A bicycle odometer (whichiz;d 6w/6cup v ,wv(ou measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheed/,(;ivu6 puz c wow6vls?

Suppose a disk rotates at constant angular velocity. Does a point on the rim havp5qb./-eca. o,9pm xqrgph k;e radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential accelerqqmk9a o5- .;gppxpb,h /e.rcation? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be ofvon (q(8 s*g-kd8 xedescribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a (xyao)l-x h* m5u-apagreater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head y,cfcd).7gy4ct ;hne w7dsy ,than when your arms are stretched out in front of you? A diagram may help you to answer ;tfd4wshcde,cy ,g)7 nyyc 7. this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at the l 5 blq ;n:hs4g0o+sfepedal 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 larg5o q ss4:lb engl;+hf0e front sprocket? Why?

Mammals that depend on bein/iz6a c0u6kzsg able 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 ku/s 06 zaizc6of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry sc*8c t 4pl6x( xqd- s,frlgf4a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net 6/axr7-u)ru akb d si /gqi:q)torque on q6airi:7d /q) x)k s ba/g-uura system is zero, is the net force zero?

Two inclines have the same height cocf5mo9w4 4,l rao+ubut make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.o9l wra,4c ouf4moc+ 5

Two solid spheres simultaneously start rolling o uht6m i 37pejmv)g9/(from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Whipi e7h36ot9ummv/ jg )ch has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the knpn5v1t/er e +)rpqujl (;6b+ lm7gl same mass. They start from rest at tllpbme(/)j++ u r le6qgnvk;n71 r 5tphe top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angu *:ckwnly( +iqucwmy z)9 a43mlar momentum are conserved. Yet most moving or rotating objects evwym k)wlmcn * y4(+z39iac:quentually slow down and stop. Explain.

If there were a great migrnw*gc:8 ;2xx4 zhjm vpied2 9ration of people toward the Earth’s equator, how would this affect th4d8*x2mxw:;jpcer 2inz 9gvhe length of the day?

Can the diver of Fig.groaq s2lnc;v 9s*v9bs qqc8jy f 828; 8–29 do a somersault without having any initial rotation when she leaves the board? s srgbs2qv8c2vjl9y8 co; 9a8fq;*qn

The moment of inertia of a rotating solid disk about an 9e7 maome 7y.m 0jdr8caxis through its center of masry70aoemcjm dem8 79 .s 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 sittk4 gu9;sfkk; iing on a rotating stool holding a 2-kg mass in each outstretchedu4;sf kki k9;g hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Hea:6kr+qk xs2nlpp qy0d. c04 owever, one is hollow and the other is solid. p4xdyseq:+2lqn rpa0 k.60ckDescribe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wg; 8szo.8b,3 ezzl6xs+ s 0czaih gf(mest. 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 angui s86+s;mzasz(lbohz0.x8 c 3feg,gz lar speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable5dakz-mfrv iq)5r-bnhjuk( 9,6( tkq . What h(nrb f )65 -akkq9 ,tmjvk5qiz(d-ruhappens if you walk toward the center?

A shortstop may leap into the air to catch ze1*peyr.pxu( yc o4v5s rq0+a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and lry e uc y4 p(1z0o5srv+*xeqp.egs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of 6 ds.vep+gbn3shfr /4 conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more wn6 bs+hp3 4ds rf/.evgays the second propeller can operate to keep the helicopter stable.

  Express the following anz *ehvx9q;cs ,gles 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 coincex1xmsp xwvb8k zd;((u0 u9a2 ,d)jeqidence. Calculate, using the information inside the Front Cover, the angular diameters,dpzuw2s xkmu9v 1xed)((abj0 eq8 x; (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divert0f g)uypj6rp1 ii;+iges at an angl;p16igiifjyp ru0)+ t e $\theta$ (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 thenh :*n/fimzaw2 osv;gs qi.: 1 motor is turned ozviw an1;n qh:/ g:ims2os .*fff during operation, 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 floor 3.5 m to another child. If t((kd slad :0mohe ball makes 15.0 rm:oa (kdsl d0(evolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many r rh. ;w1ob a,cgbwb1 xls i0osrxt .0)6tl/m3fevolutions do the wbtar;g1 mwi.0h o.fbl1,sxl6c b3txwr /0 so)heels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rota xmt )hn77t..x rnujsnll..t/ tes at 2500 rpm. Calculate its angular veloc .).tnnt .7xum/ t l.rhln7sxjity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete (behltnv (v.4l-q:rlrevolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child sear.b v4h- (lqe t(vll:nted 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) in its orbit2z9*crkgskz 8 a)bta+ around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of atdv4t5ninr0 . 7x/jua point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm t.jqp15f68 ,tkkp13 tetdgjvfrom the axis of rotation is to experience an acck 1q6tdgfttp13e, k vj8.pjt 5eleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centerxy/hz /-z2t w;b0zqgs from 130 rpm to 280 rpm 0-zhq;sw/ tb2z/y zxgin 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius dg6 9mr;l b9t j-f1x0k7lrj fk$R_1$ 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 th6-- mlok/ty nqemselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated - /tqkl6mn yo-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 resl 9b9 c8qjtve-t to 15,000 rpm in 220 s. Through how many revolutions did it turn in this time? bc9qe-89jt lv    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.le:.mvppr e4/h( *vl h5 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 f (2bui2e7.dq e 5ddscrlying highspeed jets in a whirling “human centrifuge, cedu72b5(sd 2eq .dri” which 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 acceler3 0os 83pt uuqxmo9/pokg 91deates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveledo9mdsoogp08 u39uk pq xe3t/1 in this time?    m

  A cooling fan is turned off when it is running at 850rev/min z;c.g lke/+txu2 vu44tqa2u p It turns 1500 revolutions before it comes to a stop.eu4l2g;/ 24pu v kt .autc+zxq
(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 asmn+3qeoo7ej k:i1 l 5l the car reduces its speed uniformly from 95km/h to 45km/h Thinq35: ll7 o+meoej 1ke tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 r) z0 smy6 ).pdkynrg6mh/vgl2 s4l7gyevolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.s0l ny) 4z6mg6lgr)d hy7y / gp2ksv.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 w(6jz /welse hp +ae2q5hen climbing a hill. Th(ee +shlj/a2 p w5qe6ze 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 mud idu- a;/+c 26zklaof 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if thu k2idau l+mdcz ;-/a6e force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the whe -vmzomzhw; mfq):0(sel shown in Fig. 8–39. Assume that a friction to z sh:mq ;f(w-o0mz)mvrque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m(ll x ab,hyh;:js.e0d, 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 the magnitude and direction of the net ,0s yl dbeaj(lh.x; :htorque on this system.

  The bolts on the cylinder head o,hd- qy-t3jqtf an engine require tightening to a torque of 38 q-q, 3yhj dt-t$m \cdot N$ 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 ofx-o; ujmc. yqs0p +gq6 a 10.8-kg sphere of radius 0.648 m when the axis of rogqs0.;+ypmuc6 - jxqotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheec 4o9aso +06 opmkyl(cl 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignor ( y9poo46o kcl0scm+aed (why?).    $kg \cdot m^2$

  A small 650-gram ball on the e x rf(j0rvvlo7q m)b.g4fv6e0nd of a thin, light rod is rotated in a horizontal circle of radius 1.rv (xj0br 64g fvf mqov7)e0l.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 rot6h c)zi)n1v:xtb ry6 dating at constant angular speed (Fig. 8–42). The friction force bei c6vn:hb6dtx)1z)y rtween 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 inerd29rlk 6enuw+tia of the array of point objects shown in Fig. 8–43 aboun +69e2dkwrlut
(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 3 ) 0-12muxaek3mp3mcvn,ryxin ov s,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 cylindri cpehm1)j ,9*-9dn o+ilsh7uoqvks) r cal satellite spinning at the correct rate, engineers fire s lu +h7n),*9)drv1o mh9seo-p jqki cfour 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 to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is 1i mogd06-2zyl 1.kel k bp9opa uniform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calc bo12.il61zpmd 9 kype0-ogklulate
(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, acc9dycn* vlz+ ,celerating 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 han;x +9hhw5 n+3nw dc 7eatyajc/ff;.ib d-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass n c;x9wefifn.;h + 7ajcyah5/ wb d3t+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 brou+k, ajzs jbio1jb8y )6ght uniform )ob,iaj6bjzk1yj+s 8 ly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball atr s3ht d1rgz)* 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 action;;w cj iws*8ci of the forearm, which *c iw;s8wji;c rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long fwa6;kp ),rzl yqd+-el3f )kw thin rod, as shown in Fig. 8–46.k;,a6q rl3y) pfwd)-lez+wfk
(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 osj9hgs:ne.+m0*n(g wrc9ucvii x;k. f 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 67)senn shnff44aao5o rzs/; turns (revolutions) and releases i so4n6f) nsa7/ase;n z5rfho4t 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 8d9wuvymrn; y. 0q+rn3y/gwm $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops,sn6 )vab a jcb+oi)0g 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 sl4/x q j.vjqwvodllau64q +2 xeta3)w7rdt((mipping down a lane at+xrq 3q)axv7a/(t l.duj4 mj6 t(we2qo4wdv l 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of toz. hrie/1kka6,y/ fawo terms,ik6f .ar/,kz /heo1ay
(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 ldoiklm 3s 9/.v9b f1vmc1,nna mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid 3v lnf1 ci1l/on9k ,.9mdsvmbcylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and tbx hxb:tp1bw4/g0y r iw6:j 7rolls without slippinggt1 hx:x 4w07rb 6/jybb ipt:w 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 mk0 n2ghi+ckez 9d7.kits tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before72dn9hki+ keg ckz0m . it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular mof/o 30*xzbh lumentum of a 0.210-kg ball rotating on the end of a thin string i*z /f0houlx3 bn 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 at-k)/8q:h5l;yt df zzmfbp1o zcw 76 of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rqzpzw fhfz7 -6tlb/k ;yc toda :m1)85pm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side5w.0.xfh381) +u k c uyajazey(i ukk9gd p:qv, on a platform that is rotating at a rate of 1.3rev/s If he raises his aryiugu 1:q3fa ck.)0xuz(deyp9a.8k j +hw vk5ms 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. 8–2z*k0eas2bhe5 9) can reduce her moment of inertia by a factor of about 3.5 when chan 20 ese*zkh5abging 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 her spin rotation mpw s8p p8;xk.at0in:rate from an initial rate of 1.0 rev every 2.0 s tonpiwxa pms8 ;8.k:tp0 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 axis throoxhvnc 5 ,:d ghd7tv/2ugh 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 frequency of the wheel aft h,7/o5dtnh c 2xgd:vver the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3ueoouf-36; s v 6s7rlc67eljy .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 angulawj /s11qjjia/cv0 4ibr momentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inehzx7 d -s7w/lcrtia I is dropped onto an identical diskhw7zl7s d-x /c 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.vk;ci 67;b2 jkhwx hae yda/x-bj, w8 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-round plhjx;vxqm39 rbl+plv gq81 0q 4atform of radius 3.0 m and mx 3q l8g1h v09v;+jxq mpq4rlboment 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 merryv th va1*23ee tn8vx) lluo6+x-go-round is rotating freely with an angular velocity of 0.t+a3vnl xvl 2u*t8e)1xo v6eh8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, l6 q+ j x2-nnyy f;/zyajzg9vs;osing 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 angulanzqxn aj29fys;/gy+v 6z ;-yjr momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 12o+3) zl-vb.x iqwpy8 4d2gjpz0 $km/h$ 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 0+hy: 9fqtfx m7(sws*dy-ym2 /zv cmj$ 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, thatc/vvl0))l6aq jbujh 1 can rotate freely without friction. The moment of inertia of the person plus thej)vlalv0q cbhj )1u6 / 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 abif eu c(h5p(2dn-1: pfj.x po 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momen 1npp:5 ujh2pde b((f ofxi.-ct 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 on tdj)2mla)dc ri4h;a9 umq 7 s9nhe top edge )2; a9 is4md7q) mc9alhjrd unof the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the 9lfeiztna tk(x( c5,9 mj./s jEarth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, trj(ki cfa 5txzentj s ,ml.(9/9eat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate j y wa94 i .-1tv7/lp.xaspeakof 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 0.7 *;s8 l(igvs *gy o/r6l d*ift;mwjbn20 m acquires a rotational rate of from rest over a 6.0-s interval yi8;*jggbsm(/n ;rtsd*v6fllo* w7iat constant angular 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 0.050 kg and di-eyluftety/,e xm6h 5g rw 5/h9 *pnm0ameter 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 f,hlt* / em xpg nr0um-wt595 ey/y6heend 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 spv1j; .ut2e.j upcm(d0r q-yt:n2 aekaeed 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 masv,53;n z qg9t lzmnw;cs 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were tcqtn3v;; ln9 mwzgz5 ,o undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use ene v s0n29c;ubjjrgy 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 km without needingjc2vn0;j9 b su 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 illustratesy0 -psq9z/ vyt 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 swteafjx/1d c; s ht.:f6w; p(0l uf0uon 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 3kp pm8)v0k7zkpa7fk(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 forcem z8kkpp370)p7 kfkva 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 standing vertically onb z(w ny(bup 2eyi ,ep9h*y8e7 the floor, and we want to exert a horizontn, e2(bbh 7eupyiez*yp9wy(8 al 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 turn w48ik wvs 73aid9 y2rdzith a radius The forces acting on the cyclist and cyc3ra ikz2d vw4y8 7d9isle 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 ingo ybzkr73,iy3gc 6m 6to a sling 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 torq6y k o7ci3yzbrm 63g,gue come from?    $m \cdot N$

  Model a figure skater’s bodv *oi72 5no4c svdz4o7annd: dy as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the ao 5vv2dconda7n4sz7id*n4 :ongular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch aji3lp 3nyz2ql-9mzf x (euy; 0ssembly which consists of two cylindrical plates, of 2uznq9z fj-0y(x3;3 lipme ylmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 anavudat.9z8 eaf6ek5:d 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 tvu.z: 5da6e9eaaf tk8 o reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, bu iuillt;g 9y;t-7. lgut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as t qimebizq9tk,xbo6xx2ys;b )65w8 +rhe car reduces its speed uniformly from 90km/h to 60km/h The tir29xxxob qskyz58b6we6+br;iq i m,t) es 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