A bicycle odometer (which measures distance traveled) is attached 21hk33lsad +vpp38scs iu wj.near the wheel hub and is designed for 27-inch wheep +k8 hspcsid13ajw2 v3u3ls.ls. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angula.c - sfg y2hghs /n*2se:+ddwcr 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 gd. +cg2y c- s/hfdsh senw:2*which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be describr5mqba4j5vz x30v5h; t o z7pm1 venm3ed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than ap.xtn:cq1( *k lhnlj6 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 siq yq+pq,n ap7w(3 pq.l3vf;px f4msj ;t-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to sp yxwfq;433pj qv.lq7aq,;mfp+np( answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and th y7i tuc 3pk;2fi7ceh*ree at the pedal cranks. In which gear is it harder tt 2u pcik7e if3;c*h7yo 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? Why?

Mammals that depend on being able to run fast hattxwme8ep,:ip8f 6e0ve slender lower legs with flesh and muscle concentrated high, close 8pmi 0:8ewpt6 xf,tee 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, narrow beam:37bcm l rs5tc b2d;m sa1r;js?

If the net force on a system is zero, is the net1 mfs:j ylmb9 fzc91s(2+qevv torque also zero? If the net to c+vymz vsq l2ef9: fj9(11mbsrque on a system is zero, is the net force zero?

Two inclines have the same height but make different angles 4 s ccd1u-) nsop(vhe50mc)znwith the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gremvcces s1 hn p d54nc(-o)z)u0ater? Explain.

Two solid spheres simultaneously start rolling (from jza cm 7w8vy (:v7xnb: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 7 8mn7zv:jc: (baxvyw speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same rfjya 1somp8 pd0:7 rr.adius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has thas jr1ymop. p 8d7:fr0e greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most m1 mep5 mo1pe3rvgm5.hoving or rotating objects eventually slow down and stop. Exph5v5mrmg1o1p. e 3mpe lain.

If there were a great migration of people toward the Ear,-hhi smmwu0f4)b k9b th’s equator, how would this affect the les ,ui4b hkmwb)9m-0hfngth of the day?

Can the diver of Fig. 8–29 do a vmp+8w)tf y:lsomersault without having any initial rotation when she le )lw: pfy+8vmtaves the board?

The moment of inertia of a rotatin; ydkrhl2 (ze,g solid disk about an axis through its center of mass i2;k,d( yrz lehs $\frac{1}{2}WR^2$ (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 sitting9 mh, d;z7i tki/zkqi- on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or z - z;kiqthik79mdi,/stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hogtyg)x -y*;zrl8z 1f y(sq9f sybcn 4-llow and the other is solid. Describe an experiment to determine g c8byf4ty-rf-y 1znxz) 9*l s sgqy(;which is which.

The angular velocity of a wheel rotating on a horizontal axle points weso-byhf8e(jru/ 8-j rpt. In what directionj rp8b-ujrfy/o(8he- is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. Whl so3pv .f4ul oz)o:b.at happens if you walu pl)v3lb.sf.z o4oo: k toward the center?

A shortstop may leap into t*,usu ;bhgr+pgu-g1 ,biv vh3he 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 youpg +s,g*uhibg-r h,u v;ub 31v will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of 3rm*f8 rmqd hz u/.jp)angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keeprd*.z8hpj 3 /rm fum)q the helicopter stable.

  Express the following angles in radi sval-.(ylq t5ch-e9v0y1ch zans: (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 oy1 rhhv c0vsif3r066(7i5b kjd7blo z f an amazing coincidence. Calculate, using the information in765bizy0r(o vhijd 70cs1b3vhk r 6 flside 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. Th.x(i,p at td5 7mej2fre beam diverges at an angle jt(xa dtp2.fi e 5rm7,$\theta$ (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 oej 6o5:iv0eh 6vvtq9e6y2 ojat a rate of 6500 rpm. When the motor is turned off during operation, the blades siq: vejv26eoj6 5 ovyeth90o 6low to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ball makegazwwc-6u+3bl( kxv (s 15.0 revolutions, whatzag(u-kwwl(x6 cbv3+ is its diameter?    m

  A bicycle with tires 68 cm in diameter j1x7 jav) i0ugi-nun 8travels 8.0 km. How many revolutions do the wheel-0v iniax gn87) 1jjuus make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculao gl,b) 7eles l8-p* sdzdbs-9te its angular velocit,-*l7g b -8opz) ds slees9dlby 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 one4wvrz8 1 h64rbqc9 orx complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the center?4cq14r 6zrbh8v rx9 ow    $m/s$
(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 ;-y e k7g tmxa36h6nkxorbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of fjq)+ ge:w 7hha point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axis o-fw3bdzk+z (kf rotation is to expz fkk+w- (3dbzerience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel 6vd) qv 6)44r 5r6suhpqpy rrtaccelerates uniformly about its center from 130 rpm to 280 rpm inrph6r)6t y4 qvu )s rprq5d4v6 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 az*8ynxox0z 4nuq: dcy jw85 ca3ds66$R_1$ 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 spacev+:z/lhd n v;rcraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation/nd r;:v l+hvz 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 ao/h2l ( iqc7wuniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it / aqw2ohlci7( turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 lt.,hq y+ v8 m.q2zulyqd;t9arpm 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 whirlijd +c0w+hnl;ja*ua b0x; c s:wng “human centrifuge,” which takes 1.0 min to turn through 20 complete revol0l ;sj*c u0;w wahacx bdn+:j+utions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 r: cp 9;iynnc5ofy+ukq2p 4w(gpm to 360 rpm in 6.5 s. How far will a pyn9 (gkp5 fny +:co2w4; qupicoint on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1( ii g*n;pmk zmn;)od,nnn6c(500 revolutions before it comes to a sto;ipn)z6,nkcd n ;no*(m(mi gnp.
(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 f--f;wq/b pa18jibz :feq kwcgm/q s5 1rom 95km/h tobm-wqp / ; c1s:af jqfgbki/5ew-18zq 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 reducfbr 3a mvkg)lb 9h9m,6es its speed uniformly from 95km/h to 45km/h Trmm9a6kv, )bg3 bfl9hhe 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 weigqgoe(n;mug/80 xe-x eht on each pedal when climbing a hill. The pedals rotate in a cir/emnx;ouqe(g -0e 8 xgcle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the myvyg h1*f*y6;/c j jcoagnitude of the y f1j vc*yy ;h/cgj6*otorque 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 wheel shown ila2c a,pqxr9 :n Fig. 8–39. Assume that a friction torque of 0rq2 axpla,:9c .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 rod which ppf izs6s 6,/wxivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitud6sf s/z, p6wixe and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to na.urtbyhq *p -:;l u9a torque of 38 qa.;brun *puh t:9y -l$m \cdot N$ 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.(06j40 lnvtx1iuf vxs p29t 0q+zxjur8-kg sphere of radius 0.648 m when the axis of rotation is through its center ultv+4q0p19 (0f u xxznsjt2 rvx0ji6.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 6kjr,2km qc.6k k7t/ 0rdl-d ot5yesu95+btem6.7 cm in diameter. The rim and tire have a combined tskmk,tct+o-5de k q/d7yl9 b6 e rm.205jrkumass 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 rod is rotated in a horizonw9y6p v r18camr4ww:8 tij9lo/s /hy ntal circle of radius 1.2 m. Ca8n68w1 ic jv: mstyy9 //r4rwa9o hplwlculate
(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 angulaags rgw10u3;hp cwi4 8r speed (Fig. 8–42). The friction force between her hands and thega8 u3 c0s4pwrgh;i1w 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 shown in Fig.- )igt6d eqf(bo2nle 2 8–43 abouqd lit-o) (gn2 ebf26et
(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 consistgp0zsu r n9o,zrx :h-/s of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at ;bq 4c,yehw6ithe 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 o4;c6wyqeh,b if 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 cylifg(7ygl6ek1lhc*b v7nder with a radius of 8.50 cm and a mass of 0.580 kg.gyh 7(7gvb1lfc *ekl6 Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accele oj2zb b4t2lbw b+i1l5rating 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 l,1qva n k+ab)n7*ckvsmall 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 unk,c1nva+qnv)lab* k 7iform 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 x34org qqa/+3 xclq7)gpn8ouand is eventually brought uniformly to rest byuqo3/7r xp)gx4 laoq + 83gcnq 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 3.6-kg ball at pg ,.hffxe.sa*8yo0aj yj6- k 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 2 8,awbxi6dsyo-rf s8mz.c3xk87wgr s2k/of is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of t6gckar.x/,f2w 8d3-7mbrzxwofs os k8 i2 8yshe triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as showno0*f cyi5fzk ) in Fig. 8–4ofzkcf *yi)5 06.
(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 consistyka-vn2d9ir m q; zd-+s 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 accelerater9cr0qewc u*yac) -81iv8 6 jrs+w/nxfzuy2js the hammer from rest within four full turns (revolutions) and re+z 8srj29fcu8q j*6creir0 ya )/uwxw 1y -vcnleases 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 h exeiwz+/a( 8)u*nme miob4g 5as 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 enginep w :eksu+1f cfv0.4mj develops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm roll26vfu 5 qw;q b1wqxb*c5weu;ls without slipping down a lane atq6lbbqf v;2u1 5; ewww5 cuq*x 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to th)kpc o-dwg j /jb:q+*nr0tag8e Sun as the sum of twtkr qw)ganj8p +jdogc :* -/0bo terms,
(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 164 74 mail9zf1 q5pxaj.d0 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 solidq9ma5 1z .dpxaj7f 4il cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts fro q/6qj;32+ jwcio q2; qukjtbxm rest and rolls without slippingt x3cju2qw ;koi62 bq;jjq q+/ down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is bnlgi .fi)+ a e-l+3ibualanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation3ig+eifll ) i.+bn a-u of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ballyh3o0pv5yh*k e ;x8bcm ,;wrm rotating on the end of a thin string in a circle of radius 1.10 m at an angular xemrh mp0bk,yy; vo;w8*3hc 5speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindric9;h+h6z34ncuynsm lp al grinding wheel of radiuy9p ; n3z6 4lsmnuh+chs 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his1 .d9hhv+ k l:x)mruhw side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speewvhh)l.+19xd:khur md 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)6mq) , yh ekbr3+xs5p1i lve:x can reduce her moment of inertia by a factor of about 3.5 when changing frxp )1 ex, v3ysrm :qeihkl65b+om 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 speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from 2vh,9ub vdt: zan initial rate of 1.0 rev every 2.0 s to a fh2,ubzt9d v v:inal 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 freqegk7t ,v*rg k,uency 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 of the wheel after tgketrk, v,g7* he clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure wp( dsy;5o:g:0ko4 no 3wl asdskater 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 of the Eai n5ky:xaua.n;ba 4vqv7x, +wrth
(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 inertm/ p xbncy)b1:ia I is dropped onto an identical disk rnb1:y)/ bc pmxotating 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.m- l;zv.tsb.*s w p6ap4 $rev/s$ 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 a sosny d3)xth2y: /zi9t the center of a rotating merry-go-round platform yxs2z) odh ysn9:i3/tof radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity5fdjc;4mr tx6n bj/k, of 0dc xn5;k/jf4t mjr,6 b.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 white dwarf, losing about yim zmukc;yn;s(df,c( ;gu9rrwr/)a,z y1 :zhalf its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no ak ;n; z,ma9;u,mgiryfc /)1zdr( z uw ycry(:sngular 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 s6*ywf5pi 4 to-/zlzz winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass xf0pz0 (y opnmm+3m zx k74lb*$ 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, init lx.-yki bq8bt. )lze*ially at rest, that can rotate freely without friction. The moment b *t)ei 8.l -bqzlxyk.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-mnh ro3; +k5/npv4if cp diameter merry-go-round turntable that is mounted on friction3+hp4npvifcor/n k; 5less 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 iogn.h3 o9d4j the ground 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 ont.h94gj oni do3o 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 sug4z*di o;7h ilch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter co4 h;7*z lgiidase, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from resrg 2n+uij3n/ b*cgkuj58 b q1et 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 cylin nd lu0kb09i.dder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceler l.budd00ik9n ation. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricali.ct4p*i cn m9 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 ip.n *cm4 ct9iit 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 razh; z*v e:*nssog:0the 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 timfvqk3(.7uz*dfz,rb .jxrocvxj,e ( 6es as great, were rotating at a speed of 1.0 revolution every 12 days. If it wer3.fb(v dc q6e(jj,7xfokvx*u.zr,r z e 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 the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use eneqe/.jem,c.zx4( z ny yrgy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter.eq(z xj,my zy/n ec4. 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 illustrate jj4lqe1i uq 0bjny(g0: hde9a93 qku7s 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 rolling on a hor/c: sy s:qblzm8;m;wvizontal 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 .)sy zn.eyx1t lpi9r zpq(o w5l6oc/ *+e we(ucan pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of p(yz py95+xw1s iq.*zu(lr6l) e ceeno ow/.tmass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius xe4j-5(caw r muw. *qu*w0azsR. 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 step against which it rests (Fig. 8–55). The step has.x4qc em sr(-5uw*j zwwua a*0 height h, where h

  A bicyclist traveling with speed vc(olk 2 h 2nj)atwv.z5=4.2m/s on a flat road is making a turn with a radius The forcch )o w(an jl.z25t2kves 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 gt ,wib.rj5t9m and begins whirling the rock in a nearly horizontal circle above his head, accew 9tir,t b5.gjlerating 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 rods, ma w)ql6w;qsq6oking reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstwo)wsqq6 l q;6retched arms, and with arms held tightly against her body.   

  You are designing a clutch assembk z6+h kgvk5f9ly which consists of two cylindrical plates, of masz69+vgf khk5ks $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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. 8zjqq .tw/1u-/hlmn6)-h 3h iq0jleas–58. What is the minimum value of the vertical height h that the marble musletq/6hw /h-)0 z -aujmqnil qs3.1hjt drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, buu-itxznoya0 q- patk+0kb80a1 b l;e *t do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speedg (d ;e5dq9 ib(y,tpzl uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular qi;5g((zd b9 ply,ed tacceleration 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