A bicycle odometer (which measures distance traveled) is att/i/tfn /cfb,p4l69py/ ugaxk ached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicyckfcai,4g/ uy//xpptnfb l6/ 9le with 24-inch wheels?

Suppose a disk rotates at constant angulkecw g1p23 +vxar velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/x 2e vpk+1c3gwor tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of tglwt 6*rt dr* o,1z8jpljws* 3he angular velocity $\omega$ Explain.

Can a small force ever exert a grek-fy )5o ge9dgrs77elater 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 dnl yf a8dpg3i,9)s /ljq5m4mdo a sit-up with your hands behind your head than when your arms are stretched out in front of 4,njg/f sy 3m)i ld9q5a m8dlpyou? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wn,iaauabeg9 bgr2q)n 8.xko gmy l 6a 290qq49heel and three at the pedal cranks. In which gear im9enqr2xb aqa2ugl .a0ga9yo 9,n4 6gq b8i k)s 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 front sprocket? Why?

Mammals that depend on being able to run fast have slender lower qhmx kl sbnvd+2/ -07,pdps7e legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis dl2ds +m qe, psvp-hb7 k/x7n0of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carbdr/ kcim. (5ury a long, narrow beam?

If the net force on a system f2oo)qfwl o56jn q,s9is zero, is the net torque also zero? If the net torque on a system is zero, is the net fo2,onq59fj ofoq w)6s lrce zero?

Two inclines have the same height ) y0(qf;-20iub;cieztt pulrbut make different angles with the horizontal. The same steel ball is rolled down eacu yft;upt0ieli 0)qz 2(-b;r ch incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaep. vyo8 0(u x:sueemnyw3;(mneously start rolling (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? W8ev0umx.3n y ps:(ew(o ;myuehich has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and tya(nw((w4, g yhxjk3 nhe same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational Kj34nn(wwyx(k( ga , yhE?

We claim that momentum and angular momentgg rda4wro) ns.;3q2s.5jfgf, qdd:tr rmy*/um are conserved. Yet most moving or rotating objects eventually slow down and stop. Explainf .,q )ao;rd rt:ssgr*dqwmdr3y.n gj5/ fg42 .

If there were a great migration of people toward the Eare -6s0ig3f.aucc9 vx pvr8s7x zj n;8fth’s equator, how would this;7 0fz x8gvarn6u8e9v scc.p isj3-xf affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any ini(r3i rih55 mdhtial rotation when she rd53i(rmh5hi leaves the board?

The moment of inertia of a rotating solid disk about an axis through its cehb.xg7lgg .)jbnr8s, nter of mass .sbngg 8bgrj h7.lx),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 sittingsm jqmf7/;8qw5e l07t n,ip jt on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decreaseli / jqnpqt w75e fmjt,807s;m, or stay the same? Explain.

Two spheres look identical and hanp005ujxyxd mm+b :1pve the same mass. However, one is hollow and the other iy+0x0: b1 xjdnmmpu p5s solid. Describe an experiment to determine which is which.

The angular velocity of a wheel r9i1z wqm ;lzaz1; hmv*otating on a horizontal axle points west. In what direction is the lz mq;1zm; *v1al z9whiinear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a largeultk:+*mt pi2 freely rotating turntable. What happent m:i+t lukp2*s if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly.*pd3p:m6fx( 4xbbm *-kea5 (7 ktpf1uqcxdsr 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 o ckr me1x( p(ad*mpd:x bsu5q*t6pk4 3 bxf7f-pposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why 7y5 o:zxvh-4gryltlah+;4cq a helicopter must have more than one rotor (or propeller). Discuss one or more wq 4 t av-7lycr5+:hgh4 z;oyxlays the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (+ p.8u8gvof vta) 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 coinci65+t ssrg u dx/f 0azo.xm/-jndence. Calculate, using the information inside the Front Cover, the angular diameters +-ojfz d/n.5s 6mux/xgstr0 a(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. Th c)tj q1py-xvu i 2o0oh7s t3obim;j9)e beam diverges at an angl7t 9o)3 ixstji0 yo1m;uch bo2-p) vqje $\theta$ (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.9g xu)cv:vev47vxyg7*l xt d ls/o aie+;r).h When the motor is turned off during operation, thexa)dels: ov4e 7.vl;r9ixvgu7tx) *+gv/y ch 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 the balzk2an s5w. kr+l makes 15.0 re.+nz2a k5wksrvolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manbq9lss+j01ye::z q gyy revolutions do the whzsb+: 9j y1eq:gsly0 qeels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its ang;z0fayvkme-; 1*qb)2, r ym(htss awmular velocity0h) ; 2 ;(yms r*e,yvmmazqkat1 sbfw- 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 qgqse:e3s xq *h+)24cxci .ek complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear siqkx:cse c)4sq +*3e2. qxhegpeed 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 ths(2k ibm7me f+ip2 r3ge Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed9 4t77qkcvkek(c+4h3bk oghe of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 6ykviz5-4gcl/l 1et;wzd z:xcm from the axis of roxig/ y -;d1lzz4w5:6zel vtk ctation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 2*7d0xf ug5 pxa 34hgah80 rpm in 4.0 sxa3xaufhpdhg475 *0g . 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,2 *pofpq b5rs $R_1$ 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 Apo .*zc(q.w+(*f ue dudyj y.gh9nx x;hdllo 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 d(9(cdy*d fuhyx uhxnqejw*.;z .d+g. uring 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 in 220 s. Through aya;g.ok/wbl* /vue.; iyz z0how man.ui yozl0v;;a/k*e .a/zg ybwy revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2eb c5t9)p ee2stmh h/(eidf hbg*f8:*.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 2nkforw6 b2xp3un ).jfor the stresses of flying highspeed jets in a whirling “human centrifuge,” which rn2kpxn uf)wo3.2 jb6 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 accelerat6elr k)pzkubn:n82j 1es uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel hav1r8k2npun z6 je)kb l:e traveled in this time?    m

  A cooling fan is turned off whenyg8skgqb5 )xhb,id : f9k nw -for.;+g it is running at 850rev/min It turns 1500 revolutions befork-k+b;5.ifg:gn9br,8 yd ohsf q)wg x e 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 m,5; mc7n ,76pvltksp. hq1ripb(yynmake 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.vnty .p qpy;1bs7picmn6 (5k, m,7lrh
(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 as the car reduces *blhszs/s d+ur) ;p+uits speed uniformly from 95km+ plshsdb+su;r) u */z/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbdyq e3mjrr; (j:b(v p3ing a hill. The pedals rotdje3 vm jr:q(b3 r;y(pate 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. What9hyg,kt ii 2t+ is the magnitude of the torque if the force is exertedg9ih t,y+tik 2
(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. Assumeq3x 3qqows* 61)ryti e that a friction torque of*ex1i33r y sw q)qt6oq 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, axlnyg;fe 5d, *re attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in t nlx *,5fed;yghe horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylind1 th mj, wgo-btm34mx9er head of an engine require tightening to a torque of 38 tx3jwmtg41ombh, m-9 $m \cdot N$ 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 spheris5a:4 w uuc+a* 8i9*opmxlyg e of radius 0.648 m when the axis of rotation is through its c i+8p 5oagylc u:swx9m4iu**a enter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycl3vk /dj:o eso,e 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 ek ,sv: dj/oo3(why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, ls.edfokl*0 5 eight rod is rotated in a horizontal cid. l*efek05osrcle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular spw- w/v c-s)kjunte. xrz(,zd-9eh k;ueed (Fig. 8–42). The friction force between her hands and the clay-)u x9.u-kr ,ztvk; ecdj/w-hzwns e( 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 arr li)xt:qqe 4x8(cfy6m ay of point objects shown in Fig. 8–43 abtx8f 4(e: qci6lmx y)qout
(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 whotxzwwxy2s-/ 5se 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 cylindrical satellite spiu/i :cxk uz(wcj/j) 9a7:z 9hphgy9qhnning 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 requic: ik)xhqu/hy zw9(zc:ja9 9jh7p gu/ red 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 a uniform acvpnzo( c wk8./(,lwcylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calculacn,( v.p acw8k o/lw(zte
(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 sw+1 wr e/c2a2okq*kcv;vh*b9zguy o,r ings a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-roum.:md-atzc ( 82 mnhfjnd 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 an(jdm.fmn amzh8:2tc -d has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and40xynrgn5yk4.sb3r gx7p7y* ialkn6 is eventually brought uniformly to rest by a frictional torque of 1n 7aklgny4y*y 6 bp0gkr47ns x5r3ix..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 accelerate8 cl1ef:zat.7a(s s:ekjz 5iv s 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 baopxi)frp3 * m60a c n718dujicll is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly frouonij7d8xipmr61)0cf *3a pc m 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 + f e s5rqtxca:/czgu(/1f*tvbe considered a long thin rod, as shown in Fig. 8–46r *+sc(zg :ef5t /xfcvu/aqt1.
(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 masg2dr k9;q i; z):jdefyses, $m_1$ 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 *d1 eh1 tpunlsd; xz8)the hammer from rest within four full turns (revolutions) and releases it at a speed ofdl;p1t*n 8z sdh 1u)xe 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 inertoidwy1d( vn9;. c)ezxia 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 a16 qvlo5c p0ma 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.(ivg( j60x oavqzl3 i1+nug:g0 cm rolls without slipping down a lane at 3 lg vi+0o36ujg(1v:na z(xiqg.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the su9 y lhn(h,bt8swv cl3fp8m(p/m of twtmy,b l(lpv/c83h h9 fpn(s8wo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round hasb+cj3p h1 s4sas8mv)cuj5 1m m a mass of 1640 kg and a radius of 7.50 m. How much net work is required to accelerate itm1j avpssh+5umcs cm)34b1 j8 from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and masslxiy6, skn(f3 1.80 kg starts from rest and rolls without sl n fliky63,xs(ipping down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It starts t6ldsnyf/d p;hc 9 z,k r.jgw27o fall and its lower end does nfrz67.dp,k y wlh/cn; j2sgd 9ot slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rjzfg. l t/1+x.8grwhy* tzw z*otating on the end of a thin string in a circle of radius 1.10xz8wzh.*1gz+tt /.fljw r*gy m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform ce nii .3;ja/4d m vats,umgs0:ylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? .v3u/sm :4mda i nj ,;eag0ist   $kg \cdot m^2$
(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 at a rate o8slqh7c/4z9 k r(5/ r vfxt1etgattn-rg)2e sf 1.3rev/s If he raises his arms to a horizontal position, Fig. 8r 4tt9svkah /x7l 5ts/gteq2)r1enr-c8(f z g –48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of inertiat76x;;so rbzhku:esw+t 4yl 6 by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck pos6y;;x6zw esu+o bk7tl:4ht rsition, 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 in) q gmh6)mt7wsei5,i litial rate of 1.0 rev e, gtwm7) hl6m 5iseq)ivery 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 idmzco, sxep j5n:6i2.ojc7n*ts 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 frequencyec x5j.in n*2c6spd m,:joo7z of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angulao(s - rdt:w0u1 xbk+car momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular mom-lbmv ( 7qt7us9 kh .1h,dccjoentum 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 inertia I is dropped onto an id*7hf jsvu 2lw,ij,g w:entical disk rotating 7vwjw: gi*husjf ,2l, at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ato d xaai36:z8y)l th.f4x pr uqk.i7;x 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 t 4x0mcx9dpvz9 he center of a rotating merry-go-round platfor xv4px09cdz9mm of radius 3.0 m 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 f;oa(/c,1ot5zem ikgz /0ve as reely with an angular velocity of 0.8z aoziov(51 t/k /gea, c0e;ms $rad/s$ 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 collaps ,w:h9z s, msvpb-(cdces 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 angular momentum, what would the Sun’s new rotation rate be?(robsh(dmpsv9,: z,c-w cund 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 i/zn .yp cooc(j+(y*9fq db sv3n 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 2 p6z;:cazt2u z,f 00kvoex6sy: pugo$ 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 withofd*w*u :je/u hu0+ .pp cz5lhwut friction. The moment of inertia o*+ phc d5: u .wz/u0uh*jfeplwf the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-round tur xa:0uzeb56clf i7 ;onntbn:o70 l6 izcae;ux5 fable that is mounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the groogyohz 6h6rd8n8vx (1und with the end of the rope lying on the top edge of the spool. A person grabs the end o 1no8hxdryv( z866og hf 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 Eartho0k+t1h g z;bp such that the same side 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 a1go+ 0b kz;tph particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rue):rw iin, 3 pc.y q7ys5nye8est at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquiriy8vh p0 mink/x2j/8d es a rotationalyhx/nd kmvj2ip/8 i80 rate of from rest 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 of two solid cylindrical disda/y*(3 1k0 uzry3wxpit gz5sks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kgz3 ia gyyku/swt1( *0rpxd53z and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speedz/nhfp1*pio 6 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 r:.bvq 9*xpz m8.0 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 :m 9r.zvx*qbp 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 l ; 02aqw-knichc xy58i0;on oautomobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a c0yia0xql wc n;h;-i5ko2on8 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 an 7 mqqta/ jqcpx22x z9nma-c) 6$H_2O$ 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/4enf6:t-qxc:l x en p,h 2bwq:mv q8b 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 uz:o8p yps/ lyt89 m:kL can pivot freely (i.e., we ignore friction) aboutzpupk8:s/ yoly 9t:m 8 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 the floor, *56kg2e vx eixand we want to exert a horizontal forxx2iv5e*6g k ece 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 maks6)kk a+ht1qyx5m k o jsz0,5xing a turn with a radius The forces acting on the cyclist and cycle are z1h5 kx5kxsq0oj +ysa t6m )k,the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begyf6a fs7b4ne/*sxz )7rwoyh( ins 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 whe(nazw hyy /xb4r7s6ef *osf)7re does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid s5j ;j*wr.nhuh6vdwo lu-3 8qcylinder 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 hel5w- uhd v6.8sqw;l3j*h njruod tightly against her body.   

  You are designing a clutch assembly which consists2f jm+tmb 1uga y 6 t8786boq6q:huy 4oqerf7p of two cylindrical plates, ofo oa4:y7h7myfb16br+f tj u8tpq8mg62qu6 eq mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of Fo9 ca*r6/skjlv) r9xx * govu9ig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it9gc v* ulxax / jv9or)s*kor69 is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumezde1d, yqk0 q:5.y mr(r nags6gyk; 5b $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unif;exursfa5* z 5)m.wewq0 6bxrormly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acru 5* 5)zwfaxr.s ;q0eebmwx6celeration 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