A bicycle odometer (which measures distance traveled) is attached near the whhe,fz qs0qw 3ba0 rvum(. .;upeel hub and is desigs0w uq a;vrq h u0z.(fpm,b3.ened for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at consta-/cgu wk.bo; fnt angular velocity. Does a point on the rim have 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 componen.b;cuo k/-g wft of linear acceleration change?

Could a nonrigid body be descr9/ioj*409 ph:hnbncj (yyt wribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater t7i4hne e :4prpxckr o119cb+zorque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head than wo;i1 .foscm d2hen your arms are stretched out in front of you? A diagram may hcd;s mof.o1i 2elp you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at nde.k3;pr * w1lycj;k1-creothe 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 front sprocket?;y nc*k -lrp.3;ewr1 k oej1dc Why?

Mammals that depend on being able to run fast have slenderaim23; nt gettl.;n4u lower legs with flesh and muscle concngmiant ;3e;l2u4. ttentrated 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 a long, narro+eco5dr d z.6vw beam?

If the net force on a system is zero, is the net torqumwgd1fzhdf)e2 -3cqe95mz/t e also zero? If the net torque on a system if-mwz1hm9zqdt2 e3/ f 5)gecds zero, is the net force zero?

Two inclines have the same height but make different angles with jl4flxp9sj y:nu,+/sthe horizontal.,ysjnulxpfs :+ l/j 49 The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down anwkp )*,1 wxhi+*pjjts incline. One sphere has twice the radius and twice the mass of the other. Which reachex)j p+t,jw*wks *1h ips 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 the same mass. They sta( h*p q ze6f5m:nn0+ankebw *qrt from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which * fp(ezbak nn5q+6 :*hq0ewnmhas the greater rotational KE?

We claim that momentum and angular momentumvg(cuozio,4+9vmilk 8; ynu3n m60p p w:mfy2 are conserved. Yet most moving or rotatingm8o fu;3( yin+ yu pgo0vnm4k 2 czvpw:96lmi, objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s eq yo2wro1e57m kv:q, rcuator, how would this affect the length owmr2k ro,eo: yq5v 17cf the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotation wn2layr sfu7 bf(ydw9/9a; jb.es s0bel 3a22xhen she leaves the (sds2bn2wbf/r02f la;bxlj3a7 e 9u .9ys y eaboard?

The moment of inertia of a ro(b8hquc-l/,w bzu zugw 1je24tating solid disk about an axis through its center of2ww eu4z/j bcgquz1u,h-8 (bl mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outshhm).+. uc abotretched hand. If you suddenly drop the masses, w. ahh u)b+.mcoill your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the samerbajm u0 2c.x)h (y1ce mass. However, one is hollow and the otca0 mx. r jc)e2u(1hbyher is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating ftt v 7i(dr4gyhhlf :rf-m 5/9on a horizontal 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 tangentialht gtm(5f9:r 4 fyri7lh d/-fv 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 a large freely rotating turntay 9z0es-lq*.r ebbs7 jble. What h-e eybsjb*s z.9 rl70qappens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quiy2jqetd6pl3w.(.ek+y 0 lqmuhm , an0ckly. As he throws the ball, the upper part of his body rotatenykha.etm d 0(lljqq+p0.,ye 62w u 3ms. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conpoe m5u1au. (zr*i.nqnur7 z1 servation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss opo(1nzr u m71.uz aqi*r5neu.ne or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles i4jw (k;8rf2l9vy p orf;j,pntn 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 cw6eegzg1 0yr zouu60 (1g)b sof an amazing coincidence. Calculate, using the information igcys01z(euz)ob601g 6r uewg nside 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 dire;zm 9sq*liqn40 y (nnbcted at the Moon, 380,000 km from Earth. The beam diverges at an angle*yns4qz(m9 q0b nnli; $\theta$ (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 650dj4w xpkavp8j:: hz 7ui tbku;m.,q460 rpm. When the motor is turned off during operation, the blades x:mua,qt44jb j 6d:8.iwpvp7u;hzk kslow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball ogwn hlbex1r 5e-o l*j8-+ajku5h.z 9 pn a level floor 3.5 m to another child. If the ball makes 15.0 revolutio -hg598eklj5p x l*rbu.h ozne1aw-+jns, what is its diameter?    m

  A bicycle with tires 68 cm n/ w-geq) (uxrin diameter travels 8.0 km. How many revolutions do the wheels ma )e/x- rwu(nqgke?    $rev$

  (a) A grinding wheel 0.35 m in diameter g(zox)8oyaqo) or vw2 7st2h6 rotates at 2500 rpm. Calculate its angular velocitx ty6 ()2voawg)osr7zo2hq8o y 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 revolution in 4.0 s (Fig. 8–38). (acc;uoj: qqb(bzzj2 )6 ) 2b cj z)oqqb:6;zu(jcWhat is the linear 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 v1wigc:p5 v6 eqelocity 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 so6g 9i0ffuw3. pow8kmpeed 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 from0( w9l37atg xyo0zuby the axis of rotation is to experience an acceleration 3yl(9 wtaxg0b7ouyz0of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates un k( ;ritck1o h9:q3g9iimgryh3z:.fuiformly about its center from 130 rpm to 280 rpm in 4.0 s. Determiniq9hg(3ymz;ro :fuit:r19 .kcikg h3 e
(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 n :rvnbl4 7im cm7* n7qs5gxb.1kzz0k5,le fd$R_1$ 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 abohc 3nhz+x6-za f25nh yard the Apollo spacecraft put themselves into a slow rotation to distriz3ayzxh-5 c+nnh62 hfbute 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 rpma qwjz;/b 9hmyvx :;6y in 220 s. Through how many revolutions did it turn i/6xym y9;z wjabh;vq:n this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 g6+9u dn,zm3m9 4qsgoyghuaqw)b8 d8 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 stresse01v(mq e(r (k) xwamdjs of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 ae1mr)(j0 xd(qmk( vwcomplete 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 unifody61tlw i91 fhrx/wtaed + 8*ktp5 1jkrmly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the whexe8/pt 15hy t1f+ klr*dawt69w1d ikj el have traveled in this time?    m

  A cooling fan is turned off when it is runningl3t8 /pu bza17a-v ni0(vp jfu at 850rev/min It turns 1500 revolutions before it comes to a st(pv/azn3 7 vutljiu-b f1 a0p8op.
(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 rev z*iszh b)7)nmg)vu 67j q6d.5ewjqjtolutions as the car reduces its speed uniformly fr bsqnj7*j7td zijwe z gh))v.6u)65qmom 95km/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 unifor18+d l0vgbh x8gz i9ahvlo56ymly from 95km/h to 45l+0g oa vgxzi1b689h5vd8lh ykm/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 all her weight on each pedal when cli) q9r1 jmvz1g1yyh9t lmbing a hill. The pedalhj yg rm9l 11qvzty)19s 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 et7kd/c 8e)hbe nd of a door 74 cm wide. What is the magnitude of the 8bh/ce7tk)edtorque 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 whe-.tptuv x,n0ck9wrn3ndl j9v *k;+,s uou (eqel shown in Fig. 8–39. Assume that a d p*v n0n,kce+9otk(.xu3tw rqlu , -u j;nv9sfriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends*l3f6 mbgk kc, of a massless rod which pivots as shown in Fig. 8–40. Inigm6kb,*3l ckftially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinde( .yffxt6l2h qk/;ur 48 fwrvxr head of an engine require tightening to a torque of 38y . /hxufrwvx fl4( f;t62qk8r $m \cdot N$ 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.ki7d9qrtnl +*5je fm+ 8-kg sphere of radius 0.648 m when the axis of rotationqt7ljk e+d5 n ifmr*9+ is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheelsr:g2qtko mdy(e su0/d( j 3z/ 66.7 cm in diameter. The rim and tire have a combine/ u 2(grdj mkzos/q3 d:yst(e0d 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, light ro)ubtxqz*91 bm d is rotated in a horizontal circle of radius 1.2 m. Cal ubm9*t1x )bqzculate
(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 a2 )s7 ufv+arqidsfp 36 bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The f7vd2u )qrpsaf f6si+ 3riction 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 point objects shownfe(j b256 egenoqric* z1gu0r yyc5 56 in Fig. 8–43(c e bi102e5eq5zrcgjnorf*6u56ygy 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 atomsv3n d0 rhjr,.j whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical sakfu4u 5;yh:efju : ) /q3tchsatellite 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 thj:fk3:u5 /uq4;ef s uh)ath yce required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass o wtbu-iz 1v26af 0.580 kg. i-61vwa zt2ubCalculate
(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 1,mnhsf n vom+z;a ,dj0n3n: ra bat, accelerating 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 o5at4to 6jvc3vn 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 each other on the etj456oc av3vt dge. 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 ev5hr( rjj/1wn:m pje,e entually brought unifor :h,w5jje/prj( n1r emmly 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 accelerates a 3.)r (o)xuwe,0m:v fo45zcnaz e,y j0 nf6-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 solelo lw:yeg9i9f 9y by the action of the forearm, which rotates about the elbow joint under the action of the tricepsg o:e99fiw y9l 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 ax. v nj1+xt8;7 gppnwh long thin rod, as shown in Fig. 8–4pw; t8 vjx1.ng7n+hx p6.
(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 rrhpgijp2 4-pt8n(0mu/ x 4x0pkeb4p of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four 4o :h5zl 37e0nphhrba full turns (revolutions) and releaae lz h74p nhh3o5rb:0ses 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 hacy,69o)hxr 9rx b nehdd/ -4yrs a 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 qpfnpng na6h;:tac-ai 7 sf+*) geb,8280 $m \cdot N$ 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 ro hgwm2;2mrq,m7 jd8f+ wuop2nr w1oi6lls without slipping down a lane at 3 wirjrwg22,w;qo6nfmdho 78 p1u2+mm .3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the E vka7 bg/.jpd8arth with respect to the Sun as the sum of two 7a/ jpbd 8k.gvterms,
(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;f4m2gbhp9 ltb c4 sk+ 2u/jnv mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a tu4bn 4sf bm9 ;jc2l2vpk/hg+rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fjnbd 49/xr sn(rom rest and rolls without slipping down asnn9x d (/rj4b 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 k s52a1ga1d pw uab;w5to fall and its lower end does not slip. What will be the speed of the upper end of the pole jkda51bwa2g15 wasu; p ust before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball ro5afj:ys1i3bl :n.vjh5 t c6 hbtating on the end of a thin stringj1s hyb6tc5 ji5nv ::afh .3bl 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 mon3jb1uwqv8 3ki. sn.ibua)k. mentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when w.unisib k1 a3juv3k.8bn.q ) 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 rotfo j)dipjsn)v :q-w x/u.o u06ating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig.qvn. ux6o0if js)/)ju-w do:p 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)k5k:16t x 9v)vayyh 50ll nwbq can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular sp)t qykn6hl 1v:b9xl 50 5avkwyeed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin ro n74kyeqd, n0dtation rate from an initial rate of 1.0 rev e7 n4q dk0ydn,every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotatinzj auk*r*+ uw:e4pt2t g 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. Thuj 2*+t artuewkz4:p *e potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular mcun 0gd /t6bo.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 y58clu*4ju m7+tyse emomentum of 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 droppedno ;;mhpk7ql: onto an identical disk rho:; ;kq7 lmpnotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at o vng+oynh:njz t yi:.-d7+o5 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 stany(3 pn0.1kw tc ymie.h.8e vmkds at the center of a rotating merry-go-round platform of radius 3.0 m and momen. mn3ie01t. khpk( yyecvw. 8mt 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 wxhjqkm 01ggtjf80o1l. 1aq) i ith an angular velocity of 0.8jhgg qkxo11 0fq)t al81. mi0j $rad/s$ 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 white dwac6 355w vzfrx7 cm,plxrf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away 75,v36xzc frlcx5pm w 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 cpu8jo5u *ou-klkg8*. pwqi+ excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass ,vsuuqt: m c+0$ 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 pla.tqjr opa (p41tform, initially at rest, that can rotate freely without friction. The moment4pa1tp.ro j(q 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 mv- :+hrr+kja aerry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of h+ r- vaka:+rj1700 $kg \cdot m^2$ 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 the rb)mkh -wh0d*s r;t+ xcope lying on the tomt0)-;rx* c+w hhkbsd p edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces teff8(5 pr5f:kbpu j:af j,n 5vhe Earth. Determine the ratio of the fu,rbfpv(en: f:5ja58j kp5 f 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 accelerates from re1s+s-/kty ;ebek ap9e st 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 rtwmg me8d:a+ t- hhop2+nuh63adius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at co 2mwth-6+8:mtguhna+ pdh3eo nstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid u67qch4z/qop 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 4 czh/oq u76pqthe 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 theao24ma e8t +c2m8;(z dclfsir angular speed 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 with mass 8.0 times n0ribz:9 f)jg.gplc;as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undblcfr :;g9n ig0zjp).ergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for 8 tiktce /(st:2 elr-jit to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniforml c/e-k( t j:t8t2esri cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates a5u8 vgai:i5pse9 3batn $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speesg(y lf* (1ea;75nrejo p *ehsd 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., we ignore frictiodu-+ui *qp+kan) 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. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See d- ku q*iup++aFig. 8–21g.]

A wheel of mass M has radiuv3c4 b,znp 1rqs R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a 4q 1vb3zcr pn,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 fpqxn9nlasx(-lm9t0 h , w*6 xalat road is making a turn with a radius The forces acting on the cyclist and mw hp6s ,ax0la- 9*(xln9xqntcycle 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 lja6us b052mwyk rq.k6 ength 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required tam2r uwqj6k605 sbky .o 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 armw:6e3e*8 yvk ( utns4uttaq2f s as thin rods, making reasonable estimates for the dimensions. Theyv2ekatfswte qt*8(u 34n:u6n 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 cylindr.pw* ze9gb(m pical plates, of ma* b p9.wmz(gepss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 r/4 yy(m+p5 ali crvdu.olls 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 withoutauv5/iydc pl+.myr(4 leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumw2m6vcdep( 4uy mp /k.e $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car redup f*0hc-qw+re( 9mump)+l: g hsvax3 uces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) g*p)hv 0q wrp +:f9-+hsc3ema xuul( mWhat 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