbp:+fy ;q 6)a 4zxa3 cyl6xat7 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 rotbmvx j- 1l5* r g8ocp/be.*ibaating at constant angular speed (p jb-b** lem5./x8 a roi1cbvgFig. 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 )hp2:c br7)xn )zgcyharray of point objects shown in Fig. 8–43cg)2)c zn : xpby7h)hr 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 wulw o/f yov y2 2p717x0wt:y zgrz0,)ghuu s1mhose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at thec/l.-oc: i1yjuv 3hcr/9 t yjx correct rate, engineers fire fouhyloj/:9c y3v cji. c- utr/x1r 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 in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of yfg9u8 uvv*;ddtd:8p4x8uk f 8.50 cm and a mass of 0.580 kg. Calculate dd8u:;v84gu*dx fufvp t8y9k
(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 from rest to 3 cz1f(vh9*ijb $rev/s$ 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 tangew2opu16js . 2vl e l6sn:+ivi4j1nvzintially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite ea. 2l:penn2lsjiszv1 46io v+i j1 6vuwch 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 isc h+zm4f-ob-q-d 2 grz shut off and is eventually brought un-2rhz b+zo m4qcgd -f-iformly to rest 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 accelerate ni8b (fycohd;t041aws 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 acti)f .j 8g+ id0olx4yvmbon of the forearm, which rotates about the elbow joint under io8 4)gdx mf0yvl.b +jthe 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 th x92ss.:faeex 6htfn9j4jr8rf yk . k,in rod, as shown in Fig. 8–4kj.e:js4h2 9retk,a 8xf s6ry9x f.fn6.
(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 tnjf 0h y/-5dt7gj wfmhzo.(u 1wo 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 frozj-unr j *,lc:m rest within four full turns (revolutions) and releases it at a speed of 2:c-lur*znjj ,8 $m/s$ 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 ofs4*qg/x)h f k: u tn(xh9cx2v(ybjd6r 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 c dq o: 8w4fiidn2 86q:kv-xdb280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm.8qjffkj 88cb sw-a2y rolls without slipping down a lane at 3.3as2. f8k 8qj8 byf-jcw $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy orczbike3s2h j5vs22df l5 -i .f the Earth with respect to the Sun as the sum of two tedh5-2b jecfv i l5s rs32.2kizrms,
(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 anhj2l9( ltfl;b.o m7a wd 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 solid cylinde;9ml 2 .ll7oj(hwaftbr.    J

  A sphere of radius 20.0 cm and mass 1.816k*n gcg.2mplw i- j1c fxn1k0 kg starts from rest and rolls without slipping down21p ncncm*g1kk ilg 1j-f .wx6 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 star( wh9nfp.t5d0+kjb0d jg o2s uts to fall and its lower end doesjf0+ubkg d (t2jd9sn0p5 .who not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on theh)n7k by 5j:qg end of a thin string in a circle ygq: )nb 7khj5of 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 un6/ t bh+lcbxf*iform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm?b+h ctxf/6 bl*    $kg \cdot m^2$
(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 rota5dhpy a2ri5pwj jx2qv0c ./:nting at a rate of 1.3rev/s Inw v/ d2 2j5i5rc0hyaqxp.:j pf he raises his arms to a horizontal 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 Fig. 8–29) can reduce her moment os(/5 cx*w8,+ rpfqq que8gq:zk/ t6 dabrg;mff 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 8gqsk /c6w,trg /*d bpx equf(q maf+8r;q5: zs when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initizpnct.qw; *. wal rate of 1.0 rev every 2.0 s .wn* t;p zcq.wto a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a freu30.xvwuzm-wm/ss a)t q+j.u quency 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 cm, onto the center of the rotating wheel. What is the frequency o sqtjauw3+m-0z vu/).u mxsw .f the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.5 /lqvq 9ksmd49 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of th52lknckhs /+,usmqii-6m0o xibog z n.3ca0 9e 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 cylindrica7a:ss oa./ 07e1oq;u8ujfhbys 9bw uxww 7vy/l disk of moment of inertia I is dropped onto an identical disk r q ;wvs0ebjuu .uas 9/7y1ofyb778:xwosa/hw otating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 mc4s9jhm 7ok ($rev/s$ 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 tw* z5u 7- rlbi rb32h,sxqi1rbhe center of a rotating merry-go-round platform of bxqr*riuw ,zhsi-r2 175bb l3radius 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 witq:bxc860 xtk(va0 svlzcg *o4h an angular velocity of 0t4cx v gl6q0 va:k8oxzsbc*(0 .8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a wki/) rgdj x/n.hite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. n/)jd ik xgr/.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 excess of 12b4r/x0( k drhy0 $km/h$ 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 un :+xg*zd94ubu)iertve ;-h $ 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 ca5)svya,*lxvj ylun,o mj88s 0k*a2 gnfi;s)on rotate freely without friction. The momivo,8as*f m)o a8)*,52jsgv0 yx;jnu yksnllent 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 diameter merry-go-round t hst0sew.zqxd15(zq :urntable that is mounted on frictiontqz qx1 s :0w.edshz5(less bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground wi0 bj*szi8rum6s w0 , .goc4vs wjs9xr*th 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. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? Ho0rs.br*jc4 j6 zuwosv,mw x9 i0sg8*sw far does the spool’s center of mass move?

  The Moon orbits the Earcogmcf7;t (oi+a(xqo (lg9qj/0 e mo,th such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its 9(l jmogoe(x,;ftioc a+c (omq gq70/orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from s6vv40e cga1arest 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 0.0xdp5xfei q :.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torxd0fq .pex5 :ique delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of ta dphflbg/ l0+qves vo-u 58 -pdzh5:1wo solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches5vlb-ugp d+plv hq:d8az05 e/hf s-o1 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 reh8iu.(h*b+tl ecf.rj upmu -1ar 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 a659sp+mow8 fdcyo iq*s great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neut+* y5f96qdmpiwo co8 sron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollu- dzh zc- uxw1r:)i7+vaanc1vtion automobile 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 flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needingdcai-nrhv7az zx)1v1 :-+u wc 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 illustratez*hj )oa;mox8xk vts.d z )2g9s an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rollisl4mb9276 nrp+smqw i)i3s njng 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.e., wj2t(*ub ml.r2x58 6jtx vhmw ue ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the h 6 lj22(ub umvt8wtxm5r* .xjmoment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standin /v:2hkal +r3z. rilwrt n):k0xzn+ udg vertically on the floor, and we want wa3vt :k/n2dxh n:r)irlkulz+r+0 .zto exert 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 wo- frypo( ;i-nith speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the p;iyo(n- - ofrnormal 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 slingavp839s;qk1 *x hl) ehzaw 40rrlo;vs ta97hd of length 1.5 m and begins whirling the rock in a nearly horiz1 vq l7 w;h90al43axe * )zovssaht p9;dh8rrkontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rodsq+ d6/q agsw ) uj;bgi95mxt:f, making reasonabl/f +t:aw )xuigd; jb9qq5 6sgme estimates for 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 cylindric(,e3s h6hkgzs 09l w-x3u o )1-kqm7djepzbyhal plates, of ma ez) (gxq3 u3wbmhel60--, hdsz 9hykp1jso7k ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8–58.b+.1 r1q65p wx6rf8v;ymo, qm mjcd wt What is the minimum value of the vertical height h that the marble must drop if it is to reach the highwcmvqot6dp5fbm8,11x+ m q .jr; 6rwyest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumk (q.tv, ji8 gz8t1fsqq*nn g4e $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unikge amms. :;(iformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What wassk a m;.:iemg( 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