A bicycle odometer (which measures distance traveled) is attachedf 5 k69k t dvw*:msviunb+:(xt near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24bx vd k w mi*(9t6f5:tsv:k+nu-inch wheels?

Suppose a disk rotates at constant angular velocity. Dm6qqe nthco5h/uua50f +o;k 5p*;ibvoes a point on the rim have radial andn;m;uuti p505h/k qo*e65qh fcv bo+ a/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 acceleration change?

Could a nonrigid body be described by a single value of the angular velocityvvmta)mct8s1(jv6j) 0nf r,im ;xu,c $\omega$ Explain.

Can a small force ever exert a greater torque tp0c1v-v,byg l irpt3.han 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 si/et .xw c5(rbvgdin0w o1 (sy5t-up with your hands behind your head than when your arms .rn (ods5 /v xgtby0iw5e1w(care stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel ama u3k*ln:r9g nd three at the pedal cranks. In which gear is it harder tkr :l93unam*g o 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 ablbuhu48djvg 4,xo+s7**d xkilhg p7 *s e to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution *jx sux 7k* igphl+vu8hd,ob7 4*4 dgsof mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a longmsxc;fu 6.q 7 q79ioer, narrow beam?

If the net force on a system is zero, is the netd+seag5 6 h9.word 9ow torque also zero? If the net torque on a system is zero, is the net f9sd.h w6oe9d5g ora w+orce zero?

Two inclines have the same height but make different abte y d7v8n e-3wi/t k-4lgt,kngles with the horizontal. The same steel ball is rolled down each incline. On which inc 4 k, k3t yvwd/tel-8tbige7n-line will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneousoo(9-kuef y /mly start rolling (from rest) down an incline. One so( euo/-k y9mfphere 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?

A sphere and a cylinder have the same radius and the same mass. They sv vre6r/7,z5m j-mvmdtart 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 kineti5 ,- v7 rmzvmv/j6drmec energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conservedg ndj88v1 6-dbicxf9p. Yet most moving or rotating o 6fd8n81c9 xpvbgi- djbjects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’f/+vqwz: h,eys equator, how would this affect the lenq,wfyz e: v/h+gth of the day?

Can the diver of Fig. 8–29 do a sod b63sh5iyiaole j0 ivh.gkg; f/69b0 mersault without having any initial rotation when she l 5yb3l/hhgkioi 0s069b g6jfe div.a;eaves the board?

The moment of inertia of a rotating solid disk about an axis through its cen7m() :6hxhy z(-uzb(gjkilhfter of mass is ukb mxhi:j zhh6-( 7g(yzl)f( $\frac{1}{2}WR^2$ (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 o.kwn u1-py bjish3x-8utstret j3i81.bu- wks-x ynphched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and ha8jfhz4o yw)4mve the same mass. However, one is hollow and the other is solid. Describe an experiment to determine wm wfoyjz h48)4hich is which.

The angular velocity of a wheel rotating on a horizontal7rs9 ocx j epqv4)lf)i8x gs42 axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed inilcfqr9vs s)44 xp og 8je2x)7creasing or decreasing?

Suppose you are standing on t 4zdk q2omzo-k*-ok50tp1dpv rm;ok;he edge of a large freely rotating turntable. What happens if you walk toward the cek-k 1po z;z*5; t0dor- kmod42kmvopqnter?

A shortstop may leap into the air to catch e + b: ,piml+e vg, oqxh+vzqk3n)/vt)a ball and throw it quickly. As he throws the ball, the upper part of his body rotate b e/)3e+mht,:q,xl )piv vz+kv+qgnos. 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 conservati i1pg ;v/qjhednd v8-:cs/s(y on of 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 dg sc1siy8qj ;dvep /-vnh/:( keep the helicopter stable.

  Express the following7 pje3d/qvi9d angles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calcuaa6 /jacybd- y y5q0kb38wp ,elate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moob j,bwae 05c-qy8 yk/3y6daapn, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, (fegph/ k(q (k380,000 km from Earth. The beam diverges at an angf/ek h qp(kg((le $\theta$ (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 tozwykh na,c)*x;ty* 3mw8z8 of 6500 rpm. When the motor is turned off during operationta )kchwxwzmy* n*8;,t 8zy3o , the blades slow 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 floore ai,39lck1scq+733rus m gav 3.5 m to another child. If the ball makes 15.0 revolutions, whatei asccr3s9,g3k 37qv1ulam+ is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions dnjcsex24nz c 8 nh4/u9o then9j 84hu4 2senzcx n/c wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcubn+ o)d 2c9nhk5qjcpew5p,)t late its angular velocipe9)5qbw jndc+tch2p, ok 5n )ty 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 ma)8nl,+bqk i7l yan b4,4pex4wl.ot ff kes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the cenl84 bpn4wkx7 y)4flo b.+ tfe,aiql,n ter?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Ear4e 7e2m/4 kq/k1nel,zrz xsy 1cdjmd8th (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a ii22 jc1l9d)wd4vw,oiwt iaor3 e3 .j 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 hw bu.vu:x3 ,sparticle 7.0 cm from the axis of rotation is to experience xusbhw 3v:,u. an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates rksx+mx1 u)6suniformly about its center from 130 rpm to 280 rpm in 4.0 s.s)mkrxus +6 x1 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 radiusziy x99-igi qkfs2qe2 q/ gc/: $R_1$ 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 piwtsv :om+q :9ut themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0q+s:miov t:w9 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 r ;f; 5)cs(aagyswm.i gest to 15,000 rpm in 220 s. Through how many revolutions did it turn fw;. s5sg(a;g i ca)ymin this time?    $rev$

  An automobile engine slows down f7+icp)v owvdn0o9nqp axu7,a0 -ze o:rom 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 sl(wp-mf15z, n/ wq 0ux(uzak rtresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its n0u/pu1 a(-,wlq5mz(r z kxwffinal 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 3x;ve)a kad ujc-w2*u(60 rpm in 6.5 s. How far will a poi)kej;av d2c u* w(aux-nt on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/minf(z )2 8nppfyj It turns 1500 revolutions before it comes to a s j(p nf8)zyf2ptop.
(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 r ;xho2at) 9qkel qdprl.,* qll)q5i,jeduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 mq kq)aeldpl,x qrl*)h9. jt5l;o,qi 2.
(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 revolutiu+je2s emd)x;cb l+3lons as the car reduces its speed uniformly from 95kmlc 3jdusem+bx2;e)+l/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a -,vp*a-5odgid x/s jfbike puts all her weight on each pedal when climbing a hill. The xs- i*od5,/-gjpdavfpedals 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 forcelroip.a cum)jf *r y,,u:,su) of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force fp,ylu)rcja :,m ).*,oru iusis 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 wheestld,bz8v +(0zim62xbg6 h sjl shown in Fig. 8–39. Assume that a friction torque i(mb82 hbz,dg6s6+0 szvt xljof 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of o j.5tr m8-qsymass m, are attached 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 t.symq8r5to j -he magnitude and direction of the net torque on this system.

  The bolts on the cyli9j k0vu, fi0kqnder head of an engine require tightening to a torque of 38 fu09k0q,kj v 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 bk8yd.tk tf8b du1*.gm when the axis of rotation is through its 1f.k bd8gukb*td. y8 tcenter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm 4hja3x w x3mw /g5a(xdin diameter. The rim and tire have a combined mass of 1.25 kg. The mass xaghja d5xw m/43x(3 wof the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod isfn*,aalz+e)+yl, 6wjofi y1 n rotated in a horizontal circl,zy1 own ifna*a y6+ felj+l,)e of radius 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 ro.ev moalf;4+b tating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is e m;+oval4.fb1.5 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 sheyex.sg 7f-hksfbgmv6 d-(;z; 7t0quown in Fig. 8–4307kge dm-bu fyhsq6 ;x-.7(;fvezt sg about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass ot4bowost5z:91i 8cw0 p d), waxfzr4is $5.3 \times10^{ -26}$ 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 cytri re nk hanxa.p17*7f4z6m6 lindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellitf kip r ztrn7e a4n7h.xa61*6me 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 mas*8 vzp(,w7cokqo+3mkgtbp t7s of 0.580 kg. og +8, cpw(mqt3bv kt7*z7kopCalculate
(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 swin5:kt jrj4 -hw t)b4/v bx3lmzags a 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 on a small hand-driven merry-gdvias0b9he r18o+p .qo-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 (eah810qevri ob.as + dp9ch 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 rpu ntqk-ot5 *2hm is shut off and is eventually brought uniformly to rest by atn t*u-ohqk52 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. 85 6sqar(y fwd9–45 accelerates 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 actih 86fe yyako79c*,sa.f u546edq ucrron of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated coyaf8dy s. e*59uau r6 q4ekf76rc h,uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown intio cty*ti8y1wjxvn;; b / 3fw w7-/ks Fig. 8–46. jyxft t // 3it wk;ocw*b7-w 1s;i8nyv
(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 consq1dp4.n6s-b:tbyg* a pi odu5 nw6ml-ists 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 full turns (revo p,iq5yqju17 rruf,i-lutions) and relerp ru5,y17if,q u-jqiases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia of dyx9mqh-hi 2)$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of . ixl z(z7fx bn/od)c9280 $m \cdot N$ 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 rolls without slipping dx b+xl. s 4g;k-v.uwdmown a lane awl.gb+ k s;x u4md.xv-t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with r9 .k:)ov tk/zn cr1wth:tmeugtj o. 85espect to the Sun as the sum of two terms, ./nwg15t) c. :t8jt rohoezt9mukkv :
(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 and a radius t )0kvmr0qrfya)l b+tkc;x1;:j vc ;nof 7.50 m. How much net work is required to accer xl1v )t; )fkb00c n;tmk;vaqrjy c+:lerate it from rest to a 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 from rest and rolls wv xr8;qzsx s6a 3ct/jetn9,i +ithout slippisa/v sc6r9qxti n8xz3,j+e ;tng 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 balanced vertically on its tip. It starts to dbe o4cc-s9 os/ znv q4+5c6ohfall and its lower end does not slip. What will be the speed of the upper end of the pole juqoc4edvc6c-b oso9 /n4 +zhs5st before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg a 5rox:qcu d -amfgnia6(rk4j- -h+s7ball rotating on the end of a thin string in a circ -u4aco:nq -r5mj+-as76kfr gaixdh(le of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grin* )6ll9zbg+f ck qvt1di,5 rxf(2kgy kding wheel of radius 2fg,x+9 bzlfk )( 5i1vltkdk cq yg6r*18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform t*/.q zh 0ojyq 1fxg-jshat is rotating at a rate of 1.3rev/s If0qxs. -zqyj/f1j *gh o 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) x y2x/wxu7o(ibap(i3can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck p 7/(b a(xxiiuwxyp3o 2osition. 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 heby f*bn /48lbqr spin rotation rate from an initial rate of 1.0 rev nqbbyb 4l/f8*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 rotating around a vertical ax r p2sa-jlmc0*f2)m(x u7,kxuwuz 1lh is through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequenc,)7j0-1xhcufakmup2* zs2 u llwx(m r y of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater sp77i zl6 evf-e5v1lwbpinning 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 Ear b4v w ur-l.xa.stq3au y;a3yl/7o;okth
(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 momeyk /wo). q(t ly6j+wrdnt of inertia I is dropped onto an identical disk rotating at angu+wd/.6 oj)qy (krly twlar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at,xe6+51gmzst1fo5d-gn txp a-k 4ns7ay3i k k 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-rh wor,99wqd4bx vr(y(ound platform of radius 3.0 m andwbhdr4(,( q9wr yvo x9 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-zyx4a cr)l7 q6go-round is rotating freely with an angular velocity of 0.8 z)ax 7qyr4l6c $rad/s$ 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 dwar05 7 -.9kyt:gmk uo1inxcdg-tez. ytu(e fkr 7f, 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 no angular momentum, what would the Sun’s new rotatiocfgy09nx- ed 7uumke rg.iky 1t-to.7z:k(t5n 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 ax hq) je6wgn( hqc-t 5nc1yfm/+e6+z120 $km/h$ 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 k*a27p 7pmpj/no8-mxz4 lxu d$ 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,mn fdmu +ftw cmv1 +xv6-qj*4* k:kj3f that can rotate freely without friction. The moment of inertia of the pe+d 1v6*n +vmq cftxkw4mf*3mjfukj-:rson 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-bonlo:z-tax zyj8h+u+(19 hs m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 17008 jhy9l (s-+oouz1zb+tx n:ah $kg \cdot m^2$ 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 ropeuw1 jd cjdp9 g0ozf,*4 lying on the top edge of the spool. A person grabs the end of the rope and walks a dista 14d,ojujdg fz0p9w c*nce 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 the Eaex 45p8pz(-rbvtcf2vrth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat th v8ex 5p f(vtz42-rcpbe Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest*a0nz ( emm8qq 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 uniforj. 3n+oru- h rr;y.40mdf;al9kvqvn v m cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at 3o ry r9avv;-ln qhm..r+ 4;ujvdfk0nconstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cyl 2 3kxow7.mqwfindrical 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 reaches the end of its 1.0-m-long string, if it i37xfo2wmw k.qs released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular g90hge-vdb8 b 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 3zg8;0j uno8ezh1mxm of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitatio xmu8 ze 3jmz0n;go81hnal 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 f/or(sv wj:-db or 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 kmr v/:(d bs-ojw 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 d cmfy, h-c5d3an $H_2O$ 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 horiz evt8do6a(6hl9sc rbr, d v-o+ontal 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 frehz eai4.yo j46ely (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 mass of jaoh64ze. 4yi the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor,u.2,ya rz g3ps and we want to zp r3g.2usy, aexert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a;e + sa ;9+k;jqq*sksxm,dh gv turn with a radius The forces acting on the cyclist ;qak;j q,*sv +;msk9e+hgsxd and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begirz 1.a4igh/zb ns whirling the rock z1h a.bgz/4irin 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 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 thib5oct zs- kq5w.1xw 3d*d1opq n rods, making reasonable estimates for thqwoo5p tdzsc 1qd35k.bwx1 -* e 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 assemb3gq,ec (n be0hn;vka5ly which consists of two cylindrical plates, of ma0,ha ;k3cgv bn5e nq(ess $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ank:s( . z(xwfcd r,z;avd radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume z:az(;x,(c.wd vr sfk$r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume do3wue6, rfo.$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions m k gmo31w3i-cq1g+u aas the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 mqaimgc 1 1wom3 -g3uk+. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s