A bicycle odometer (which measures distance traveled) ilyjw1l ( /bwc 2q56nffs attached near the wheel hub and is designed for 27-inch wheels. Whatn/5yw ljlwqc ( bff621 happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a pointl yc. 166sihznrce;t7 on the rim have radial and/or tangential acceleration? If the disk’s angular tn ir167.c;e ycl6zhsvelocity 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 igjk4u/s2 v mfeq+,9qthe angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forcc2p n3feerguf1j 1y kq)rt0 3mz ,ac-.e? 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 b4w.(;2yedy ( 2lhnbpn dsm+ abehind your head than when your arms are stretched out in front of you? A diagram may help you to answer 2 bslm+ny.d( a; pbhe4d2 (nwythis.

A 21-speed bicycle has seven spt;klfr he8 5na w;u7.qrockets 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? W;fwq a. kt uhlr75e;8nhy? 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 haf2 lb.wwd;5joss9cm p -izs2.6 i*bzeve slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, so msl *;. .cz2wz9j- fpbd2iw65sbeiexplain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narroy/8okjrn*49 v 95*nwg ptgvei w beam?

If the net force on a system is zero, is the net torque also zero? If the netf9p;./83 umjelg b kok torque on a system is zero, is the net uopkjmkl ; /fe 83.gb9force zero?

Two inclines have the same height but make diffb h bz9x-ea+r2* :a2gar doit8erent angles with the horizontal. Tbb a:erag zdao+*9h 82txir2 -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 start rolling (from rest) down an incl2-.cfeo 9wd*1prp6y o aib*va m4mtg 8ine. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the 8pd**9cv6ergaiytpbo m-w .a21fo4 m 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 from)b ona ntw1cen e5);5t rest at the top of an incli)wc)n aoet 1t;en 55bnne. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular moment ;g+.:slk4,q ;femov ylt;ky vum are conserved. Yet most moving or rotating qtg;4eyk:om vs;f;v,l +l ky.objects eventually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, ho 534yvupo ghe+w would this affect the lengthyhp u5vge+43 o of the day?

Can the diver of Fig. 8–29 do a s3hgcsc-. gq 6gomersault without having any initial rotation when she leaves the boag36ch q cg-gs.rd?

The moment of inertia of a rotating solid disk 5x d2wjd-qz1 c8nfsgz8 y 96hjabout an axis through its center of mass f jn z dwj89-sy5dgc6218hzqxis $\frac{1}{2}WR^2$ (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 0;-jnbnv:-op7+wx,q *bf j v:wfhjf ka 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrejvfn,; q0wj*nxp-hk7b:wjf :v -fob +ase, or stay the same? Explain.

Two spheres look identical and have the same js o q5)ye6rz5mass. However, one is hollow and the other is solid. Descri 5jz 5)eros6qybe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle poi:w-pialykbzam+ . p-d ar8-)wnts west. In what direction is the linear velocity of a point on the top of the wheelw-p-za-r ybi 8dm:laa +kwp.)? 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 turntable. What 5v hm uz jeg)):1zhnx;happens if you walk toward t;)zv1enh5 j xu:gm) hzhe center?

A shortstop may leap into the air to ca9s67mvk fe)rxtch a ball and throw it quickly. As he throws the ball, the upper part of his body rotm6xr)s9k7v ef ates. 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, disok 9k( qlabmr, /;mz(bcuss why a helicopter must hav (;ar(z9 m b,olmbk/qke 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 in radians: (a) 30 xiq0bu+k rqj3 : ik(o0$^{\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 coincidencem 89im-k d2 kkp2.1wijg j/tja. Calculate, using the information inside the Front Cover, the angular diameters (iki22a p kj1i-t 8kjdjg /m9.wmn radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at thr ad-j9 9 xb-w /qo1p+7umefxme Moon, 380,000 km from Earth. The beam diverges at aw p d-f+jr7bm1 qaeomux9/-9 xn 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 blender rotate at a rate of 651d,yk0o p 4sgu00 rpm. When the motor is turned off during operation, the blades slowp,o4ygdus k 01 to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to 1hri*xd 8h o+temx2s, another child. If the ball makes 15.0 soi82t mxxh1e ,+r*hdrevolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many - 6h;1zvn z1gtqx465mvsgfb g revolutions do the wheels mak g;v v61z1sxzngtqm4f hg56 -be?    $rev$

  (a) A grinding wheel 0.35 m in diameter rota/m.ohqciy;6o tes at 2500 rpm. Calculate its angulamo 6.;ycq/iho r velocity 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 stq6f7qr(-uwgcsq5 8j (Fig. 8–38). (a) What is the linear speed qjrwsugq-qf7t8 c(56of 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)y;n a cx3e(slg-vj4zg v wn*1.4ry9p l 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 point jn. 5 o+l)n exmd;m18tnba9cf
(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 particleak p/8xh+ cqj7r) 4 m8ckcn6gz 7.0 cm from the axis of rotation is to ex6)k7mr48/k h qzxgpncc8ac+ jperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from hzo+e6xs ao4c-/- ub4 -acbco130 rpm to 280 rpm in 4.0 c4shz oa/4 uce+cbxo -bo-6a-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 radiushvz1lp vsg:wk 1d k4.9vz;rs- $R_1$ 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 aboardh mvd crmc fj c6(*4 lv5v0+9upzpym1) 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 rotation to 1.0 revolution every minute during a 121v(49rc0 u vh )*5vccdm+mmy p6jlfp z-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 bas17hl 4urr 0d5s0lkin 220 s. Through how many revolutions did 0kl rblh5as74d1su0 rit turn in this time?    $rev$

  An automobile engine slows 0;fyv cn glq1ki7go qsg 099x 5rswp7sc d//f1down 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 for the stresses of flying highsu/z4 okdvaz-xl34*e.sd *aispeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before ri* kld xzoe*3 as/a4s-.4dvuzeaching 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 /wsv e liie)6ssz c356rpm to 360 rpm in 6.5 s. How far will a point on the edge of the w ws/3ssie5vcz i6el)6heel have traveled in this time?    m

  A cooling fan is turned off when it is runxoy21mlkr3-a9tb v7shv *s + jning at 850rev/min It turns 1500 revolutions before it comes to a stopak1jmvso7rby3 hx+*9 ls 2t v-.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speh0rh:lgl0:)9:e hl; wjwbus ued uniformly from 95km/h to 45km/h The tires have a diameter :lwuj0l 9rhhs);:w ugle0 :bhof 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 re yxswdb::4*z;s e5ry8xc2 zhxduces its speed uniformly from 95km/h to 4x2ysb *sxwd;8 :yx4 hz5: ercz5km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a ob8;i2bscks7pfu6 q4 kh .n)b bike puts all her weight on each pedal when climbing a hill. The peda4 i 2qou6b7f;nbh)s.kbs c k8pls rotate 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 enx;(qy+endu+u d of a door 74 cm wide. What is the magnq+ eyd+( nxu;uitude of the 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 axle of the woq+q8ue h j*.lheel shown in Fig. 8–39. Assume that a friction torque of 0.4*+ql .8quj hoe $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a mass7fixilnb8h (5yj u95a less rod which pivots as shown in Fig. 8–40. Initially the roy8 ajh575(n9 xbiufild 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 require tightening to a toqpbj 8yu-0 orawlv7 s6b f9;7jrque of 38 l7jj96-uy;wro70fb8bva psq $m \cdot N$ 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 when the x5mpsf8, *wjn axis of rotation is through its c f*p5sj nm8x,wenter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Th1empj.q qt ij u2,/od;hs q+*ve rim and tire have a combined mass q +mpt .hdj jo1squ ,;2ivqe*/of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on t3 rq2 kr bn*ha/kd r hj5ay)p/l/e7/gwhe end of a thin, light rod is rotated in a horizontal circle of radius/h/5jw/r bk)d3knhay r prq2/l* g7ae 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 b+9mmsm+5zi0auo8l a u owl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N toumm z+s+la5i8u 9a0omtal.
(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 ofg,j,*idn3 *fyyx(rfc inertia of the array of point objects shown in Fig. 8–43 abonfygf(c,yi,*d*3 x r jut
(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 atomlo9k v.np1inyry-r6 :s 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 spinning at the im;dl6)/(m gmqkt.-sfpnd q*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 ofm*fmq6-ksp qtlg ( n;.dmd/i) 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 of 8.50 cm and a mass of 76 lmsr* szns60f t/p/hcl/wr0.58 6t lh/7psr/lsw/6n cs0*mfzr0 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 ba m0sg0kpphk(ksu(9gxjh; h7 (t, 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 smaluam50(;vqncgh (b*n+4c x tow l hand-driven merry-go-round and is able to acceler t5 g(4x;+a qc0wovu(nchmb*nate 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 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 eventu 9c:wpp5t vq/*6jhuh pally brought uni*pu9jw :q5h6 t p/chvpformly to 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. 8–45 accelerates a 3.6-kg ball at (pj(d wp, /yto7 $m/s^2$ 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 bynk)r (y8fxk2 l w,1u(hzwfh7 t the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45(fkwzt2k(h1, nwyr 7 xl8fu )h. 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 g5vsld0oz 5 if ya5i-(shown in Fig. 8–46. o5-i if zldsg0av55y(
(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 masse/ pjy -2-*lnwucy 4eres, $m_1$ 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 acceleb .95kw;k rc rajgxip/7j jq61rates the hammer from rest within four full turns (revolutbjkxqgr59rp.7akw /;1 ji j c6ions) 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 moment of i lja8/ rg.fkf 86g(imrnertia 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 5n; -wadzzg -wtorque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping dowjkb:y*p3i ;eqzffi )sll )l3(n a lanlyiflk:bse*ji; p)(3 zql 3)fe at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the snr9:n;x5ztkj ( wd eq9 6-ck6yrvn mk3um of two term ztey q3r w9k nd9 6n;kmrj-n6xvc(k5:s,
(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 radiushqlp 1k/5 switkl.0vq;bf(( s of 7.50 m. How much net work is required to acce kpvl;if/h((1kt.5w0s lqs b qlerate 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 mass 1.80 kg start/zc)ov5nqc31hb5px;) x7 ipptgp0 p hs from rest and rolls without slipping down a 30.0htp7ix;vg)x 3h0)qb 5zccpnppo 1/p5 $^{\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 ver(:zu)r;2 oemfv9lx o0cob j0mlf n9 v:biz+z5tically on its tip. It starts to fall and its lower end doesnz ;orofb):lz i (v+l9 e mx9mjf0 buz25c:0vo not 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-kg ball rotating on the end of a thin sthsn qwy1/( qfzr0).o dring in a circle of radius 1.10 m aqs0.zwqfr y /no)1(d ht 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 grinding whr 2: 5 urzz53la.j3gmzpt gt/aeel of radius 18 cm when rotating:g grtl zz/.3jrpt2 mu5a5az3 at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating 1xhm9a:wr pp1at a rate of 1.3rev/9rapm w11 :hxps 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 her mo-sdn 8duh 3ke6 d-;hpjment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when ik 3p8du-dde;-6jshh nn the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin r6dvd/k:gg .uq otation rate from an initial rate of 1.0 rev every 2.0 s to a final rate g:quvg dd6k./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 ro- pd* o3q(v:i;2fikv .jf wmjstating 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 the rotating wheel. What is the frequency of the wheel after the cl2: i3wsjf* .dvq(ifmpv- ko j;ay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure r y4+hjxr +9pyskater 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 angula:/7flqsq oivhww *(- (q9jh eyr momentum 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 ifv;txdx ( ) xrhrgkwtd4/ x6bf)we*;8s dropped onto an identical disk rotating at aw)rrw ;xf4)e d/(k*v bft xhg xd6xt8;ngular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns aat-5o ;vaw f6it 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 of a rotating merry-go-round platforo fbi7f+r ,m-rm of radius 3.0 m and moment of inertia 920r mif ,-o+br7f $kg \cdot m^2$ 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 fr- 5:m axmy 8cr vr,f(xenx4cf*tk*uxs:- ff-x eely with an angular velocity of 0.8y5nt f4ux *vxcr:x*s-x-(m-c8mr fe a: xk,ff $rad/s$ 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 v xdvbm5nyl1-vh/u 13 white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carnm bu3lvvh1y/ 1 5d-vxries 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 5 yxx/p mbm+q+*lk :jmin excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass t qkpl:5se6- za,d i+q$ 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 witho6lqii)/f u /)w *jbfvyut friction. The moment of inertia of the person plus th)*6 ql wfjuibv/)/i fye 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 t8-fqrmq)- dx.h:u3ruxkj* b the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictio xhu) r8*mtqr f --jx:qbd3.uknless 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 o04xfsu.* qj 9fuj3 5hm -nzjmin the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The4nqz *f90-ui j u3xf .5jhmjsm 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 suchwwe-,x7 eowe7pv9 5/hl( kxf e that 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 casko5w/ewx7p e- 9(,veh fexw7 le, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 7cd.yd4neh z(9)vwz2htnu0 cl7f 3ak 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 shapez 7) gvwfeg,- sz)/lvj /jpmb3 of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 67m/g gzz /,jew v) vsjbf3p-)l.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 :+bzd2d p4ppdh n/ i2rmoe*:vbv )rozh 2((gusolid cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical+2vbnbmho g:4dhvzpzp/ er( ( 2dru o2*i):pd 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 a7ule 5t*kk xy.. seh77qe8z)quspvpp9(iv d4ngular 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 wit. vf :uznn.j5uh mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that thn. :nvujuz5.fe 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 automob-bj i1le4/d cw3esf8 xsk8-vaile is for it to use energy stored in a heavy rotating flywheel. Suppose suchbwjce8fxa -s/i3-8s 4edkl v1 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 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 illustratx8di(g 5rl4ab o15 kjc2e(eej es 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 4nz :32 v*q ku3nwdwxbbz) nf8rolling 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 length L can piq) /cqqa dgk*kcyt99,d n2em ;h2rb4z vot 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 n;k*rbthqdzcq dk2 ) q9,42e9/mca yg angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on9px pn/dfoik,h2)/ yh the floor, and we want to exert a horipd/,fop/ 2k yx)nh9 hizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a fv m ecu.p cuwf0;1 (rvzfn388blat road is making a turn with a radius The forces acting on the cyclist and cy c me(08;nvbv.8ufcrzwp13f ucle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 bbgcvkme1 kxy,)+;d: vwu efjhz01/ *m and begins whirling the rock in a nearly horizontal cg,mzj yv)c :kb*0e;h x/k+ vb11wuefdircle 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 from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder ak+3j gl(rtc-o nd her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outl o c3+kgt-jr(stretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, 3a2;7 f6jel3;ek xnf3tkju j mof mass xne;3j2 jm3u jtfkk 36afl;7 e$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alo mgzl8th( - lpod50xp.ng the looped rough track of Fig. 8–58. W5m dg-0hx8t ( pplolz.hat 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? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not as1 zt0hvy a31ersume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revn:3mzp5d jm l tyaikx(f h2509olutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accele: nt li59 mh2k5 xzdpay3j(0mfration 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