A bicycle odometer (which measrdw l8vl-d1ea l-,5dgol 1sk+ures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it o -dgll l,d15k val8seodr1-+ wn a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on thes) nad48 )t brh+7ivjo1y*djy rim have radial and/or tangential acceleration? If the disk’s angular tn d s*o vj8+ )yiah)y4jd1br7velocity 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 described by a single value of the angular v5 c2 fhi-et9-vmhrf5kbgkh/uo:77 u felocity $\omega$ Explain.

Can a small force ever ex-kcp m cmshk 0/7p4.rbert a greater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up w3rr mul 0+y3d(;ufz p2 mdhlq:ith your hands behind your head than when your arms are strequphm(:3frr0 3ldz m+ ;dl2yutched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel ab- d(4s6.) c9df1hp djc8)gq50mpc khrd ovxend three at the pedal cranks. In which gear is it harder to pedal, a small reddovh ckgdb.f59j) -0r cce6 pqms)p h1 8d(4xar 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 lopnv(wu1lpkko ie/mc9m 75i 5y q6*i2a wer legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why thi*5ii6oqwnve py p m1cu75a 2/k(lmi9ks distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, nan15edn ry9g a:mxa:/r /bmnw(rrow beam?

If the net force on a system is zero, is the net torque; zb6g1flm:, wgxe;rd also zero? If the net torque on a system is zero, is the net forc gfdw;l 6 z:,bexmr;1ge zero?

Two inclines have the same height but make different angles with then- c:- vzn nf6l018 eh mrcbi/rus-2zk horizontal. T- z 0fmbnenzskc-v6: -rr8n 2ic hul1/he same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously stay- 5a+1dl- ah3t, rk xb9c:.jf wxovxcrt 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? Whiccvt o ac9-j-f,b1. lxh3x+daw y5x:krh has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the samq b-n44 pc*eh5qv8uvrc+9j ck e radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational + cu *pv8bqjc v4-kc95rqhn4eKE?

We claim that momentum and angular momentum are conserved. Ye9il;8 x4w fcs1h ho4ult most moving or rotating objects eventually slow h8c;w9hxslo41i4 lf u down and stop. Explain.

If there were a great mi1lcg6i+ y luw-gration of people toward the Earth’s equator, how would this affect the length -wg +6lcuil1yof the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rot9k l+5 jj cophco9zo,7ation when she leaves the boardkczj c95+pl,oo 9 o7hj?

The moment of inertia of a rotating solid disk about8sh8wr6,w tvope og8 cd8gvk qi8;v7- an axis through its center of m8qgg ch7-wok;dpv6w8ts8er ,8o vv8 iass 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 holy pvdnot+2agvb 0;a(2ycpl9.ding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angulptvoy+ga.y vd9c;l20 n(pa 2b ar velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one m6 yun7p );h 3ubhwm-qis hollow and the other is soli b-73u6qpn; hh)y wmmud. Describe an experiment to determine which is which.

The angular velocityq39m3a9d t wfx of a wheel rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is tam39dt9qw3 xf he angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. jk ,i onef9*f277hwidWhat happens if you walk toward t7ifhn ij2 *wo9fdk, e7he center?

A shortstop may leap into the air to catch a ballyc8u 4w (+umbb;p,jbm and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice upj (+by4mbwcmu ;b8,that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentu0ne 4d r i*joy-g h3babaulm5ez*g;,d6 n(pt2 m, discuss why a helicophan ed0eg(tb43,mnor;5bpg j di2 la*zuy -6 *ter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles id2 lmz;,.tr2: lf, uxlai5qgon 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 coincid,+b7):*ua up*hlo1h snt 2ibxfqs wi2ence. Calculate, using the information inside the 1f,*72 ohu ssu)*bptl:nxa2ibh+wqi 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 fri7b, . ljk-pjiom Earth. The beam diverges at an ang ijp7-b.i,jk lle $\theta$ (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. Wp:nhx/6wb7s zhen the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the ahpb s n6w:7xz/ngular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floo , *vyhi3oxlp::5z / fd1mcxwbr 3.5 m to another child. If the ball makes 15.0 revolution 3/vx bihpym1,dw*fclx5zo:: s, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.5osnv urs2mk7g 1ho )h3i2 zx9fu o0e*uuxl3(0 km. How many revolutions do the wheels i0og)2u oh2(v3mn sf5kouzs7u9e1xxl*ur 3h make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. C i(;5jaam tdk;alculate its angular velo;k(mdi 5;tjaa city 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 4.0 s (Fig. 8–38). (7- gdf :hi9tlf(7 nlzca) What is the linear speed z7:fn-l gf h(7il9cdtof 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 (ah )k03rc vej+ey7:mxj) 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 pointwr6 sr-*wc4e r
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axis ofrih:dh hk5 (-ghzc06t rg: h-th0k5ch d(ir z6hotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abo:d gak3 v/ qe+ k-y2wcm;yr 6ms(tdr7zut its center from 130 rpm to 280 rpm in 4.0 s. Determi/k+g zwdvc:s (2-md3yk6 tea; r7mryq ne
(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 radius9gn 5h(r4b ztb $R_1$ 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 sl-(o *fpb*3zgj 5u rjMoon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rju pfbl5 (jz*3gr-* sootation 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 :y fn5gg g ra hr8ox12:*vppxn.oz3* ms. Through how many revolutions did it turn in this f:*r* on2pag.v1oz 3x 5:8mgxnp ryhgtime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculat z*yqcn;odc fei-p )s o7a)pzxv.m+3 9e
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a p uk3eu0: h9oxeix97vsa oy(.whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions be7s:(ooxee90 9h3.y kvup aixu fore 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 6.9)zq98c b:rw ejtrfv( 5 s. How far will a point on the edge of the wheel have traveled in this time? fq8( wtz 9be9jvr:r)c   m

  A cooling fan is turned off whenc*lwd.zt )qhl9 u f)6q it is running at 850rev/min It turns 1500 revolutions b lluqf.9) tz)q* wd6chefore 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 revolutions as the car redm jt 8pnv+ dvc0pc77+cuces its speed uniformly from+n c77cp v+8tmpdvj0c 95km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unif68aeh)2di d jgormly from 95km/h to 45km/h The tires have a die6hd)dij8 g2 aameter 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 peda*agi 1jf1 ic2fl when climbing a hill. The pedals rogi121f fcj*a itate 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. What is then+/u;wq)z ztr magnitude of the torque if the force ir)qu/;nz wz+t s 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. peeup+iyy;k m1tqk4 ly:7 wa q75y+zuj;.e .nAssume that a friction torqu . ipelk.y+q;:wu m e+1jz47yakqp5e un7 y;yte of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to thtbetv g.6 yiw-k3r; finkj2,,e ends of a massless rod which pivots as shown in Fyt;vfr .kek btw2i6-3j, ,ingig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requjm19j dsowxh.- . 6go1fcj p.fire tightening to a torque of 38 fh 1. 9wmjfp c-o61dx.o .gsjj$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m wyu/0t);;wyik2qh,t. v msskdl li9;zhen the axis of rotation is through itd s s) mk2k yziliyw,.;l;9 t;uvqt0h/s center.    $kg \cdot m^2$

  Calculate the moment of inqkx2jefiz( 06 ertia of a bicycle wheel 66.7 cm in diameter. The rim and tire0 j2fk6(ieqzx have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of z3uekpdav:p9nf- y+ad m,)/e a thin, light rod is rotated in a horizontal circle of radius 1.2 m. /m9+nf,3vpy- aekd) :pz ueadCalculate
(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 a6m.xga+t a*z(b5n cjp bowl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction fort*6bzxam j(n 5g c.pa+ce between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment epeh*pgfo(lya11tfy* 04 -kn of inertia of the array of point objects shown in Fig. 8–43 abofny*gy et4oh k appf101e*-(lut
(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 consyo ggw27g 9c7vj0y:k e6m.wt cists of two oxygen atoms 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 cylinft1 pc4*fr7evk q.-fjdrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of*.p1 k7tfe-qjr fvf c4 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a unifok)ym. eo54b; m1 +2syl, 9noxfva rbvsrm cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Calcul;orovalnsbv.1 ,f m 29x )my+ke syb45ate
(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, acceleratin8(n y .fmstmkcz+2 2bmg 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 h55llj k7p*p mmerry-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 torquehjm 75p pl*lk5 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 offx nz6fh;mv tv)590xime ;c yt+ and is eventually brought uniformly to rest by a fmchtifm ;txe ;z v5)nxy6+v90rictional 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 lwd6 hqp8m 43ta 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action ot 4y-v)uja:ugf the forearm, which rotates about the elbow joint under the actgj-: ty vua)4uion of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8cgdy8wn12 dy 5t,jq a4–46t4 gyqjw28c1 ,dan5yd.
(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 ofg o5fxaa/yi03,o dae ,z*2 fwv 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 accx.u86 nzg i6ieelerates the hammer from rest within four full turns (revolutions) and releases it at a speed of 28.i6ixg z8uen6 $m/s$ 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 inertiq/z5xabg+ye of 4;2l ta 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 og. y 0vq:vbq+5xh7e(n xq:wxhf 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 slipp. qqs7fi zv8, 9)3magi;nesloing down a lan fo; z,sn7 q9 )i38a.qievslmge at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy,ggf0 25udmyqw:4j. s rie-ui of the Earth with respect to the Sun as the sum of two term,-.di:jyq4egirsf u w0 u52gms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass od()vzurfj10p ih.m(j *hck; df 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from resth(vzkdfr)ij(m *h p01 ; cudj. 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 mass 1.80 kg starts from rest and rolls witf gaf, gek.ju)j9u12m 65tett hout sl gttj2g. )m5e,6juf1tka ufe9 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 itsaqj)l;2c;9d 9npz 8le* gfcg s tip. It starts to fall and its lower end does nofcc l qze*)d9gpan;g;j l92s8t 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-ktusz dnntdq5i+(*;*. em q8lk g ball rotating on the end of a thin string in a c+i.n m( te*8tqsludkd5 z;q*nircle 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 etdi4 krs5; -xlho0pqkr.4*k uniform cylindrical grinding wheel of radius 18 cm when rotating at 15qp4k it rl0k.x;5es -4o k*rhd00 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 lh/(z- l1yk g9ap1tyathat is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decrhy -taglyk1a9/pl (1z eases 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 redubrf48t:)s 4v0 p1auef( pi pfb1ijk 8uce her moment of inertia by a factor otjbk: prf1af eups4i41bfuv 0(8pi8 )f about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can :*un92xuyzjkp ekb5 6increase her spin rotation rate from an initial rate of 1.0 repkjb xn5 *92 yezu6ku:v every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis v)s.kq+/af eo 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, approximately shaped as a flat disk of radius 8.0 /q.a)oef sv+k 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 mof.vs0sb6n l71 a 1uiiy q5pw*smentum 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 momentumgytv4 * 1cbi0dmja35,u1co2aumdd kpq*-i : d 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 droh ughq19/d5ab bw11pxpped onto an identicu pdbwbx qh911gah /15al disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2-2k2rqjiu;/q 0i hlxm.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 th9n 3rg 0ob30*qcgku bse center of a rotating merry-go-round platform of radius 3.0 mgo 3sbn*0brkgu q 309c 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 merce3cqgw6) )x1s un ivro:r:8a ry-go-round is rotating freely with an angular velocity of 0.8 icsn)8: 1wre o g3vcrxq6: a)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 eventually collapses into a white dwarf, losing about half its,/ ;rm bq+6wdylayn2z 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?(round to bw/;6lyzaqydr ,nm+2 the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excest*-c3g lwhbc2 s 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 c3 754t8dkzih d dres8$ 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 y9gl1m 1veuf.tn4 9an9h et3oplatform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the .mege1yaunv3htfn 1 9l49t9o 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,fbk*lj /f. yt 6.5-m diameter merry-go-round turntabl/ k fb*yj.fl,te 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 ogb c:j ky3tigt 7d3m*, nw8cw,n the ground with the end of the rope lying on the top edge o*imn ycdwt,3k:, w8t3gcj7bgf the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that) + ov0oahq 2ob++uzyq 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, treo2z+)byq+ aov+uq0 hoat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates f3 t) +,ixvqfprrom rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone int ewlf 92a6md( the shape of a uniform 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 delivered 2 w96td(lme afby the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical dis f3p uo o.-s4wc mbum-++bs8kdks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindricacfpwssduo3+mkbmuo4 b.8-+ - l hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the 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 angule(+xdre i6/ 6sz0a 61xbze-likr k3tear 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 timesuwgqe/( g,ysp)qm5m bu ,v).a khy4*c 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 of its mass in the pro)4 gas,c u)h*qmkb.qy5u m /wy g(p,vecess, 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 .iuno,t5p 2 crit 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 diameter5pi u ,co2n.rt 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 6 kshin::qw: /fyu x/qan $H_2O$ 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 sp) )+yvvsr ,rsfeed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L ca ue9nad5 849(i dfl8rn1dpcqr n 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 ti dqdf(1lupr4en 98 a5n8dci 9rp 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, and we we k7-z,qet irvw94pgg, *x hyt+w p3/bant to exert a horizontal force F kt yh t93pgire 7*vew+qw4x gz,- p,b/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 sazhf8u fd,q 4o9 x8kc(peed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cycli4cu8 qf9ax 8(d, zfhkost 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 0.50vo a2p30 3boqm j:oga4n9u;gv -kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the t3j:gv v34m2 poqnuoabao; g90orque come from?    $m \cdot N$

  Model a figure skater’s body as af).b0 zh sxdt bw c;t-rhw(:r4 solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning (0sxfr b .t r4w;hwc): dth-bzskater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembhhpyw- ,9 .sqqtvj 31ely which consists of two cylindrical plates, of qh,hw 9jes.yvqp1 3-t 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 kta gdyb43/ s-6 jz;9d1vnpb er rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving;bvs 6g3/1j-bp9edz yt dan4k the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assua 9zx p6fx4b7 2siaj*fme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the bejf5d +;tcx6 car reduces its speed uniformly from 90kmexdtcfb; j6+5 /h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s