A bicycle odometer (which measures distance traveled) is attached tvvo1 th0.n-xnear the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with v1 tx0-ho.t vn24-inch wheels?

Suppose a disk rotates at constant angular velocitde.rc u;2 z9vey. 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 component of linear a 2dz rce9veu;.cceleration change?

Could a nonrigid body be described by a single qmlr* w7wr, 1wcyw69 uvalue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larg98h+qrdnu7i ti 9zq y7er 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 ha3rjtf -k cvc2s:/xxsm f3 kz..nds behind your head than when yof23k 3c -rszc.. mjs:xktf/vxur arms are 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 and thrj fs18v1wj k w.mqvd/*ee at the pedal cranks. In which gear is it harder tovf 1d/j8wsj km*qw1.v 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 hav7ga4p -skr bk9e slender lower legs with flesh and muscle concentrated high, close to the body (Figa9-g4ks 7pbrk . 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fi;9. 8hu4bfqvreew0 ;+ eovnzpokvt n,.o6fv 5g. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? gq/r;,llom x 5If the net torque on a system is zero, is the net forxo/m ,q;5gr llce zero?

Two inclines have the same height but make di.x e meztli y c:z(301k)t;mszfferent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the kltiz xz.)z:emsc;1t 03my( eball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclinew x(ud:og/w+b . One sphere has twice the radius and twice the mas bwwd:xg( +/uos 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 sttau/nz0 6ay8h:: zy koart from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Whicazou/t6 :y0nz:akhy 8 h has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular mom.c+ it.-p9padh y5h-pcw) ckltir / )oentum are conserved. Yet most moving or rotating objects evento ytppt5h -h+9).icwc/d l- .kra) icpually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woul5crv6+p9spg-* kk e,p2fe y nfo)x(tz d this affect the len+pszy65 )efn9 g-* p vefkt rxo,(c2kpgth of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatianzp5l7:*fr wmh 2u- non wh* nu al pzr5nm7w:2-hfen she leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centera; +iqh5*f zap 5 zp ihaqf+a;*of 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 outsttf.**zrv u; d;sqh2vhretched hand. If you suddenly drop the masses, will your angular velocit .ruhvs*fd h;*v zq;2ty increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However/z g(5 1sdcxob0zt e*l, one is hollow and the other is solid. Describe an experiment to determine whbs 0x*o zte1 gdc(/5zlich is which.

The angular velocity of a wheel rotating on a horizontal axle point)t yx;l4vx n0q1 6cpvzs west. In wh x l)vz4p v;0tc16nxqyat 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 increasing or decreasing?

Suppose you are standing on the edge of a large freely e.wmuubv*b2* rotating turntable. What happens if bemu.b2wuv** you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quicklhyv5n d0l4p .ay. As he throws the ball, the palh4y05.dn vupper part of his body rotates. 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 conservation of angular qj/-xg9kj*yy *ri/ qamomentum, discuss why a helicopter must have mor9qj-r *yx// k*yijaqg e than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3 jtloin slm) y66y) 4+x9fsow76f32yp5vtccb0 $^{\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 amazinqep n1(- g7taug coincidence. Calculate, using the information inside the Front Cover, the angular diameters (ine7q ga tu(-n1p radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at tmzay0 :mz jgz: j35r npjv5n;/he Moon, 380,000 km from Earth. The beam diverges aty;5/g:0zm a 5vz jn pm:n3jrjz an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is turned bmn 2o+w kzj96 zzd)6hhj3 nt(off during operation, the blad ) tzh w dmkojn+9266zjhnb3(zes 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 floor 3.5 m to another child. If tl:j-zutbct p/8 o .c3fhe ball makes 15.0 revolutions, what is its:3ot fj.8 t ulbpc/z-c diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How mang ; ey ,-hkxf)/mzq79rypy8fuy revolutions do the wheels make?qy/pem9r7xf; y)k8,uyf- h zg    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at rc8 +o9e rf9mf2500 rpm. Calculate its angular velocity in +rrf9f8e9cmo $rad/s$ $\omega$ =    $rad/sec$
(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 (Fi(-jsrc 2 yv-8b g z/absgo(/ntg. 8–38). (a) What is the lineagsg -vs(82o jr/z b(tba nc-/yr speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) p8hrpj 56vx4e.o(. npw pc4xoin its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed ov 4(yow-.fda;oqv +wgf 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 i*a.b4w:u0a5uota-2 ztfwdq rrnbj) /q5rpw 1f a particle 7.0 cm from the axis of rotation is to experience an acceleratb r qw)- *r:2d/oz.a 105t qfuwbatr4j 5awpunion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 281koicgz *c2:n0 mbyci86 tp:a 0 k*ya iz:6nc0oc8bp2ig:m1tc rpm in 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiucv*e -v(s6wg0fld j g7s $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put themselve0sx o-fp8n0 n.hnjr+ os into a slow rotation to distribute 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 cylinde+ ronh-n00 pxof js8n.r 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 un oc* lwhihsm088p65cviformly from rest to 15,000 rpm in 220 s. Through how many revol h8h5s oiv 06ccp8*mwlutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm mg8t2 qcx8: w-x5 numcin 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 stres/idf;x3 ylu rqq1 )uel/om3m) ses of flying highspeed jets in a whirling “human centrifuge,” whicfmyireqmx)q 31u; d)lu3l //o h takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniflbxa(d9 )f0y- t u(gnrormly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in thi tx( u0d9-fnl abgr)y(s time?    m

  A cooling fan is turned off when it wff/xz k3:q r )x8s8bdis running at 850rev/min It turns 1500 revolutionskrf /x83d )sbxf w:z8q before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformlyxpj o/2tbe 0n. from 95km/h to 45km/h The tires jbotx.n /p2e0 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 revolutionp e +bahm0 zhb8-z1x5cs as the car reduces its speed uniformly from 95k-+0hb8 bhze1c5pam x zm/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 bike puts all her weight on each pedal whei-fzt 5ag)e0k z-s9u o;mls 0xt sdh 7icb.t/3n climbing a hill. The pedals rota3bt/x0stiscs9 f0 mt - a ) i5-.;zgoudhz7klete 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 th + /w 0q+.zc7b6hdjr3rcyjm rme end of a door 74 cm wide. What is the magnitude of the torque if themqz0b j3. dy+7r/mhc6j +wrc r 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 65e:h pshtsou-)t2 kxt4lkz *of the wheel shown in Fig. 8–39. Assume that a friction torque :k stleu p-2k)*t6ot hhsx4z5 of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massless rod wh* 1ilzq. j/do a+lw;nhich pivots as shown in Fig. 8–40. Initially the rod is dl/jw;zl*h. noi a+1 qheld in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an e( eqk lyom4 7mxomv0*vd 2)dd,ngine require tightening to a torque of 38 0)2*7oxd,d v 4v(mmm dyo qkle$m \cdot N$ 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 oe*ad/m jgp/55+yul ye f inertia of a 10.8-kg sphere of radius 0.648 m when the axis of ay5me+pj5e*u dl/ y/grotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm hf 3fe;l c7y 4vz:uu/tg8mhh2in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be igh2 ft cul u 3y;8e4fhmhz:7g/vnored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end gasw8tee/g 60hm8j 2x of a thin, light rod is rotated in a horizontal circle of rat/h8s e02eax8mjw gg6dius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular spe9kh5mn7s 3byjed (Fig. 8–42). The friction force betwen b73h5m9sjyk en 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 jfx3rl-e7rj8 j9u,i a of inertia of the array of point objects shown in Fig. 8–43 l9j-j7r e 8j3xfr,u iaabout
(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 vy8(:ln ysjd :d -jgq8whose 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 cylindricg2b5,ip:de;x1zxu) i:jj oeial 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 satellite is o i2b5exigzp: i:),jd je;x1u to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder0 (w3:l ;ht4pukd1r)wnjwj wz with a radius of 8.50 cm and a mass of 0.58k 3wrpjzwh 4wlj;:wd( 01tu n)0 kg. 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, accelerating it from rest to:4.qgy:o+ qsh* x zkrxsoc9-g 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-go-round and ibfty; bc+sz z;,j5//c 1p 7qbxhdk)d ss 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 /x1psdy +j,s7dct b5 zfb;z;)/h qbkc radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually bl7vr/; ej ao08akhpe :rought uniformly to rest by a friction; aa7j 8vehe0:lpok/r al 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 accef r y3emc,.fw3lerates 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 solelypbzl;,p lhk(*sp 95ag,kyh x1/r r*jx- ta u/y by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle x,y/rr/x -*lhl,bya9 kjg*;z1 tk5pa(psphu, 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 consid*v:y:yvp r)hqv m(d;cm1ty1f4kkp 5yered a long thin rod, as shown in Fig. 8–46yy h y :mk;1pr c:qpvmv4*vk51f( d)yt.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses4vknv+0gg; 6)rt uni q, $m_1$ 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 fou ywd5iy/uj.u6 (lfe(3bqftykbz +(0tr full turns (revolutions) and releases it at a3.6(+uydktqwl5/uf tz(by 0yfeib j( 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 ha kuzp f16d2w-qs 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 28hesr7 c7 6,bwo0 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and raq:z/)zrw: xv0m7wd;/ ktpvv jgm- jp0dius 9.0 cm rolls without slipping down a lanzp r7 tv0d wjv/-/q x jmw:)gpvkz;:0me at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to tcg f0dd wdf2x4.7z lw0tp+n3b he Sun as the sum of twogzbc70+ 04 ld.ndp3 df 2wwxtf 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 16409h x 7iqwn:/6h m0t3jq l9ck 0wm3dwyl kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to 7 3h mqld0lc9nijq w09/:x63twy kmh wa 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 f6tnloxl v2a:,8j 4yu:zzx quv:3pr-*h3z m y from rest and rolls without s2uyl,tf: v3-yn8m: ahlx z:xp*4u j3qovz zr 6lipping 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 bal48/wg(xe8;ap;bnyg +pdjf wo anced vertically on its tip. It starts to fall and its lower end does n(wwgp4pbyan;f8odx+j e 8;/got slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of)kg)+ ke*,s4qxexb ro a 0.210-kg ball rotating on the end of a thin string in a circle ofo*qesre +x)4b, kkxg) radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular a/pzk (*jvd tjwx ,+v6momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rp +p6j, j/ awkz(*vdtxvm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at:y*;cwa4nm, ;gtyd i)v : vaea his side, on a platform that is rotating at a rate of 1.3rev/s If y*g;;m iatnaw :,):a v4cdevy he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce h07 o k+zno6)gfy(heak er 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 speed hg0kyo +oef ak()6zn7 ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of - m c )2+gqd3o5alvhmh1.0 rev every 2.0 s to a final rate)m 5dco+vaq3lh hmg-2 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 yp7c,ka3 cxpbimh* *- 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. The potter then throws a 3.1-kg chunk of clay,-hp*k ib mccx,73*pya 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 ct*a mo2 5znzp+mmb/w5c ,yh) o )o7gumomentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of tgh n;i p;l.2uohe 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 dropped onto an i w6cf u:zq*d: wcmr (7/uvmjf+dentical disk :rwmdcf*q vu wu/c+j67:f( mz rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4s ri0h-3x6m id8qq +mfs*5bz u $rev/s$ 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-round p/ gni j .v byaqz/5/q+ ntz9udw06dx6zlatform of radius 3.0 m and moment of inertia 9b0dtj ngq/+nz 6w/ xy.ua6z i q/v5dz920 $kg \cdot m^2$ 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 velocikf45a2 zux f-rbgq) h(ty of 0. kux4f-5gzhfq( 2arb) 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 event*t d.(v6cti5 aky pb 9wn61mrwually collapses into a white dwarf, losing about half its mass in the process, and winding up with atwt ny*r5cw (dvimk6p6 .b 91a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winhokx:sa*5 khh 03uro(ds 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 b6,*v*e5jj von holrfec v6+ 5$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely withouhgv9937n l*af-it )d35g j*qgjeei xct friction.3e- 9hila 9)x3gefgn*cjtv7 igjq d *5 The moment 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 i6-fwgrg w2r+merry-go-round turntggwwi 6 2f+-rrable that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying k6(w3inmf-dk y1b(vvon the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the3kyk d ((i-wvm nbf61v spool? How far does the spool’s center of mass move?

  The Moon orbits the Earb*:,advy :dtz th such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) :t ady,zbdv* :to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerate 8 boh8,i s *u6bp6hhter/svz+s from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m a6 q3qj js l;4mj5c8.8tkwnlxyhr.0vqcquires a rotational rate of from rest over a 6.0-s interval at constant angul0th486jkx3q.;vjqqj sl wnr5 mc 8y.lar acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.05x/(ax2 0os yann;o*sb 0 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 x /nbx ao(*no;s0s2yathe linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of d1x sw p1+6oysthe 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:zu 8)fd +qiyo 8.0 times as great, were rotating a +o)dz:qyiuf8t a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automsd2s jcu(yvd29z4a1bq j2 yc1obile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a tota(9sq1v2c dzcbyu s dyjj2 42a1l mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without 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 jubc0u -zvcd (10nays++is l8 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 horizontal surface avji1 2wob m249tmy 6het speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely ) ry(rbm8).fryo z 3nk(i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and tho rz).8)r(mykr3nybf en 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 Fig. 8–21g.]

A wheel of mass M has ra.8in aa2z9vkvzrf*n.gr2y - 5e/a hxvdius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that itvyraan2k.z *.vnixe5a2/ gr zhf 8v9- 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 turn x nv58fm*l1vuwith a radius The forces acting on the cyclist and cycle nu f5l*1xv mv8are 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 s93t(a nmxs9l3vr+j 0/fid rgwa dvxk+;ug.m 6ling of length 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 to achieve this feat, and where does the t6 9 ug(knl.dgxwvm dv;x3s0 jr3 aa tif+/9r+morque come from?    $m \cdot N$

  Model a figure skater’s body awfk- 4u ui-3g*nqa9ias a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the anw qf4u-9ug3a* -n ikaigular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates,w-)1e7 +m u+alo6rzszw:vs knu29bin of7l +6m zwo: )1-+u2v9ibuswnez anrsk mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radiusto3vgkq 65c9u la0m j, 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 leavj9tqv0,3 mokclg5 au6ing the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumesi oq1in n.tr4li)(,n e9 c3ly $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolujg ddpel8y8n4.c jnr8 24z7tjtions as the car reduces its speed uniformly from 90km/h to 6.j4j84 nylred 8dj2p7 tnzg c80km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s