A bicycle odometer (which measureaqyvy3;z;()-zqg-8t y krvzoxg3 hm -s distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it o-qm3hvzx a3ko)yz- g ; q(tg-;rvy8zyn a bicycle with 24-inch wheels?

Suppose a disk rotatee5kwl1h:q(m vqc r: -qs at constant angular 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/or tangential acceleration? For which cases would the magnitude of either component v:5:e -(rqqc1kwqh lm of linear acceleration change?

Could a nonrigid body be described by a single value of the anva+ wvzkut7hvxp8hz //,p c z;we :;e(gular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a v.p/svt n0i . )lx5wlmlarger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head than whm ;zyulje2j/ 1en your arms are stretched out in front of you? A diagram may u1lz ejjy2m;/help you to answer this.

A 21-speed bicycle has seveem7 y9zbi;czk jb- o+d7 cj.o;ee3yifnd /.6 wn sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is itic6jd7yw-oez. bfmy39nb.+dk z /j7 ;o ice;e harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run 7cw+x r29 gaeryg.,yb hxo6:bfast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution y b7c r:gg+29o, xxb6ywahr. eof mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, n80k6w pc/dxbq arrow beam?

If the net force on e:oz2+eqv6l8 vw gh :oa system is zero, is the net torque also zero? If the net torque :ove:o+w l2vh8gq ze6 on a system is zero, is the net force zero?

Two inclines have the same height but make differpf:b*(4kftje s,rs,l :* qsvxent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will t ,*s fj4lf ersp:,s:qkv*t(xbhe speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (frd vwq *oa1oal(s: 4y9iom 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? Which has the greater total kinetic energy at 4il*do:y qaw(9v1s aothe bottom?

A sphere and a cylinder have the same radius and tho nlrqc 7e86l(e same mass. They start from rest at the nc o8(6qe7l rltop of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular x)8 a)cqcp.bla,+nlw momentum are conserved. Yet most moving or rotating objects eventualq.bnlpa)wa ,lxc)c +8ly slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woxd x x3s6/ofb8uld this afd8oxsx b3f/x6 fect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having anyg-fwqv zqlajo *6+z,u8 z 3ln; initial rotation when she lnlazzw6f;+quj gqz38vl o- *,eaves the board?

The moment of inertia of a rotating solid disk about an axis throltr7w xhd gy10w90xo 1ugh its center of mwx1rol w091xg0dy7 htass 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 sittinuy4 u2qz1f 0 k4oo9asyoikm,+g on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decr42k+fou4usmq, koz1ya 0y 9 oiease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howeverk.i9ek1 cujkk cy)ref,g m, *-, one is hollow and the other is solid. Describe an experiment to determinecki. k ,grmkjcf 9y*e)- ,uke1 which is which.

The angular velocity of a wheeeos prig4+1 ,uk3qqr 7rkno59l rotating on a horizontal axle points west. In what directio+r 3rk45or,7 gk9siq uno1qpe n 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 decreasing?

Suppose you are standing on the edge of a large fl(+. nc(qub zjreely rotating turntable. What happens if you walk toward the centl(nj. +zcbq(uer?

A shortstop may leap into the air to catch 3yz1ppiv)lvqh 2k3 d 2a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8 12dq)3ph2k p vv3yzil–36). Explain.

On the basis of the law of consbuw683 o8 x-yu,cucd;bk 0ejsbq* jl;ovy( / lervation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller ( -;o8q 8 b s,jbyec6 uo/kbuxv0;luydc*lw3jcan operate to keep the helicopter stable.

  Express the following angles ikg+yy+w :8uu in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calg5q w)cc3okdl 36q .nfculate, using the information inside the Front Cover, the angular diameters (in radia5fkoq w6g)ld3. q3 ccnns) 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 diverg ew8g tfc.knjodrs1:7 -4oisc mb +,u;es at an anglc4wbrk dis- 1t: g nc,umoe 8;o.+7fsje $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When tmfs o;b )uri*8c9kjj 308hwjr cuu32fhe motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelukj*f)o2ru 9jc;j3um sch r8 fbwi830eration 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 ball 0v37vt:wvq/ske r qb6makes 15.0 revolutions, what is its diametrqv evtbq/3k70 6 vw:ser?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How q.v ,qpc8cxcs;c72n 2 ijg2 ksmany revolutions do the wheels makc,kgcv;cs p2qj2i2 sc8 .7x qne?    $rev$

  (a) A grinding wheel 0.35/; m,1tubtss-e 2qqwa m in diameter rotates at 2500 rpm. Calculate its angular velocite mas1q2t /qtu;ws,b-y 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 in 4.0x,4 jc(yw jh)tiy 24hd s (Fig. 8–38). (a) What is the linear speed odjyc,24(h ijyw4 t)h xf 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 osejkvt , +;v-- 5x.+p-inmm o/ctidaof the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a points+ a.m gf(kv+7tzkqe5
(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 7rp c ;hp3knr0ux 5b,s-.0 cm from the axis of rotation is to experience an acceleration of 100,000 pscn-53 r,k; p h0xurb$g’s$?    $rpm$

  A 70-cm-diameter wheel acck hbj21wd5.;u 6k6o d .w+dchujcg*buelerates uniformly about its center from 130 rpm to 280 rpm in duwkw cco1; . .6g26dj u5uh+kjdhb *b4.0 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 radiu61h nhrzj;z6m 01lm y h;,ngnf4tom )ls $R_1$ 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 Moog- ;tw;q tgtd3nw;c b a8i)9pvn, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to dist;w-3d; ptnitt 9w8gq b)va;gcribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s, 7p 4/o2ynffa tti)00d8;mywplo z mc. Through how many revolutions did it turn in,lyi;8z4/0fpd7) ctot2f mywn mp0o a this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcula7)h2v p5nou jw4ib6qw5:u ons.jp3wo te
(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 9r 2hto:;mlbhs0 j.ca jets in a whirling “human centrifuge,” which takes 1.0 min to turn t lsh:m;rh9j0b2 c.oa 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 inr hr,id7tt j0; 6.5 s. How far wil hi rt;7tjr,d0l a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is r a.i(: rs2g1 rpbaxzxm-2hi* lunning at 850rev/min It turns 1500 revol(i2:*gmxx b .2z srahap-1irlutions before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutibvh i3itfq 3j)-covgizex-rz0) y,6y 0q, p 6cons as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a dia,xq-qtizjc)z,30y-vep3coiyhg 6 vf i6 rb )0meter 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 redue, rkdw873z wkces its speed uniformly from 95km/h to 45kmd,7rzwek3wk 8/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 ped5uy)+ to5r:qn -l8zx v pizm+nal when climbing a hill. The pedals rotaz-rzmt5+:p5 n u8yv n +oiq)lxte 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 ;j ycc0nvv*lw *2 h8omwide. What is the magnitude of the tocvvj08*w;ln h *omy c2rque 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. 8–39. A ky*gbv 6kr4uf6pb8n8ssume that a friction torque of 0.4pn64fy8 bgvk k6u 8r*b $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the endgzl,/zrar 98z* dc x)feyh,-bs of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then rabh9 8clr,zgdz /)*r-ze,yfxeleased. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head )s- r6clgu+ ujc5 *lxqgb m3b*of an engine require tightening to a torque of 38 x3slbu ccq 5r gl6-*)+gj mu*b$m \cdot N$ 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 rahhdk9ktka,zl w z:; 7z4 vj+,gdius 0.648 m when the axis of rotz4,;lh zkjkk7z+ gdhw,ta:v9 ation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in di).:q,aca 5fy akgi m9oameter. The rim and tire have a combined mass of 1.25 kg. The .iag ocq,: ama9yf)k5mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod , fu0g;+lzmx5/c ; las-z lcbgis rotated in a horizontal circle of radius 1.2 m. Cal/;mccazfgb,05-sx u z;+ gll lculate
(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 a5d386tts6 iitd :rwvangular speed (Fig. 8–42). The friction force between her rad6twstt63i vi58:dhands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown*4g/i 0p.v mll i98aawo2wwvj in Fig. 8–43 abowio i9v*j/0 8.l wmaapv24gwl ut
(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 whosezxj jh6 4.8f84blxx yn 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 spinning at the correct rate, e q*3:8lx+urunk5n,)po vju pdngineers 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 in 5.0 min:jru8p,+) vu nlupkqn5oxd3 *? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder w2s2gf1)x+v7)1 jt q:c ku4zjdhka hc iith a radius of 8.50 cm and a mass of 0.580 kg. Ca 1j2i)s4 vd hk+hcug cq2jat:f1x) kz7lculate
(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 from re) hi gmpu268.mr 0yjvhbu:+* irzet 3tvb*x9mst 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 smalwnd) rre28gy( mw.szi1 f j:cbw:;u v0l hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the toy0u8 ez c)i2rs: .jmw(;r: wnvf1wbgdrque 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 10,3 ;/ o:4lmgcsum00 rpm is shut off and is eventually brought uniformly to rest by a frictional tor gm/ clm:u4os;que 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 u/3rbfber n kf:+4 wfy9 3)n.lni2dty7 $m/s^2$ 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 tdule:o;;joq 2hrown 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;jo d2qleuo ;: is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can pbor)q 6t2(0m+pv jtzbe considered a long thin rod, as shown in Fig. 8–46.zj+)tb6( o2qm vpp 0tr
(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 ota-wb d( 7o4ucf two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four fullf2lq rqy-e7+g g:.bc l turns (revolutions) and releas gf2q: q+.byl7el rcg-es 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 momenb567 w2tacr xj,va7k zt 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 torque qut 091 yoe)oiuzt,x 3of 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 radiuspe 3ref g7v16 tki8 k:zlx*d7b 9.0 cm rolls without slipping down a lane at epkz16g*rlv txbe 37 dif7:8k 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of tg*m8i :qgcdk8 w88:gkiqg* mcd o 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 a massxagbt6n+s *c 0 of 1640 kg and a radius of 7.50 m. How much net work g c *+06axsnbtis required to accelerate it 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 cmaco47k+ fo9jibjkvj7, q 2rz; and mass 1.80 kg starts from rest and rolls without slippi,;jczo ji9+krj 7q4 7ao2bkfvng 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 v(e5nmj) o,9zw8 wlrofertically 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 n9ofzm8,rlw o je()w5? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg*vdyudnx 2:ev 3x.w ) nctk5( zmdz7mq +7yrm2 ball rotating on the end of a thin string myvq2xu7)t 2nmz.7 3cywdd+dv*e zm(nxk:r 5 in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grn q,jahk ;1pw 4e40ielinding wheel of radius 18 cm when hejq0pl,;i e1a4 kw4n 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 plats2c 0/ uk4dcifg6gx 1i/s8pqnform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal positioc4i0kq 2gx 1 snfu8s/6p/cidg n, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce hel9ej*-p*tap g r moment 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, what is her angular spee -jg*a9lpt* ped ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can incg.1 xlal up0kqkx,4:arease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to1 klxau.klx0pa4: qg, 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 verticamgw 5t7oxh*dkoz +6+ml axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, app7+o 5 o+mwx 6t*mgdkhzroximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a ficwq622b7;y msn wsjt 6gure 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 Ear6 d0 xg/ebqs)e9;z koyth
(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 iden wbfeyv ;h+d j:/cq2k+tical disk rotating at anqcj;d hyb:+vw+2 /fekgular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsv0-qs5 0ekc ch at 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 5v 5xifdcg5w7 at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inerwx75d cgfv 55itia 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-g 8z+z3v2ql/ ,je)i g m7bqezfpo-round is rotating freely with an angular velocity of 0.8 )z pe g qil/+zb8ve3mf,j2qz7 $rad/s$ 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, losing a1*xuh f6m -9foqq k+m;z5vtds bout 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, wha6;z 1uodq mm9kqh-*5v +t sffxt 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 involv no5/k6m3ln ymfzzw8.e winds 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 tj6.lf5p hq5knye/ 0 e$ 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 a6d2enns4m* , ncv -wgy platform, initially at rest, that can rotate freely without friction. The moment of inertia eyn6sn w42*-,vngm dc of 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 *t h87l(+lspe 0 ieekyedge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 17 e7ik +yepet*lh s(8l000 $kg \cdot m^2$ 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 gr 7ef slev36uw8ound 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 rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the s fswveuel7863pool’s center of mass move?

  The Moon orbits the Earth such that the same si g iy7 h(drhcn6 k.eo3r5/fayvfty +(9de always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its owgt9 nec 3r65k( ydy. vr/fyaihh7fo(+n axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 m/9axh z55n pnrkc-;j-ages ,b/$s^2$ 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(rfox3(;lq ul.20 m acquires a rotational rate of from rest over a 6.0-s (( l;fx3lqrouinterval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dtn2q qaj(+ l n1zp)v+*yoq2mi isks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.00qmzi+( nta+qqnyljv o122)p *50 kg 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 i jubx+vtj(8v+ s the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times m0;um3c n 2j:ln(wjdm 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, lo n mjcdm(u ;mjl3w:n02sing 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 gkw-ga)n3tusy- )s (nfor it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diamegn (--kg)3any)s wts uter 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 illustrat :l5v4nf cexr2 8l1rjves an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v=3obzi m30j u9g kb,+l0t.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 lengtl : :)lefq :te.t4t bjs4ls7smh L can pivot freely (i.e., we ignore friction) abets:s ) jtt:lll. 4:eqfms47bout 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 verticallr*;z xa7sr2vo+zkw f )y on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height +)fr* 7sz2w avkz ro;xh, where h

  A bicyclist traveling with speed v=4.2m/sni9 v)2an) qlp on a flat road is making a turn with a radius The forces act 2)i 9lanpq)nving 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 into a sling of lent2 l64 x onfd--ejiev7w(tw8ygth 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rn(l-te2o-7w46dw xe fyv itj 8est to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms :s + ankpdh1c:as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held ti:d1s:hknacp +ghtly against her body.   

  You are designing a clutch assembly which consists of two cyline-qie9a,beef:18v los* e(d,) m duz7wo sa 9ndrical plates, of el-umav9dez o:f,ewbn *q 7ioed( s8es19,)a 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 t jh+kw 0(de,5q hqu4qgrack of Fig. 8–58. What is the minimu,0 q4wk juh+ed5(qhgq m 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 track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do j h+ta5g95a9qs2i;a4amyvyp z .g nt-not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces ol22 swlng; m0its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was sg02nw o2l;lmthe angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s