A bicycle odometer (which measures dis :wly tp*c5o21 ib/chcgcakjvy,682etance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What t52 c6:/2b kyhpiwvoce *c8,l1ycja ghappens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point (dpvz2ee i7 m po:g21gon the rim have radial and/or tangential acceleration? If th:ei p72zmegg1 2( vdpoe disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velocityao7 y*/ oof /agg8bpn6 $\omega$ Explain.

Can a small force ever exert a greater torque than9qum1qsrm a.u a8z1 (p 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 behb- elc:kdl k9bkmlks k)ozo 9x4).1:aind your head than when your arms are stretched 9eomcd:4k )lk1:l-x k b az.skb)9 lokout in front of you? A diagram may help you to answer this.

A 21-speed bicycle ht6,x (c74rq7dexe 3tvj5mypsas seven 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 it harder to pedal, a small front sprocket x,c47j5epy(6e7m3xdt v r tsqor a large front sprocket? Why?

Mammals that depend on being able ofe i7sq+/ rr*4h wdu(p( yo3kto run fast 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 of d 4f( u+r qyh3oeo/pwks( *ri7mass is advantageous.

Why do tightrope walkeorwj42 x7sp9drs (Fig. 8–35) carry a long, narrow beam?

If the net force on a systhb bt3el6y7wnq mdw.vj 56rg5)c- 6c sem is zero, is the net torque also zero? If the net torque on a s d6ytw.6wg j-5mh)rebsbc36qnc 7 v5lystem is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontjgjc6/u,z 9yoal. The same stjg/,zo9u 6cjyeel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneousln/d7 o+dbhb5s y start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which rob/d bhs7d5+neaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass 37+4jj9 hn 8kwpnwy.9g2pddo q.kv dd. 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? Whicdk3j99dhk 247 n.wwn+dp.8jdp yqogvh has the greater rotational KE?

We claim that momentum and angular momentum are con g(e+v;jl*.a19myaet *qir -*qtmp z cserved. Yet most moving or rotating objects eventually slow z;rgeap* i 9 ec-jql.(*q1m t vmyta*+down and stop. Explain.

If there were a great migration of people to2w- c2zgjz)t pward the Earth’s equator, how would this affe2)cwzz t-gp 2jct the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial r;c d:(f5k;vd lbmua4l otation when she leavesb4; mv5ku:ld cl;df( a the board?

The moment of inertia of a rotkz m +,-ee/e3ybb*;slx oc7yq ating solid disk about an axis through its center x+ eol;m,ebc q*7e s/b3ky- zyof mass 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 hold46)iubap , .utyl iiv+ing a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity i6pb)uiuvy i4l + .ti,ancrease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Howev0ve.r ioaa (83hvhsak u 2u (oxhy* rcr+9t9(der, one is hollow and the other is solid. Describe an experiment to determine which is whd(eavs0h*oi yhkchau 3vx (r8t 2u.o ar99(+rich.

The angular velocity of a wheel rotating on a horizontalh. ;r)j8vkn vg axle points west. In what direction is the linear velocity of a point on the top o g;8k jvv).nhrf 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 freely rotating turntqfossca07g 6,d (-jesable. What happens if you walk to(e7-,sod6a c gs0sfjqward the center?

A shortstop may leap into the air to cat( mkq.3(c joidch a 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 hipsm k(q (coj3i.d and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, 4p)xobq7ck2 i7n oja 26vixz(discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stab7xop 2c 2jqio7( nbz4a i6)vkxle.

  Express the following qr+d 7)jh lf3iangles 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.k, l6mx( wwmgmj7y gkm7e;,w apd 0;0p Calculate, using the information inside the Front Cover, the gm(d ml, xp0wp g0;7mj mk6w;ekw,7yaangular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direcp tx9yiz4-35(4lk9vjj kxz8osby- 2c pv6 de uted at the Moon, 380,000 km from Earth. The beam diverges atkjvj uzkzv9op -43bc ydlsp 9xty25(68 - 4exi an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blendau gi2+w yn55 p5i2nol0gljn5 er rotate at 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 slow down? g0+yi2wo5u a 2jnp5ni5l gnl5   $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child.ml; j.c)v2o m;e 6*sn 2xc3mr:ecguxl If the ball makes 15.0 revolutions, what is its diam)noelc ; emm;22r lcjv3x6u*cm . sg:xeter?    m

  A bicycle with tires 68 cm in diameter traptz e8)i/a ox)n7*x gkvels 8.0 km. How many revolutions do the wxgkoap/)xe*tz 7n )8 iheels make?    $rev$

  (a) A grinding wheel 0.35 m in dja5 *0xbb: 51 ikkni8gx lmb3biameter rotates at 2500 rpm. Calculate its angular vi55:kal0xg3k*i x 8 n b1bbmbjelocity 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 revolut 7)xgjli*q ;hoion in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m f h*oq7gj)i; lxrom the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular vel 40k49mledmzw;fqtc i,7p tu +ocity of 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 o oh-xe* 0 zvc/+ik7jo+bct.fuf 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 adpdc-9pd ci rh6+x*( c centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,00 c- *6pdd(9dir+ hcpcx0 $g’s$?    $rpm$

  A 70-cm-diameter whej-:iba6 sx qp9el accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s.- bixq jas:96p 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 radiusu+v bh1uro.1z $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard thl3j*lt,8m s vze 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 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 8.3l jv t*lm,sz85 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. Thro5*,uwo ,9as2qa k skssp-z zq1ugh how many revolutions did it turn in this tiksqzws az 1k ,q*s5ao, 2pus9-me?    $rev$

  An automobile engine slows / /qotgk spvj/o5t5b5 down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested(6,qx ;lva: e8r vgtrj*rngr*liw(tjnh b*7: for the stresses of flying highspeed jets in a whirling “human centrifugtin;j j:( bn*7 raw( g6,qr*gh vr8e*x trll:ve,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 36e t5r xm,,i*zl0 rpm in 6.5 s. Hozr,l *mix5 et,w far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It tmc g.h .5(nyn 0qm*sxwea5 p2purns 1500 revolutions before it comes to a s5xgphs0 emyw*(a2 . .qncp5m ntop.
(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 rk11s)z7nug7v t dtc5u evolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hav 51)us7tk7ntduzcgv 1 e 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 syva2k4yakw)c 6c sr09fi4fx- peed uniformly from 95km/h to 45km/h The tir44 c2 9rvsa k)x6ka0 iy-wyffces 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 pua5 fxra8d5. dits all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 85adrxif5da. 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 domu(-9hl* 8 g/hrwvvojor 74 cm wide. What is the magnitude of thev m9/ugow *v(hj-8rhl torque 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 a 5t(:mszq csrqs3em:+3 su rg)xle of the wheel shown in Fig. 8–39. Assume that a friction torque )s:3qg ectsr53s:u+srqmz m( 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 the ends a 5bv(dm; ba6+l/jcvq,n ya 9k y1alx0of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the0mq;,ana v(lb d/la9ybjy +61 vkcxa5 horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of n,880t96kjcqcd0oco7no ;dna. o u wg an engine require tightening to a torque of 38;88nqoo 9kon700n t6c wdo ,dcjcuga. $m \cdot N$ 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 ra0i-/mc mdk,z tdius 0.648 m when the axis of rotatiocmizt,m/d-0 k n is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of 9uigc 2ni4- (mual,etes. 9gea bicycle wheel 66.7 cm in diameter. The rim and tire hav.-u ug t4n(lai, 92egesc9ieme 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 )t1 h +va*qmht z:xn/e ,/pfcwof a thin, light rod is rotated in a horizontal circle of radius ,1 pm+):*q/thfe /hvwxcztna 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating asjz id6: btx8x(/wds*t constant angular speed (Fig.(wdbs/xis 8jztx6 :d* 8–42). The friction force 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 off8 hh ;)1 lsgja49f:vt /zqxwt inertia of the array of point objects shown in Fig. 8–43thj g/ : 9z8ts1f;hflva)w x4q about
(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 oxy au)yikw1d/ i.gen 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 cylindrical satellite spinniqoj2mb mvlwsr/-.6 w 7ng at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if th-mwb.jr m2w7/q6so vle satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinde+k. 6z4cx kwu9js-qu9ees37na; q yvnr with a radius of 8.50 cm and a mass of 0.580 9k u6ss3v9 jxk-qqa +4e; u7zwycnen.kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, acczut3e zt56b* tkk6+plebp/2 j;krhy /elerating 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-drj1g *oxjr0d0 ;o;- 6husnlpyoiven 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 torque rg0j ol-6hd sxjo;0uo1* ynr; pequired to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300ts*+l)fddq7x87 jdtnf4+ee0ip o7 fb rpm is shut off and is eventually brought uniformly to7 pof+bdtsijtd0 efx+* )7qfn7d48l e rest by a 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. 8–45pkn-4at.xmpi *7 ti 1n accelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely bq6zlm:naos0n .2.n fuy the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest tnqasn.0n u .lmf:o 26zo 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 Fir h9ov/ 8(ngdwlmm6 h-g. 8–468mm6-hh/v gdn(ro 9w l.
(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 masses,ep20 sg9:n ln. p g;vibyrpylhs8fb6)g;x 3t4 $m_1$ 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 (revls6fv*wjftl9i 1 +m:k olutions) and releases it at a speed of 28sw9l+j:f1ml ivf t k*6 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia o85z,b7ql2 zymnq cum8f $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 280 rw k0 ok,ng//b$m \cdot N$ 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 slnu6fu.kp 9)*:tgsqv7/s mvn ;f)wxb jipping down a lanek;7p)sv nf /jnuw9 bqg6u m).xf:*vst at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respec4+5tjchd m4cyrme ()8t .tpiyt to the Sun as the sum of two termm ct+i y.m)p8t4yh(c 45rdtjes,
(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 164n1q 6/ lx*1sds2kxllb0 kg and a radius of 7.50 m. How much net work is required to accds11xxn26q *ll bk/sl elerate 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 cm and mayimvs 2diem(r9x9; d- mch3y* ss 1.80 kg starts from rest and rolls without slippic9hm*(i3d i sex-myvd9mr ;2yng 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 vertical e7v(jr*0vm gcly 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? [Hint: Use conservation ojrm7ce (0vvg* f energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of 6r93dfcm /y4v3egy5 b laz ek2a thin stribz ek2rga v53m3f ly4/ 69dyceng 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 oufv :;o3+pd04 wzybl uniform cylindrical grinding wheel of radius 18 cm wh3op0: d;y l4zwvubo+fen 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 oxw bu62n6gd j 28y0kq y06 ok.-uztlgside, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position2y.2 kuou 66x8glzg0y -n bkq0twojd6, 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)2,/reqmn ukd: can reduce her 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 id,2 kn/: qruemn 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 ijdd/w: ri9.srz/ yqg;i,(( qbf8lvuspin rotation rate from an initial rate of 1.0 rev evedqs :,f .(iu/i8y /ibdr9;jg(rqvwz lry 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through +n7q)s8) iahx4amumde-s 8hi 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, q)mi mhxd + n)sauis8a8-h7e4onto 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 figure skater spinninny,70pqmby)b ztupf ,uo 9d)- g 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 l3 76sv cgcg1iof 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 vr,k3mgt 3*n;- hkpag0m;khfl-o c ; iof moment of inertia I is dropped onto an identical disk roth, k;toanghkm rf;p3 c 0*lv3-mik;-gating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turnsq .d-xz+k6xkd q1zy9p 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 at the center o bg z,6o5ys6tyrfix**f a rotating merry-go-round platform of radius 3.0 m and moment of ineyz6s x*6 or5 gb,ift*yrtia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an a.j)le*b 6hz u:oinxrdu 9bkv5w( v )/nm)dw- qngular velocity of 0.8 vubd.wl/v5h wn-)bm6*)): rk(djiu9xnzq oe $rad/s$ 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, losingbh .f( b:a 7uw-bxtnt2 about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no tw(2ba bx:hnf.7bt- u 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 excesbu b5 g8;)lskos 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 8zhuya+ibz(t(d t( (g$ 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, initiall(ou* z 9ywfkq9y at rest, that can rotate freely without friction. The moment of inouqkw* zf99y (ertia 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 personq.zq56)mxhtci ),9wju ;gz c /w djaj1 stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has az zj q ,hxi aq)5; .gwj91tw)cuc/jd6m moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground wit+zl. k8ft bp*x)5t/4nwx5nv d b9hcbrh the end of the rope lying on the top edge of thecz9xvrnh t*tk8x lfwb4p5+b )5n.bd/ 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 the ewvg/d0 y2pt: same side always faces the Earth. Determine the r/wpd: tvge20y atio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratepityhw3 ln ),,s from 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 in the shape of a uniform cylinder of 95i ynpwg wl5lb/g)(e ;1zoknradius 0.20 m acquires a rotational rate of from rest ovwo 1bnle i5k5ygwg/p 9ln(;z)er a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg 50lm :ckoti w wo3-+rdand diameter 0.075 m, joined by a (concentric) thin solid cylwir0:3 l-d +kmoto5wcindrical 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 angular speed of the re5x8kuh7y* jd5v1. m ps)luue/z9wygfar 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 tip km*5.f bwh5xmes as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gra. pxw* mf5b5khvitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy stors44p0y) z hvzj1zeij2ed in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a jzip)hvy 2z44jez 0s1 uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustra7abpqp9ac )*+ z3v9bur hdf;,yy zx2ites 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=3.3 vmlxe9s-7 -u+wzyl+n9s nuhm ; b ,v9t$m/s$ 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 can pivot freely (i.e., we ignoreqva ,8xhi* vhz-r/ikoyz( .m 2s96rqx 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 accelerat9ri.qsk( xzvr,mvy2z *8oi6 x-/ haqhion 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 vv, j+p+h8sxc pgj9,dbertically 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 sthp8xs,+p, bj d+vjcg9 ep has height h, where h

  A bicyclist traveling with speed v=4hxu7qt2m+f 7 cc+n+ rs.2m/s on a flat road is making a turn with a radius The forces 2fqmt s 7nchc+x+ru7+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 into a 5hdpw,z 8bd5jq)d2 ms 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 torque come pd sh wjd),25 8qmbz5dfrom?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms as thin rodsq 79r-)hcqd7/rxcb2k vd /fms,m x v:g, making reasonable estimates for the dimensions. Then calchxdg fqm7bd r/,:c2)m/rq7vcs-9 k xv ulate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which ldw3,-j,wbcfn8)ac r v vl*6uconsists of two cylindrical plates, of ma-wn rwfvllv,jd8 ,)b cauc6*3ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped3mp +0(/5qbcqsccef;60i iufi rrg +o 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 loomq bs +i icpr6iqecg0;ufc/+05f3 r (op without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assume tnsply k:vvzcx7j9a: 0,u25d $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uniforme:w4jtdd3g8(fp *w ozly from 90km/h to 60km/h The tires have a diameter*4t eww(o j: pdz8fdg3 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