A bicycle odometer (which meyvo6.j2kow9k7up.c :fv t l)m sxo59easures 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-inc wuktpvco269x9j)eo.:y57 moslk fv.h wheels?

Suppose a disk rotates at constant angular )bk 5-lumtnb,nd dl36 velocity. Does a point on the rim have ra5b,6dbd3u)k nlt -n lmdial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be desj; jr hwe/k*,fcribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thatb, ( -woo)ei ,wuu.9lchmh3bn 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 bl6hv3 o(lko8qf v3z s s7b58mhands behind your head than when your arms are stretched out in front of you? A dimv(68l3 lz 35ofkhbq ob s87vsagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel afll,-l s vo( e50k f,b/mblii+nd three at the pedal cranks. In which gear is it harder to pedal, a small5kfi(iobv+lsl,/- b l fe ,0ml 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 sl/tc0) x 0kgmdafzdu2z6aqw ) 4ender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of/ 4df k dwt )mau2)xza0gcq6z0 rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers h;vo*) a dvr*e(Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero,rza+.pj e 7o-c 0;i4)dalhg uv is the net torque also zero? If the net torque on a system is zero, is the n+erduj a hz.;lcgav oi04-7p )et force zero?

Two inclines have the same height but make diff- ys-1y( vxqpjerent angles with the horizontal. The same steel ball is rolled down each incli1 psv-yyx-jq (ne. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling gu7 x(.yelxb2k)to2m)x :jxai *o hp4(from rest) down an incline. One sphot al:4xxb.72xig ku )y hp2x(eo* j)mere 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? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mareej 6yd98pe/qg ( ,jass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at th9ery/,ajeg(e p 86dj qe bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum3c ;yayf u8c:b are conserved. Yet most moving or rotating ob3acy y uc:8f;bjects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, h2o f9uzm4ks c1h3r0+ad*ssooow would this affect tozm+r3 c9sdsu0*o2foa k14hs he length of the day?

Can the diver of Fig. 8–29 do a somersault6e+x t-rs v( 7 3khr9k1sdleqz without having any initial rotation when she leaves the klvr hesx 9tk37 (rs6z1+de- qboard?

The moment of inertia of a rotatingcgbdq x40t*)mmkn 4vjch.i ), solid disk about an axis through its center of .k40j)qic * )dc m,hb4v xgntmmass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in ea a4dn9o d(szhxac w35l a2m84rch outstretc3z98nd o(54xsdml4a ch2aw arhed hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identict ;ee :vqshl km4k+*v0.e, kjaal and have the same mass. However, one is hollow and the other is solid. Describe an experimen: kevm,e l4+qa; .*jtkskhv0et to determine which is which.

The angular velocity of a wheel rotating on a horizon28 ieergel n f-uwq-qs*9x pds3gcp,uo 6u971tal 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 inq1g,cp9 7sw egof-le8-3eur* s xiqp9u 2ud6ncreasing or decreasing?

Suppose you are standing on the edge of a large freely rotating zm:pq s-y u8.+fsz2el turntable. What happens if yzyp q2smfeu8s z: .-+lou walk toward the center?

A shortstop may leap into the air to catch a ball and throw i a4dovqdmmab *3.5j8 ft quickly. As he thq43jf mmob*dd av8a5. rows 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). Explain.

On the basis of the law of conservation of angular momentum, discuss why2lt :5z+gc )s4u8s u7y+ cz tojqb(qdy a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller ca27l8scuqt ud gcbo:t4)5 yy s +(z+qjzn operate to keep the helicopter stable.

  Express the following angles in ra; ik9eth*mhp3s7ub d( dians: (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 ofz5jd*ca )tti (b*yr3c an amazing coincidence. Calculate, using the informatio3t* tyad5)c* br(c izjn inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergen f5uwz1r5, dqs at an angwq5uz 15 nrdf,le $\theta$ (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 r;t9dk i g4:d:.ig yxmtpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. mti:; .ytggd9i4xd k :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. .fic3l bp5 imrz5*of20ddm bj7i9 z .zIf the ball makes 15.03 jfdz f ib.z or*2l.p07iimz59bcd 5m revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolution8u;7jc 6x(f a ckp(kwr sy+s6zs do the wher8z6c a+s jkp(kyu6f(w7 ;scx els make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcull )lx 7y-m .fz u8js; nzdtvc+fuo*t:-ate its angular velocdt;z7 u-.+sf8jy-lz:*lnmc)v tx fouity 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 revolution inx :0oa: tqybd nz0-hi- 4.0 s (Fig. 8–38). (a) What is the-b ohi -:xd0nty:qa0z 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) a28wxa :nr klxx-ifkbk,1ga: i/7p* zin its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin3 qm hz2ykb:l6x,;y ipt
(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 o .9pxwyjv4 .z03whyz7.0 cm from the axis of rotation is to experience an accpxw4yowzjy3zv90 .h. eleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its centehjuk8q+h;p zmc5(*t8w /cu qdr from 130 rpm to 280 rpm inh/+;8*j8q q(k5 d uzwhtcm puc 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 radiu :kw6+d6x jzxbs $R_1$ 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 spacbg37zu6a(mj *y /b hcpeak4s u b*r5iz;(k1wzecraft 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 rev6hi kzga uup5akw4ze(zm3 *s *br(b/7ycbj1; olution 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 fropk8 z,lbsiu1, m rest to 15,000 rpm in 220 s. Through how many revolutions dbu ls ,pk,i81zid it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm ,)7v fpi0 a*gex lm4 xo0q5mr+( htiylto 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flyi-a--pjekq) zung highspeed jets in a whirling “human centrifuge,” which takes 1.0 minaj-ek)u-zpq - to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6. p: d-)8m.nn gt3+ju( qygxzea5 s. How far will a point on the edge of +u3 gnp(qe-ta.xjgy)dm8 z :nthe wheel have traveled in this time?    m

  A cooling fan is turned o9, 5 jl2o5b v8nvexzscff when it is running at 850rev/min It turns 1500 revolutions before it co z5sxjl2v,c5eb vn o89mes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed un7a5.e8 qsyt j6zra8vx iformly from 95km/h to 45km/h The5azvr.8 x yj67sqae8 t 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 as the car reduces it/4ucx xga 3n5ts speed uniformly from 95km/h tgnx /43 c5atxuo 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 pedal2loz2qgc059/ ytkb xz7cw4e b5jxb u+ when climbing a hill. The pedals rotate in a ci9kj5cgt5xu722z0c obb qzw / bx4ley+ rcle 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 exmrw( 7t6lm- g2;esz,3itq w 8xq9ptand of a door 74 cm wide. What is the magnitude of the toraqi(mz2t8 -exxtpw 973w ;rs lq,6mtg que 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 thedn;4 v3r4y.ojumw4eg axle of the wheel shown in Fig. 8–39. Assume that a4y4.dm;w jong evu4r3 friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are atta1vbaky yeol5j7zz/ew3x 6j (-ched 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 th/bze6yl(a jy k-1x v37oe5 wzjen released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require jb;k d007m pth7gv*r gtightening to a torque of 38 vg7m7 0tpb;0 rdkgj h*$m \cdot N$ 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 sph,89 k 1sm/xcyaz xr/wkere of radius 0.648 m when the axis of rotation is through its cekc189m /wxrs xzy,a/k nter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The aa.wnyr l8nfiv .g/.8rim and tire have a combined mass of 1.25 kg. The mass of the/a l nrg.v8a8i.n. yfw hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in aq,g*iwu 0 )s 6fvgowh0 zz(ntis 1c7b4 horizontal circle oh , gnw(v6o cz0z0qt4*7wif) 1gibussf 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 fnj)*f r/ye;-hxd+ *lruj/mr constant angular speed (Fig. 8–42). The friction force between her hands and*j-jfmhrr*/)u ;n ry xf/d +le the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Figps+*yaqv,/u w/skaq3 . 8–43 abk v3 qyaps/u,wqs/+a*out
(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 atomb2m:r74r . yfty:lfcxs 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 cyl r+ychov3 cx9l1;5nqs indrical 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 sty 3n5r +c1vs ;qlx9hoceady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a rax3-pzqvr m8-udius of 8.50 cm and a mass of 0.580xu mz-- qv3rp8 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swinf jv:6+leey/szw+m a( gs 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-roundr1r63v51g ga9 o klfhn 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 afovgk315h1nl 9 6rgrradius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 1q(shho( rjn y: md(v910,300 rpm is shut off and is eventually brought uniformly to rest by a frict m:v1hr n(h9qsjdo ((yional 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 at 7 :n 0etuxaq1,t$m/s^2$ 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 actio1td6lv ah) 5yvn of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball y6)tla 1v5vdhis 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 thin r,rqo c(;rvr 9ntg: ffw1n.y- * zi-cwgod, as shown in Fig. 8–4w;c9vcw.* rito y(1rz-qf :n ggrn,f-6.
(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 m:lu49a+ nigjo ee 69yjhl8j5two 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 t6o.vv;8 c+ npdwhw-s-yyu q2u urns (revolutions) and relecvso.;qww-8yd-h 2puy+v6u nases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia jjcnu7i ;3 z5yof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops i wvtv3.u3c2 edxm)3na torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down a la+nk z3v (fys i4xvgic:xpk 6o(l++lkpqn370hne at qlk( 6i:3nixs 0+ k7+4 yzfkpv l(vpcn+xgh3o3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as th/jvwea.t0j 4k wm* ti9qmf5ig71aw9 ge sum of two7fg4 igat mke qw 9*w.0a1/j mwvjt5i9 terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has upw;.0b t .vpitm2uv) a 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 v;wv2i).uppm u0tbt. 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.8qwsyup 3 w6e2qt/y4c- fh )9gn0 kg starts from rest and rolls without slipp)w3/e4c -puw9y n t2g6sfyqqhing 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 tipx:,ib 28fjzku29 ;py(c fe lqd. It starts to fall and its lower end does not slip. What will be , 2cpj fbf(:yx2kq;9uz dl8i ethe 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 0.210patxqd(200xdih khgk k8ej ;(x;qi21 -kg ball rotating on the end of a thin string in a circi82 2 ge h (xkpddx(k1i0akq;;jhqt0 xle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentlv ug7v5fu h5zjl/* c9um of a 2.8-kg uniform cylindrical grinding wheel of radius 1cu7 v j5l95gh *uzf/vl8 cm when rotating 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 side, on a platform that is rotating at a rate ou+-6whej oo)4d+h-kve b ,pt if 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of roo4eoh )di j6uk-,vte+w- pbh+tation 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 mom: azt0acqxg97ent of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position,x9 a07zac:gtq what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation ratd-e3kg viy7k n;e jndw/(gwzrpo-jna j 402+9e from an initial rate of 1.0 rev every 2.0 s to a final a j; -7won+ r(d/v g4d-gp3y zenjjwk0n92ik erate 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 centeri/ 5a61up dfr5xpsal) 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 fres/1ral ipa5x5u)df 6pquency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure7;nz965:3( f8ryip rd ;fsa t zbphwle skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Eartr6wq3t5ca 9ve, l8bjyh
(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 a4u9o(sg1l ef/h4gxu6wy,tf inertia I is dropped onto an identical disk rotat 4 g46x1tfyeagw hs(9ul/ofu, ing at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ak1e1+ qkg)(3gzd+uvft7 uyajt 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 2z5vs5jwhg/yu x-g:y of a rotating merry-go-round platform of radius 3.0 m and moment of inej hgsygw-z2 uyv5 x5:/rtia 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 rotatiaka z 6vle1 0hugepa+ rp/p)9-:hz; ujng freely with an angular velocity of 0.8 6jh -p0: uek);zheg paapar19 z/v+l u$rad/s$ 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 evensw6uq( :brc *d*h(w .lwn1+ lwfq 4lxefitk*;tually collapses into a white dwarf, losing about half its mass in te(li*fb(wlhws*wf.1uqx w rc*;6kdn:4tl +q he 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?(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 windh x2np whpjnxv)x;/;4 s 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 egw e*b9t *bkuduq429l ns08g $ 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 withouk70sxcwmypw4 9l w0v5 t friction. The moment of inertia of the person plus the platform v4w00 ylm 9s wx75wpkcis $I_P$ 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 stu; 7fgfex/ hoa( /-zioands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momeh ie xuzo(ag;o-f7/f/nt 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 rollsxoth/ me h47i- on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of them7h/ otehx -4i 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 afe2q k.a**4ht7g6is )isbgv the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to itsssh2kag4gvq*)f 6ibe7.t *ia orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at ,zj.4cdss; s .u7nq zta 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 unifo i r w5:owg6r+w,0xiw iee;f1mrm 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 delim,reo i+w0fwiix: e wrg5 1w;6vered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical di5nzcd12k j-et smr, y2* fwmv9sks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy tn-ktjeywsv* rcm 1f9,d 2m2z5o 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 speed of the rearep+qj ;b* xn bofl;;/f 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 oeu 96pogbzc ,;bim3cc6-hzn4 ur Sun, but with mass 8.0 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 radius 11 km, losing three-quarters o6 izczoe,c;umhgcn b 369 4bp-f 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 energy stofl e4j;fae5 e3(uw +afred in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindric3+f5w eeuff;e l4(aj aal 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)*d -besfbry7 $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surfa )4- *c0vws0lr .s/joovz qpsvce 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/paq +um5krq9 ,h ,2 t2staaky2+ysn h length L can pivot freely (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 2hra y s 25hm9uknstt+k/a,a, q2y +qpof 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 a3 r (s1j)p;oaq dzz-c+gl *4eoidch 3is standing vertically on the floor, and we want t)zpasj oaohz*e -1r34cqd;ic +3g (ldo exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat r;n-mxk0 zliyeqz( x06 oad is making a turn with a radius The forces acting on the cyclistx-nl y6 0mex0zq;(z ki 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 into a sling of length 1.5 zkj3xv2idrl k9r*k,+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 fexz , 2jrlvd3k +ikkr*9at, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms a+(kuxs7nao7rer;i 6v s thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched au(x a6ir;knosv+7e r7 rms, and with arms held tightly against her body.   

  You are designing a clutch assembly wh9:f2gag8jb nk ich consists of two cylindrical plates, of m9jg:k8 bgf2 naass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 roug7ldotpt ,*enm,.n 3o5 toqte3h track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the*d7m 3.tq3o5,,topn tntloe e track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not acj mh+cn7ykq / h***cussume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unif;e j r v:xbv0cu.uv;e(ormly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each ve.(0b urv u;;:ecvxjtire? $\approx$    $rad/s^2$(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