A bicycle odometer (kfuo0vim+ c 2:c-iex+ which measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens iem:+-i0fk +x c2vu iocf you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the 2:yd6gd( ym5 ,f0joem3gp ftmg/f, c xrim 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 c 0gg5 ,o:mtmg3y/2 f 6 (dmpxj,feyfdcomponent of linear acceleration change?

Could a nonrigid body be described by a single value of the angujpi53gv q v30 47n9ys:cpap7ehxd uc.lar velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expl,;v(*qjpr jn9pbpgk. ain.

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 don1mczk 9he2w* a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may h9ez n*w m1c2khelp you to answer this.

A 21-speed bicycle has seven sprockets at the rear,hs f;,m-zjg u0cho n1 wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rszgo -cmhf1j;,0u,hn ear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on be(nj5qo j k1 -zx9wxya.ing 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 rox(yko a51. qwj-xnz9j tational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–3z0 zeq*8i7/ppgro:rs 5) carry a long, narrow beam?

If the net force on a system ikxv(i++d.ds 3jdqp8aem 5 *u us zero, is the net torque also zero? If the net torque on a system is zero, is the net foes3a.*d8dk+ v(upm iqj +xd5urce zero?

Two inclines have the same height but make different angles with the hori /4i(tur ,kxjdwq.f/tzontal. The same sq, 4/rtw i tk.xujfd(/teel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rollizh1xhi4au /m0 ng (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? Whim0az/h1x hu 4ich has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same qd9 chqpa;46tradius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bot6 9ht q4cd;aqptom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved(250u 6fpq b9bkj br/ juluwe). Yet most moving or rotating objects eventually slow down and stop. Explain. bu f e0prbujj2u 5k()9bwl/q6

If there were a great migration of peousv op,o ,34y+nm0mrbkf (,ckple toward the Earth’s equator, how would this affect the length offm(o y,34 bv,psc,nku0omr+k the day?

Can the diver of Fig. 8–29 do a somersault without ha4o*ygk /n 8rxn-qai.uving any initial rotation when she ln.4kq-nyxuo8rg i* /aeaves the board?

The moment of inertia of a rotating solid disk about an axishx;ke 2:lxnbd d664)po(fz ke through its center of m:dd4k(n z62x6 eb; x)plkf oheass 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 tbc01wk.d59b gx 2,z(qdolm j in each outstretched hand. If you sudwgk5 (zd 1m0 9lj.xoc 2tqbdb,denly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Hozuwx,0 ld.dap 0y1h9iwever, one is hollow and the other is solid. Desc1, lypdxh. w zuida090ribe an experiment to determine which is which.

The angular velocity of a wheel rotatingimlhg*hf.5k, 8p-.b bts8ncx on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decr-.x ,s 5nhl*.bphim cgb t88kfeasing?

Suppose you are standing on the edge tpof5 w2jh 7d aa2ygk7c;)fz,of a large freely rotating turntable. What happens if you walhp c2afo d5g7 a7yfw)jk,2zt;k toward the center?

A shortstop may leap into the air to catch a ball and te,98 ;j2:jztiztlbu ghrow 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 legs rotate in the opposite direction (Fig. 8–36). Ex ite2g8l z;jb:9jzu t,plain.

On the basis of the law of cons1 ibpd95tjr .-: rgaqwervation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate toq9r-a:5bi g r.t jdp1w keep the helicopter stable.

  Express the following angles in radians: (a) 3k n8xu;x,1x s9 kl)oqy0 $^{\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 coinciden,ty 61l :k /jqyxapp6lce. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and alqypx pk61 :,6/ltjy the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed atmv/8h ohj at:1 the Moon, 380,000 km from Earth. The beam diverges at an anglej:1h 8aovt h/m $\theta$ (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 rpb-2b/k e )bfggm. When the motor is turned off egg -b/b bkf)2during 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 anoqi ;a e1:r3dah0j:1dr sb3yw other child. If the ball makes 15.0 revolutions, wha jo :ydqia d1w03:rhb13res;a t is its diameter?    m

  A bicycle with tires 68 cm in diameter trav l:g5vv6p4 *qc(dtygaels 8.0 km. How many revolutions do the whee :pca5gg (v*y ltdq4v6ls make?    $rev$

  (a) A grinding wheel 0.35 msy.r a t/+7 g.16i)qj*eeeafvltio 6s in diameter rotates at 2500 rpm. Calculate its angular velocity in sf1ti6a 7/toegajs)*eyl6+ r q ei..v $rad/s$ $\omega$ =    $rad/sec$
(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 (Fhlgcu.7icx t7bve7rm 595 )avig. 8–38). (a) Wh9baem .gcu7 v5lrvit)7h x5c7 at is the linear 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) in its orbit around t bcp4v+g4 dxn o/n2h+uhe Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point n. drq7g5n, 0dlrhfi2
(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 ,gaizi /,bb g+ (e;+qgad:u gccentrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an accelebu: gg g +a(;,di ,qgia/cbz+eration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly a47wfidyjo5o41pv7y ,qop b l,b,j( o5z 0jmmwbout its center from 130 rpm to 280 rpm in 4jj ilow 7qj1d57,54m 4powvf(yo,mpb0y z ,bo.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 radiu4 /sl 5v 8xzt:dzpqqn0s $R_1$ 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, astronac333 c-ru7e niojc sew-n 93aputs aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-micp33we3-un9sa 7inc r 3je-con 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 r ggyk,v ::d(expm in 220 s. Through how many revolutio: vdxyg( e:g,kns did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcu0*qoe* k,6 -w.msi tc:xsgmq glate
(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 whirling /b2 wh79.g m4qff ndnf“human centrifuge,” which takes 1.0 min to turn through 20 complete revolu dfm.wfb gqnh947 f2/ntions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm h.bh7uidll3x fu 8bu xoz; 23eytt0+ 0in 6.5 s. How far will a point on the edge of the wheel have traveled in t0f2xhhbz;8tbt u7uulo.0y3e ix 3+d l his time?    m

  A cooling fan is turned off when it is running at 850rev/min It turnsm+/o(b)etv ewd+8 vkxf*zk3 p 1500 revolutions before it comes to ab d3z*m/+)8ep(w vekfotxv+k 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 uniformlc96v c40i n:n)emkvnu2yhh( by from 95km/biekyuh4(vv 6 nc0mnc h9)2n: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

  The tires of a car make 65 revolutions 2ff08bcn6nwo 2 am6 kras the car reduces its speed uniformly from 95km/h to 45km/h The tire6 bf8w 2rnk62nm co0afs 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 hdxs 4v;mh+.xlx(+r zm er weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 cxxml sx4vdhz;r .++(mm.
(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 t8(s aisto9 m;yc8k b(ohe magnitude of the torquec8 ysi(9atmo bs8;o( k if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig hugv)w oz//m8. 8–39. Assume that a friction torqugvz)8/wh u/o me of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached 5uiryp nnjtm:voqu7 kv;3u2e*+- l3o 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 magnn y j qvkum25v*itr:uno ep+7o33ul;-itude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine 7npelj-vm8ta5 86r(b xnc m4b require tightening to a torque of 38 tj( 5n6rl4b8ne pm7-8cmavxb$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 me kdz.z;9o;0d rkj0;zvhl u2n when the axis of rotation is through id ;.uoldnezz;009 z;2hjk krv ts center.    $kg \cdot m^2$

  Calculate the moment of ino +cc +uly-js1ertia of a bicycle wheel 66.7 cm in diameter. The rim and tire+-c1ul oyj cs+ have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated7zmztzr+p ;b . in a horizontal circle o.mb+zz zr 7tp;f radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bl,)ln8hv0dh142nk e0+6 fia ylfyl obowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force beba )y0fn+21o lde lh v60 nyf8h,k4liltween 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 z3 2i4 yzp)zhax fyo:fo9f 4.jarray of point objects shown in Fig. 8–434y x )93hzazf4y.:po2o ijz ff 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 atomst.t e wp.ac.-r)aig/ pog,eh4 whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cyf f4ywf ;:;ohuub9qsg9agd)9lindrical 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 to reach 32 rpm g)uyfw; fha4s do9qu;: 9 9bfgin 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a rqfmwnu6v6 i ):adius of 8.50 cm and a mass of 0.580 )mw:v6ui qf6nkg. 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 hp1 gtf1h4+ox from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-dri(jym)irluj,2 ven 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 childrjj)i( mulr y2,en (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 evvih o*dj:9:vwwyw :uxu0 a30gentually brought uniformly to rest by a frictional to x3how0*:0wg:vu u9jy: dav iwrque 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. 8–4/0k91wbwrsf x+) t4,hbl cn zw5 accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whic7c 4guesdks)8 h rotates about the elbow joint under the action of the triceps mu7cg4suk e8) dsscle, 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 bladggrmf7 rqifi e7h9n d5g( ;k;1 kl:nb.e can be considered a long thin rod, as shown in Fig. 8–46.(grehf1r77i ; . 5qflnkdkg:9nbmg i;
(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 me+o u4+7dc6 w5dewu+sk fk -dgasses, $m_1$ 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 ;ppsg5,zr2nl /xfo t4hammer from rest within four full turns (revolutions) and releases it atr5xp pzn g 2;sl,ot4f/ 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 has1:p *9)x ss/ xbzjoj/ekjs x;m 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 torqlqtu*5z.jhpy n c0o07ue 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 down a la/ i ,c* )(hebnqdor/;t1znbxkne (/ )dnn tk;,1bb *xh/zo eqricat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earz4f*z m i4eue/th with respect to the Sun as the sum of two te/uzz4fiem*e 4 rms,
(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 osvv3 g,g:v ioj j.(jvh:*1lb 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 sol1b3j:vvghvov:(*l , sj go.jiid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from r0 luk kffoy0z)bd e+kbk,c:-mr9w/ 8z est and rolls without slipping down a 30w/)c80bkk-:f muod 9 zfelkky r,b+z0.0 $^{\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 balanc t8j*vztl. sa)ed vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use j stz. *a8l)vtconservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on f xqc2rxa) ,c83xq1zcthe end of a thin string in a circle of radius 1.10 m at an angular spee, c8axq13 xcx)c2qzf rd of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical gacso*vmb/f3j5kt- ixh p*1s 5 ru6 m9qrinding wheel of radius 18 cm when rotat hts/x6q*rmamk p-i* jc b53 uf95vso1ing at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his sid zi7a48g 7ffaoe, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, fgiaz7f4 7o8aFig. 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 Fi:b)hi ltpv24jn ,:zg wg. 8–29) can reduce her moment of inertia by a fa vt4ig,w) pj h2n:l:bzctor 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 ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial in*x. ,82)vfeaggru5u bk:jh rate of 1.0 rev g5,xrnha)b :v8je u2kf. gui *every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at a freqhs cg (q+f3o31q wwx8duency 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 the1(+ 8xdh33ofg wwcs qq frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at .* is(q- mrc/5reox7p znk fd)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 momentjl;+we 8lu+i2 e d+bfhum 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 inerf7oyhddxk 2g0kq5,pr3 p( *gztia I is dropped onto an identic2q*(kp d03gphkf5,g 7 o xrydzal disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns aal , ipr)o99-kvz hv3rt 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 xy e +blt::2 meljm 22ora.b8yplatform of radius 3.0 m rbx .b22m:let 2ymal8oejy+ :and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an 3vm 8jnmolp29 angular velocity of 0.p ol3 jmv28m9n8 $rad/s$ 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, losi q, hrv-;ro+bxx8yd+eng about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’srxo;x, +- +8ryvbed hq 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 wimbol 1o8sr,, wnds 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 b wl-( sa8/g //zqv3wdxyy+kb$ 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 ww/.h vyr/k.sq ithout friction. The moment of inertia of the personq/svk w. .r/yh 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 diamete raxy+q ,ji(3qr9m .s owe 04y5a5eelur merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 17je9+.uyl 5 mor43wsra5ixqqe0e( a ,y00 $kg \cdot m^2$ 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 ropm0)ol.zv gk/j e rolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool l.mjv go/0k) zrolls 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 Earth. De /;mk2p6 ut,go edvvs4termine the ratio of the Moon’s spin angular momentum (about its own axiuvp dmtk ,;4e/6so2v gs) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates fro+ndcga i9na/ 3m 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 unifcn 8.wta1n5; kff l3klorm cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivere;n3cl1 5nf8w kk.fatl d by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindricalznez ytw; q. tvc2 1fwq1og,63 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. Us of vyz1;63gtw ,q2tcn.q1ew ze conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the an+6temhy phu7;j o4p5bgular 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. o42swrx *c5sdgi-9do 0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radior4dcwds2- *5s x og9ius 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 iw wo ld39+,jyuse energy stored in a heaw3yi+dl, oj9 wvy 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 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 *w3r ;jqby*fy1zr dx9an $H_2O$ 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 horizonkmfqa7kuuh.0) vs d:8 kw- 1xa,pqd2 gtal 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 ek:9nboaxl75j8 wu 3/ i vz5baa9: 2qz vtiu,xfreely (i.e., we ignore friction) aboub 5atz8:9 iq vlauxkwvbu 3eo59 ,ji72zxn :/at a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on thay1wx .d-4 m:vg2znyc e floor, and we want to exert a hor1c-mwx2na y g vd.yz4:izontal 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 7)ueicc 92hk croad is making a turn with a radius Th)7h 2c9c cieuke forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock ix):vw,iun5 5rs+kt t0zs vx+tnto a sling of length 1.5 m and begins whirling the rock in a nearly horizs+it5 vxv+n0:s 5t,) rzwktu xontal 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 soj2a3. cco w qdpm t22./hvmz5xlid cylinder and her arms as thin rods, making reasonable djt.h p52 caxmqw22.z o3cmv/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 body.   

  You are designing a clutch assembly which consisgcvs18aw 99s.bqg/l t 2qfavj5*oa6 fts of two cylindrical plates, of ma2a6ovj a *wc5/ b1gf vat.g9 8sfsq9lqss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fig. 8–58.1b *8 rdedd6bw8-alny What is the minimum value of the vertical height h that the marble must drop if it is to reach the hig8ea6*d 8rl-wb d1ndybhest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do no0,fp : zp,w xh)wv(oqpt assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spee:jo49fvp yl z0d uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleratov 0zyj plf:94ion 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