A bicycle odometer (which m6 a d2s wjdcho 3tkg+f0fmni6i ++*tr/easures distance traveled) is attached near the wheel hub and is designed form2t sncfwk+d03r/66hg o +i tjf*dai + 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at cons jwjhyu*i+3 n5tant 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 woulj+5uih w nj3y*d the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single valu ok0u,nm; 5zn6ijexfe 92 v2nbe of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater tourzn8s- s ifo42+ yk;wrque 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 with your hands behind your head tj x+b 1u7n2 bdmk5husnb, ;f-khan when your arms are stretched out in fr dbu2-skmb7 5b+kh,u1 n; jxfnont of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thres i+v+r+q *ej3e-y wgce 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 it harder to pedal, a small front sprocket or a large fvyqg+ ee w3sjr-*+c+i ront sprocket? Why?

Mammals that depend on being able to run fast have s ),3mp kuum6ovlender lower legs with flesh and muscle concentrated high, close u3)u6kpo,mv m to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fi c;;r- qux( v44j.2k2os cthgj9qvvrlg. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the 7e 3gy1ozudseq v nkh 4 4hbgf/u7t0);net torque on a system is zero, is the net fgv/hf3nk4q7 syud)e 0h47 g eb;tuoz1 orce zero?

Two inclines have the same height but make different angles with the horizontald0l( 4fuj4wo e. The uwf40djo le4 (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 simultaneouslyin3:z7m3tb hv start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the iz:n 7hvti3b3 mncline 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 mass. They start froi rfnasz0pjp03,vbo+dk+m1 s /.n g*hm rest at the top of an incline. Which reaches the bottom first? Which has 3s0znnsm, k pphvoa* /0bi1gf r++j.dthe 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 momentum are conserved. Yet mi5(*ean wp )q741pv o3ivak icost moving or rotating objects eventukie*oaiv713qwi p ( p4 van)5cally slow down and stop. Explain.

If there were a great migration of :l/r 6es vq.blql; y2ipeople toward the Earth’s equator, how would this affectle:y/;2vi l6 q .rlqbs the length of the day?

Can the diver of Fig. 8–29 do a somercadcz yhqzt ,)4: 4i4lsault without having any initial rotation whzl4y4qdat h ,zc:i)4cen she leaves the board?

The moment of inertia of a rotating solid disk about an axisgb+,e) 6zrrqa9bhr +y through its center of mass 6zy)+ 9 rh,qrgebrba+ 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 *v pq7hq6jmc vz,lud370 (n rfeach outstretched hand. If you suddenly drop the masses, wipd z6l vq *nu70(qh3fvcm,j r7ll your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same r2pn/9b lcabu y+:0vp mass. However, one is hollow and the other is solid. Describe an experiment to b0 2acrp: p9l+ynb/ vudetermine which is which.

The angular velocity of a wheel rotating on a horizontal ax xdsk pzbp bf 18.o+tr5:zm4d8le points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration pointszordb5 d sbz8: pk ftp1+.4x8m 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 stany2:eto tg 1fj,ding on the edge of a large freely rotating turntable. What happens if you walk toward yg eo: 2tf1t,jthe center?

A shortstop may leap into the air to catch a ball and throw it quickly. :e4:7lt4dx r agssc8;6 dabraAs he threc :da 64xa:ta7bdr;g l8s s4rows 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 why a8lw0ed +qpxe(,h 8:u qqts: da helicopter must have more than one rotor (or propeller). (l+qde,tq8 wp:qds0x 8 uh a:eDiscuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anglo2yyy2xr m*q+ go8u 2wes 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 coine 0t2/dbr*jrccidence. Calculate, using the informaje rcr*/2t0bd tion 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 Eartd0 6gz+4speya*c0jffb6m jm (h. The beam diverges at an anglzm0* gcp b64eysjfd6(f+0jma e $\theta$ (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 atz :16jb ;r9w dt rdi(-mc(px*elelg-:rc2jh r a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades( r r ig2rltj1 eh*:dcpwez:bjd6 rc-x -(9lm; slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anotw98m7cv.aql /(1og q g m:kul6/gr nzaher child. If the ball makes 15.0 revolutions, what isg/lw nma( k:/qa 6ul .m7r9z8qgco1gv its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manydu/ ipcsp,x 4 f+ d84hw/quty2 revolutions do the /u hcdw ,s8+/ uqytdpx 24f4piwheels make?    $rev$

  (a) A grinding wheel 0.35 m in diammn.) li+lr26hsx /h evb2cd3aeter rotates at 2500 rpm. Calculate its angular veloi6 . eh)r/s vlb2h +xlm23dcnacity 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 compwb:pz gv)2c3 hipjp8 1lete revolution in 4.0 s (Fig. 8–38). (a) What is t8ji )c3vh21 pzg pbw:phe linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around the Srg1cxa)ptoqqp dg b 2- mc;.(4un    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speetx:rbm 3p 1e47h dtv;sd of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a c6 8 owimkk/+ut1l,vm2 wa9tibe +h3 daentrifuge rotate if a particle 7.0 cm from the axis of r+,mh1d +ao9biwwv83 lme6k2 ti a/k tuotation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter whe l1):msj/ wtpwel accelerates uniformly about its center from 130 rpm to 280 rp/ jl1mswp)w:t m in 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 radiusp y9n;b, gqkb4 $R_1$ 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, astronbuc46in ,qqy* auts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s eneq u6cby,iq4* nrgy 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. Throughqg. m:ff5x np0 how many revqff5 :n mg.p0xolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate (*czbqlhr r w;rshj ii2(p:tt 1l,l:p ,.yo -a
(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 +so v6i qatjoxr27c+)5x +ds swh:5 csthe stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reachings+: 6vj+xa ow7c hd )5xtrs5+2c ssqoi 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 rpmjt up(9pv()w (g7rnq s to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this t g7p (uvw9tj)(prsq( nime?    m

  A cooling fan is turned off when it is running at 850rev/min It tug e :n kad8g,/q:k5knjrns 1500 revolutions beforeg5 g ,e/:kd:jan8nkkq 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 m2 fz.fc h1e.fas the car reduces its speed uniformly from 95km/h to 45kme. 1zff2.cf hm/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 reuy (lctj1bj*9 duces its speed uniformly from 95km/h to 45km/h The tires have a bjulj(1c9yt*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 bioro96:gy-n lj ke puts all her weight on each pedal when climbing a hill. The pedals rotate in a cy9-j6:onol r gircle 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 da6duxul-a+ f5 oor 74 cm wide. What is the magnitude of the torque ix fua +a56-dulf 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 torqueh 6qm81 b*xgls about the axle of the wheel shown in Fig. 8–39. Assume that 81mhg s bx6q*la friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of ..frp, z)k zbgmass m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. .zrg b zkfp.,)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 engin3vef4 )kvx4 1xiyup3fvr4 e ,he require tightening to a torque of 38)hef3p 4 vv34 1eurvk4y ix,fx $m \cdot N$ 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 drg-id2t*xbv/ * fk9m-kg sphere of radius 0.648 m when the axis m29*gt v/b d-fix dr*kof rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim*3 r/6x.p4e-e4 x6 nmco-,tt w eyowoeeuy;pc and tire have a combined mass of 1.25 kg. The mass of the hub cate* n4c, exw -y;pe43mroc. o -yxp6eew/ o6tun be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is de.gg+ *tuhg6gm(doak5v7 8b rotated in a horizontal circle of radiu*ugbg v+odk(.t7h 5m8d6 egag s 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 oqwd 6 3( neo-iot-:: iyizqs3rotating at constant angular speed (Fig. 8–42). The friction force betw 3y oi: 6on qii-(zqo-edw3st:een her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objj 0x 4ay1,rqlbects shown in Fig. 8–43 aby,b r4lx 10ajqout
(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 whose total mass is-vr blr i)2h-njd.c+u $5.3 \times10^{ -26}$ 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 satel bf;3s wshrz0)lite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If thezh;sf)wr s0b 3 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? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius o dsplq 10v;l-fg:erj1h*:y khf 8.50 cm and a mass of 0.580 kg1lsyh fkphvlg:q:*j;1 e -0d r. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings c;kxwp u 1v2ht9o f03ya 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-d.7o/w6wyra/b)0dnb (jp xyr h riven 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 unif xph /)r wnory/j76(.0b adybworm 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 torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventuallg r1*7dmx* pl3 mesf(rgo1 p1oy brought uniformly to rest by a1*3xrs(mo1g 1l7 o *gr pfmepd frictional 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-kg94o8z ptgmd ya84l0x4l f4,jr x7dvyp 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 h0wut2t0kac /q m1s*wby the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerate 21/* 0wtusqkmhctw0ad 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 b*t, p e/6cvzpa long thin rod, as shown in Fig. 8–46. t* / p6bvp,zce
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two z prcoj; 0 kf-o4;m(phmasses, $m_1$ 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 turns (rmpt0lsfuu m+cu + p)di2e50x 6evolut 0 ux)+6fd+mm pstp2culu50i eions) and releases 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 g4 id ,kfus4,amoment 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 of 280ie,7cz ei62hbyiq6oxa4)i-f $m \cdot N$ 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 with uqorqp1ku:z8nei ,5x8kw9 f.out slipping down a la8, 1k8 pi.o5zqf 9uqnuekx:rw ne at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect t;c1w2gid) tft 1ycu3 bo the Sun as the sum of two terms, 2) cgtc1y;buwid 1t3f
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. Hoiy d-cb*p*94f a fcd7dw much net work is r -fc9acbfid* 7dp dy*4equired 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 2) *3 cv7ohvkx 8tqcv.g0.0 cm and mass 1.80 kg starts from rest and rolls without sli3o.* h)vtcxv 8ckqg7vpping 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 balhf7sezxs4 8/7 dk z+ccanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the groundz x7zc7h/sd k4+se8fc? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on thkqyej1y -s 5m7e end of a thin strinq 7jyse5km-1yg 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 gre-n71y mtq pbwrzi,1 hv/m1i7inding wheel of radius 18 cm when rot1vmit,h1e yzw i7 7q/-pmn1r bating 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 9riycl4st 1;8c 18rw 8nrnjqmplatform that is rotating at a rate of 1.c9r8q8ircy ;tl4snrj 1n8mw13rev/s If he raises his arms to a horizontal position, 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 1(ixw+,+cccr1 ep,khy o( iofher moment of inertia by a factor of about 3.5 when changing ecfo(x+,,khi y (1ow irpcc+1from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotatbsxl d:fb .rn/itmw y;6lfz2(l1 , n*yion rate from an initial rate of 1.0 rev every 2t(mn byif.2lz y/bs*lxf1d:l ;6w rn,.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 rotat r.rop :9/;ccnb0t7wd,q qxpjb h2*xving around a vertical 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, approximately shaped as a flat disk of radius 8.0 cm, onto the center of t .rh9p:/bjdt crx7c0ob*q2 n wvx, p;qhe 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 figure skater spinning at 3.5 o83y 2pd9.v7doc0i(va d w 0,epzz ygf$rev/s$ 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 ofwnptv;). ao5 t the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an idhb zy5b q:3bws g*/+vc0id)hj entical disk rotating at a3i+)j*q0bd 5wg/b hyc:bzhvs ngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.( esk (upim(s)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 zh pu49)dpgzqqd 1,p48x hrd)kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and momentdz h8gzq4q4 u 9)p)p1dhdrx,p 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 merf e. vii.e8 enjc.ixej5-nh;*ry-go-round is rotating freely with an angular velocity of 0i nije *ce;ejix5..- e 8h.vfn.8 $rad/s$ 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 wc*/gvx8/7q59ds w,nr dyzuw 2gzb;xa white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. q/,uv7d 2xrw9x; s n5gwwy 8dzz*cg /bAssuming 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 winds in excess of -18.pdv iea e;mt;zpt120 $km/h$ 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 ,ladhq7eq+: / bietn5$ 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 withou7npp:t(,ig/9 htjn c lt friction. The moment of inertia of th/n7gi:h, ( t jcnpplt9e person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-g9u 74 siaxuwqjh2p4:sdtw,h :o-round turntable that is mounted on friction2x9 iua :sqt:j 4h,udp wh7s4wless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on tyjz4yrjg0ta0;mgobz6.win h:y ;d 9 2v+-vruhe ground with the end of the rope lying on the top edge of the spool. A person grabs twgtj y oba0zv;+:9gy ud .z;2m4-yj6nhv0 rirhe 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 the same side always faces th-r nq e,avh0/re Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentumrv,n -r/ahq e0. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a ratewamy(cd;o l17 of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder okzn)i )xsz7r5 f radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calcu5rn sxizzk)7)late the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylinr; *)kncha0 b:u v*unhdrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg anbruuv kcn*:)an0; *hhd diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wheel bumhjc9( /u56 sp wax* s7kjj(($\omega_R$) 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 as gs .m ) sgsmox:;p;sc1freat, 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 1cmfpm; 1sg .:)sss;ox1 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stor w ih*v,rl(:ysu5vg63o9ll mgi jsb 7:ed in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needin 6lm lw*,g 5 ou:hrvs7(bsliv3igy:j9g 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 c:npv(:kt6wa+y 8zi w 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) im,g.ve+-jc hc7ftzb ;j:vf/ es rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and lenk z n*/ug7h* oot52dvmgth 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 releasez/hm2d kvno gt*ou75*, 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 ra ubf ;*im.q bgvk.;w4ydius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step againsvikbu .gq*yb; ;.fm w4t which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist travelinz v7x: nrddh*zx(+wd3vd5/prg with speed v=4.2m/s on a flat road is making a turn with a radius7 rhp:x *(drd5zdvwn+/ xzv3 d The forces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock intoxj; zhj9p.o/ s 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;9xp zsjo. j/h 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 as thi8ze n*lfh2, 2cz c6mv e9ooo,bab )(rxn rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular ob9lo,rhm*nea2, x( bf cc68z o2ev) zspeeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly n6 ld 6-e 3hih,+kha1jckc.dx which consists of two cylindrical plates, of ld+3a kchjik1h-d 6en6.c ,xhmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 an8vdp)o f k v/a63oap2 cy,/twld radius r 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 the track? Assoy aow2/)/ c v,pk6f8dl3vptaume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not avx96j (; 4u fq2jvxjqessume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uni *3b riqsgsj,0l14en6bu9z bvformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? re6ljb buz*,1 sv39 nb0iqsg4$\approx$    $rad/s^2$(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