A bicycle odometer (which measures distance traveled) is attached nearvo)v8* , xkkom the wheel hub and is designed for 27-inch wheels. What happens if ykvvx ,*ko 8)moou use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poinx,lqwob0 fs;w-y3xu1uuuvc 45:z, tx t 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 acceleration,lqu0w1;:u ctsz x5,xyouufx-3 wbv 4 change?

Could a nonrigid body be described by a single value uansul 87z3y0a y(ta0of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger t amgu.wrb1ztp6mpz 22 (t 3d78 3gaflforce? 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 sitgdy:8yx9 vyc d/7* seqcnj.2w-up with your hands behind your head than when your arms /xny d:e wscqg 27dvj 89.*ycyare stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has sev/fy/sav k4w 5/1 znqxeen sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large kf xq41/5ew yv/ /szanfront sprocket? Why?

Mammals that depend on being able to run fasj 2xwf2yab1utgr46cuo; c45f t have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explau 2o4gjbc4uf ;cw2axf 56rt1yin why this distribution of mass is advantageous.

Why do tightrope walkers 6jp*bi+4s qbk +tcea 2(Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, ,+8q j1vukd3fj s(ae.rs9nduis the net torque also zero? If the net to319er+ks.s df(a,n jjuvqud8rque on a system is zero, is the net force zero?

Two inclines have the same height but make d:od.c xp-c)o3gxcxsl q,v2z. h8fwn / ifferent angles with the horizontal. The same steel ball is rolled down each inc wc:o df/ccxox8 ,lxgh-.pzs nq)3.v2line. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an in,jdz, shtwe* ,cline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline fj s,tz*e ,,dhwirst? 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. :vaq6:cml5s-es j*d aThey start from rest at the top of an incline. Which reaches the boc-s : ajvs6laq5de:m *ttom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are cogx hp vg mv0nmiee17n3.9 0;odnserved. Yet most moving or rotating objects eventually slow down and en07gnphm13 mdv9ov; ie.g0 xstop. Explain.

If there were a great migration of people toward the Earth’s equator, h2f63 tr3xih ;)tavlr sow would this aih tx)2v3sf ltrr;6a3 ffect the length of the day?

Can the diver of Fig. 8 y;c+86zpiq(tgew 39(qmk j+xdq;q p k–29 do a somersault without having any initial rotation when shej6x+8epq(3 ;;+g i tqc yqwp d(mkzqk9 leaves the board?

The moment of inertia of a rotating sol:+4qysfdpz(l/t ipf0 -kx( sh54aupj id disk about an axis through its center of mass is q4d at: p(ls k(4ypufh/-izx+ sfj p05$\frac{1}{2}WR^2$ (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 rotatingjf q7(qmxe70 r n,mo3y stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stayxyroqqnm73ef (m70 ,j the same? Explain.

Two spheres look identical and have the same mass. However, onos ny6 t egal* ch/(4.-knfxw(e is hollow and the other is solid. Describe an experiment to detewct * yekonn(6/(lx-agsfh 4. rmine which is which.

The angular velocity of a wheel rotating on a horizontal axle points.. z do ,yf+fnf:dgf bpw9(d6i west. In what direction iszd.+:(g,fwo.b nf i9fd 6fdy p 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 edghtikxjn mlh 19;q(3nm;q,,t ge of a large freely rotating turntable. What happens if yjmt(h; nm n x9gqh,ik l;tq3,1ou walk toward the center?

A shortstop may leap into the air to catch a ball and throw s;yqm mc6k5jym3bf8 7 it quickly. As he throws the ball, the upper cm ymks63yq;mb758f jpart 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 -2jw lcz gl(k93bu y9wof conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or gywb3w (lz lcj99-k2umore ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (k/rqx:v mmnzu:d -3-qa) 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. Calculatet1:jjsfehqpep: 11 6a , using the infe6h1:pajet q:1j pf1 sormation inside 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 Mwfglg t;-k,k/d: a b6soon, 380,000 km from Earth. The beam diverges at an fba/g;kd,l-g :w6sktangle $\theta$ (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. Whenzjcp 5(yc+f-d)1k c0m)tw2 qz1brtw f the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accel+ctf2) -kw5zwpt)j1dm (r qf1bcczy0 eration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another ch) a (aqjxc a3zlk-s ---,cwyxhild. If the ball makes 15.0 revolutions, what is its dix a,3 c-(cwks aqja-l-xzhy)-ameter?    m

  A bicycle with tires 68 cm in diamet3 *blg9losb* *g7vmnger travels 8.0 km. How many revolutions do the wheellnbgvog 79m* *slg*3 bs make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate w7d:mz xcy(luv08um.p -p: b gits angular velox:- (b.pgv7mwzu 0upcl d8 :mycity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one :xux.dxaq e0. complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child d xqxx.a :0eu.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 tzmg)k9 khxc2e y/(y7u 579( mwck4 dayqswvg/he Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of8irdt;.y vto) 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 centrifeu;okc ;b6f2buge rotate if a particle 7.0 cm from the axis of rotation is to ok2b eubc;;6fexperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 1 gzxapgx7*4oz dx7-d-30 rpm to 2847 *odgdxxpa- - z7zgx0 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 radius8f:9cu t3 dizwtxhm01 $R_1$ 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 Mo f9/kr1x;g)enreqpl 2sri3l 5on, astronauts aboard the Apollo spacecraft put themselves intorqflxp5i ;32e e n/ls)rgrk19 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 cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm il6uhb 6p:* 8echiy87axokb0rn 220 s. Through how many be8ico7u6ar*x:80hky6b hlp revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 r86ixlrmi6z zbe;p-k2pm 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 whirli;46 mr ve+8iwu-tievfww.t-t ng “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching it-twm4tu8 -ww6 irte+ v.fev ;is 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 fg9 fp:s w5zac 1pf bw 6xin:8f;d.3kuaccelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of n1ff98f;p g:w bk5ispu:adw6 xc fz.3the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runn1fft.eo f51lg hcs;i :ing at 850rev/min It turns 1500 revolutions beforeloeh: ;tgs15ff1i .cf 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 65tecnk nb0;pcfv 0)-0g revolutions as the car reduces its speed uniformly from 95km/h tovepc0)nft-0 n k0;gcb 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 makey )bscm4 j4euio4gk-9 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m. bg- 4u4cskyo ie)4mj9
(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 pedaoqgnrdv63 -2 gl when climbing a hill36g go-qvd 2nr. The pedals rotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What is the -imdtx(wz/ ;h2uc+z t magnitude of the torque if the fthwc2t(u+im /;- zx dzorce 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 in Fig. 8–39. Assum / m1n tdih11nxgm9z/ue that a friction z1 /1nhdxnu9gtmm 1/itorque 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 massless5szf f2ike6/j:0d1.9 eg.og i dftuop rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizonko ide9e5f.df tz:160 ji p/of gug.s2tal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightemh864 dw5 c:few)g gznning to a torque of 38f5ed8wgwgm)cnh6z : 4 $m \cdot N$ 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 obd7xc l,fq8:v 89k ptmf radius 0.648 m when the axis of rotation is througvb7fpt c9m, 8dl:8k qxh its center.    $kg \cdot m^2$

  Calculate the moment of82 jvjteeabkjp(f/+5 inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?). 5vfjpkja j 2+b8e(te/   $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a h5a,, l kbyu5jc.5so j0 f-g mg+rynn.gorizontal circle of radius 1. y bjgj g+ .n manc.o-s,,ryu055kl5fg2 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)2uiphy9)y 7; tfqdbw4b iz j+ speed (Fig. 8–42). The frictii ;)u7f2yq9db)4jwp z htb+i yon force between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point ob5yx-8l+ qt 7cnb3luozwgx0 s.jects shown in Fig. 8–438t+.zcl73byo l0xx su 5ngw q- 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 tota +d6maw6 sjnvtxt4*i0l 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 a5:m9/wvofyl k t 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 :wk59/ y flvmosteady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a ha( 2utdg jn:r:81 k ;lgga9ejmass of 0.5jde2g;g1la:u(8 h 9:kjt garn80 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 ,s6ft s:5f4pil d:hlhfrom 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 aiucs m,n7- bj)+2 jy1yur*ign small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-)1n* urb-uyjg ic +7imnjys ,2round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the 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 10,300uv9dade jq ytal6; 89) rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1add96 lj)teqa9;yvu8.2 $m \cdot N$ 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 asthk5 c4/m :v13 l)craao bqy6t 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 thro 8ir;w: 8ew8sbpb7 tly nhfrp(4avb.9wn solely by the action of the forearm, which rotates about the elbow joint under the action of the tri9y:8;(8vrp8 7 plw . awfsentbh4bbirceps 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 considc1i 3dc :ydyvr4 vuh60ered a long thin rod, as shown in Fig. 8–4 4 dh v:yci3urcv0d61y6.
(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 mac 4zjr-g16oq bq;7 pzxsses, $m_1$ 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 f*x/ bt5bo5r a342- n boz 8vkksviy7ibour full turns (revolutionsbns55bkivz ia /-b oxvyk7348 orb 2*t) and releases 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 -hwionnk/22 x 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 sn au4 56h;w 3o,rnkzpdevelops 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 rolls without slipping dod(clgyt t k (:d-la67hwn a lane atc-a( y (7dd6kh:gtltl 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of t*kfba.f( ry l/he Earth with respect to the Sun as the sum of two tf (y* r.lfbak/erms,
(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 ofb7ycjr)xzs q(5. y2qoy; bq/ h 7.50 m. How much net work is required to accelerate it from )yj/y h yq (bxq;c oq5r.z2s7brest 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 in n)6 wv5u2gwc,zo)t-gtu0u without slippin6g , t0o5n t gvwuz)un2ucw-)ig 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 sn87qs yv *n p ,/fzvw*hm.agt)tarts to fall and its lower end does not slip. What will be y*vsq.p n g 87wtm/, v)*nahfzthe speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the f) qw432fhi8 cr,tubs,:j mbgend of a thin string ifq2c t)g bh f3i,wm8 :bj,u4rsn a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum khf) 2z to5j3sof a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 )jft25z3soh k rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating adhu uqq4(llf e -ahj5+.fd*p1t a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rot+-fehp(alfd d. hlju15 u4qq*ation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown0+urtsh r. 4e5i :txxy in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when chury.t40 :sixrxet 5+hanging 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 ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase gfg6p ut yp vcv8o4uq1lc*efk d9y,72q 5d9*sher spin rotation rate from an initial rate of 1.0 regfcqk e4o p*q9y 6v18dsl2 9gy75fvd*p, utc uv 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 arounoza0uza0efpmk0) 0 p (d a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kgp)0ap( fozkm00 u z0ae 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 the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning atjna0 x6 -yae.i 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 tr+psm5a8;x qyor n2+g53y u behe 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 momt1kp9 ex l/hw8ent of inertia I is dropped onto an identical disk rotating at angular 18txkw hp/9el speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 vq7d e4m 1:a5wrf7toj $rev/s$ 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 kgkh0v;sox6m l19 rlww* stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment o6ol0vxh91 wm*r ;lkws f 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-ro21 ;jndxax v5sund is rotating freely with an angular velocity of 0v xd2aj1 s5;xn.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 4x4zdc 0tkbs/nq vm 3*collapses into a white dwarf, 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 ackzqt 0sn md*/3 xv4b4ngular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds qi nz4gus:. eg;e/b48k d*zs pv3rbl 6in 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 e 1jxn38 awlg6;iz7wky8i+ qd$ 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 r wn0115sc6vmd yiwy z7otate freely without friction. The moment of inertia on ycw6yw1 5mzsi07vd1 f 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 l lh. ya-*/u+0a.pdgofav7eb at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertodh0.aepau. fvb gl7+*/-ylaia 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 lyi,vci(g tqept( 2(vd*zlvq j 74ng on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person withoutjcdqg lqi(pt, 4vv2(evt *7(z 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 sid)b c ze2x7z sz,rwlp ;9:8l g6s5vieyze 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 case, treat the Moon as a particle orbitingb2xz9 r5y : szgzp c,6zw7;eevl s8i)l the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest a(w7orx5oi x5fe u1g .dt 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 cyi cvbxn5(aoh ;:;4o wclinder of radius 0.20 m acquires a rotational rate of from rec (4b wni;vh ;oxcao5:st over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made onk389+so7sl3snl r gl f two solid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-o 9lngls+33s8ksnrl7 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 th7:)n) (u7xuqloou zll e angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as grde-gu -(m8zvo eat, were rotating at 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 ovu -d8(g-z emno angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy seb0: may/rx)7nmx+l;n jffr zh2nc ) 2tored in a heavy rotating flywheel. Suppose such a ca02z xmrl;2rnb / ahnf7)cje :xmy)+nfr has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without 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 8cp;e4pyo f o /5:kaluan $H_2O$ 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 (hl, ejdynl g-b*ko)v+x-v0p4x oop) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore frictioe ifc;g gl12v/n) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then releasedc1ie;g2l vfg/. 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 radius R. It is stn o6:fv/9mq+5 r20j pzd*6npo+ vf:kplswklranding 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 height h, wherpk6 v+ dofj +rflpwnq :6ok*z/s: rm52l0nv9pe h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn witjk5lh.cd(o :hnr9 gro 1t,3beh a radius The forces acting on the cyclist a,ch(5j1od:.3rhn glek o9r tbnd 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 0.5 z2y7rt 8nqj kb*-hd*bfm-u5a5ci4hg0-kg rock into a sling of length 1.5 m and begins whirling the roc ycd*bthkb57qi* u fzrhj28-nmg-45ak 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 torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid b4+ c.6 rf9h6kpnjqyqcylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her q.jn6cybhf+q46r 9 kpbody.   

  You are designing a clutcrn y vky4ozf.6t5u48gh assembly which consists of two cylindrical plates, of mass4n.kv y4z tyorfug56 8 $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 tr uqzopsu,6 )gfhy)+.back 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 o6h uy )+ozfupsg),.qbf the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do nota ll1t5hi6k(h assume $r\ll R$ h =    (R-r)

  The tires of a car maky ;;2 y0dkkcmae 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration 0;k2cam yydk;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