A bicycle odometer (which measures distance traveled) is attached necnist3 h )1d3car the wheel hub and is desi1ti3c dh3nsc)gned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on thgl 8, 5i;e y5z*qiqv-yfhi 6koe rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential accelerati , 5 izkv;y65 hqlgy*feiiq8o-on? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a:- +zokaz;n tj single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forcqo 79f,j hxhtz0p-.ef8 tar: ge? 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 youe:y:;wwk pezt h9c4fez2hk:6v8) twar hands behind your head than when yo:w zwak:ecwy) ;t9eetvf24h6kzp h:8 ur arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has sevensygu hd oahg-82c167t 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 whtc2 -g6sohag 81hyu7 dich gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fs4.v3m o5mew-m57hvb md,eih; z0e hs ast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotatio zews3e5v - sdm5 vmh4.h e,m7ob;ih0mnal dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35).e n kf +8mt7lytqq;s. carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the loi78a guu .k)y- +js5errc )dnet torque on a system is zero, is the net 5-8. )rl syrco u gi)ejku7+daforce zero?

Two inclines have the same height but make different angthy: :/xtt //p b(uyxkles with the horizontal. The same steel ball is rolled down each incline. On which incline will the b/yt/x p: uk:(htxt/yspeed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an incline. One c )8gcwhjn c3;jqy 94lsj4 8 ccl; jyg3wh9)ncqphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radiu+o * urujs*yhb x;moh5nq08 d5s and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greatqhonjb 5h 0u*d5mxso8;yu *r+er rotational KE?

We claim that momentum and angular momentum are conserved. Yet most m saa1ts:,+h6zbledvu + 9zrm 2oving or rotating objects eventually slow down and stop. Expla+lh+as:s dz ,e 2ar1vm6zb9 utin.

If there were a great migration of people toward the Earth’s eqt 5m v2s/e kma6opz88x/z hq)juator, how would this affect the length of th2/8avmz6oh j/x5tmk8 )zeqsp e day?

Can the diver of Fig. 8–29 do a somersault without having any inii8c7.1 tmzhgu tial rotation when sc.8h7t zgm u1ihe leaves the board?

The moment of inertia of a rotating solid disk about an axlu mxz(8f;qb p 5,sybq/6i jt 2h1xgj)is through its center of mafxbj,;hq g 5/ 2u6 ptxmli1q8z bs(jy)ss 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 holfa**:ea 7o* vtq*tk qwding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the * :7w*et o**kqqaftvasame? Explain.

Two spheres look identical and z zzt4u07c g9phave the same mass. However, one is hollow and the other is solid. D4z pu0z7ctg 9zescribe an experiment to determine which is which.

The angular velocity of a wheev4thujh/ m9+q l rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wh4 j9 mhvu+hq/teel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotagm 2kfpwa9s*) *ji4avting turntable. What happs mp*)aa9ijkf 2vw4*g ens if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw xb* 0 e5vpp 6zykbv2e +.lai.cit quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you w*e pvp0 a2v.k.c+ b5ibxezly6 ill 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, discuspj wiyz5 .:.rms why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to kzpy.mi:. 5wr jeep the helicopter stable.

  Express the following5 (f extmag/9u angles 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. Calculate, usin g5f +mp6kc(mjz:.hwa +zb(rmg the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen ma:( wk .mjz+g(mzphcfr+ b56 on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam divergel+,9o jxx6ldj+nl do6 .qg ;pjs at an anglj+ + 6n qxjg oj.lodp6xl,dl;9e $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the mo0e-p,5qa a cu4y -yowetor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as te-qp4e o,ya 0wc- uy5ahe blades slow down?    $rad/s^2$

  A child rolls a ball on a leve px8k22 yq yp;.o)enkpl floor 3.5 m to another child. If the ball makes 15pkoy;k) 8e p.q22pyxn.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions dojc ej16a htw/ ecs8b1y3r(sx/ the wheels make ar 6e1/(yhjbscxe1cs twj8 /3?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 25hvpa61whb/ 5 k00 rpm. Calculate its angular vel1hkwab5 vh6/pocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fj;e r9 k r6-*q-yxdajuig. 8–38). (a) What is the linear speed of a au9y*j- r;q -dkx jr6echild 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 thcoin+nd0 6(m pe Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee;. xk eu v)hgqr)s rf+bxe/()jd 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 centrifuf4 nyy /-rq6baj jj1l3ge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 1 j/ryqjj3-alf1ny6b4 00,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to z:ma1/km q5xb ecy2 t3280 r m:ab2yzc5k3xm /tq1epm 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 radius dr mj6u6)-0p rvm0 j ;jekk7ga$R_1$ 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, astronaudadhcf14z4s:l:(kkwa 4b 2 uyts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no 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 d4a:1fhk24sdckw zu4: y(abl 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 accelerat( wkah -bn7 ,h m;n,1datp dbif80eqn)es uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this td;k)hpb - na1(qatmn ei8f,bn w7dh0,ime?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpwz+d-g gc sk1.m 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 highs-xykdg,e)twd 9h/mv6od69f, gv. iagpeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.wfx,yd9g6h/g vdte dm av,.6ig9 o)k-
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.57asvv r+8;fel4sw i.hdbvi 21 s. How far will a point on the edge of the wheel have traveled in this time? b+v awevr 2s;vi.filh8ds714    m

  A cooling fan is turned off when it is running at 850rcwwjj5b 2fw1e/ n k *9)6)mszcwk9oyb ev/min It turns 1500 revolutions /nez)y)1 bfc 59ckm2jkws*wj 9 6 wbowbefore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as thwy ( c w)/4i;su;ptgklcz,o-a e car reduces its speed uniformly from 95km/h to 45km/h The tires have a dstc yz kgw/;l ac;4u-(i)owp,iameter 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 tqxm,lll 2 9.d /z3ytrxqu.9i, 8xrptthe car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameterxtly. r8 umd.pltr t,xxq9 z /il,3q92 of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal whenutzvo7)9 an;,6fmb wq climbing a hill. The pedals ro v;t)n9qm, ab76uzfwotate 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 ose/r4r 3yxw74x vin9d c 6v:d73c kfcpf 55 N on the end of a door 74 cm wide. What is the magni3 k9c p sfwed:3vyd4 rxv ccxn7/ir647tude 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 du p0l4qn vl54the wheel shown in Fig. 8–39. Assume that a frn4lqvd 4p 05uliction torque 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 thep2r 1ku/srf +v ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the hori2 k/rr +ufspv1zontal 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 tightenin8x;ig ev t7xg8q s3cw b6rr8(jg to a torque of 38c xvx8wrgjt8bisg r;qe3 786 ( $m \cdot N$ 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 b l*w c0nla3+pradius 0.648 m when the axis of rotation is through its centerwc a*pl+30nb l.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in dia x4m;f,sdfhxl .ebw bpn4w (b0(-r:hcmeter. The rim and tire have a combined mass of 1.25 kg. The mass of tr(x:shbwwe0ffb4 .,ndc x m(;pl-bh4 he hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontal4vx5ol x9y h8k1,sf fe cf5eos,4xvf l8 y x19hkircle of radius 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 at const.of+nj,mdr:c ant angular speed (Fig. ,.:co mr+fjdn 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 of inertia of the adr8 wdj)-. zvt,9c o5mdma nt4rray of point objects shown in Fig. 8–43 abozndcd5 9rt8 .t- ao,wvmm)jd4ut
(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 consistsvbq t qw*5dz k0nev-1 k-pae/o.hm30t of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rate, 8hj u:3var.fx 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 the satellite is to reach 32 rpm in 5.j :ha.3 f8vrxu0 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 ofh,0nu-ye7u0;,sju uxpavj9 w0r rj: b 0.580 kg. Cal-0yehbu0s;pxar:9,j wvj u unu, j 70rculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it +jwh xn82 pn6+mek-gr from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round and is ab+hsz)mr8n87xb cct *i v.yj7gle 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 tbvs*zj8t r n) ig.m87h+cyc7 xwo 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 wr3e)5 sgqbc3 sd,r- yoff and is eventually brought uni,-yr3cr )wbss5 q 3gedformly 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 accelerate )jqbh5 gdi9kacr 70i-s 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 b-./ coz wy .qa:xf6eyuy the action of the forearm, which rotates about the elbow joint under the action of the triceps musclox 6.yz. /a:fwy uceq-e, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in: rom d2b,2.do 25tefjuipp u8yp 5xf) Fig. 8–46foixu2 eb.f:p om, 5jy2t 5d rp82dup).
(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 +k, zs77w brk0xaqi6itwo masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerateszw14a*;t: 0srls af5at /wqwr the hammer from rest within four full turns (revolutions) and rele;rww 4s*1a5 r/ql:at0t wszf aases 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 o6+*a+3i jy olt:og66qjhjx vlf 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 torqa-r 2ka dqbwr0h*j:6 que 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,yrs e;trldt23 h5hp3 radius 9.0 cm rolls without slipping down a lane at 2yhtltsr3 ;dhe,p 3 5r3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum o3reb,mmc(0 /lj 1xplqf t lxm c,bmpr(/0lqje13wo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kgay,luyn,j gst h2+56 po)xoj * and a radius of 7.50 m. How much net work is required tjt5 s26 aj+no,,yugp)lhx *yo o accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without .lpems) fb.,8e a yf6ge d:mo0slipping dbl mfefsy)m,p.08eaoe6 :gd .own 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 verticall bg-x; 2) bcpww.kmu n1yxz;w4y 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 c4;1g- u;. p wcxw )b2wzkxnybmonservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on ths2dgm,;ykcq; e end of a thin string in a circle of radius 1.10 m at an anguskd y2, qc;mg;lar speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum 8oob pg +b7pcn*xit)3of a 2.8-kg uniform cylindrical grinding wheel of radp7xgc 8*3bp n )ob+tioius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate z.yx ckoctj ,q q4j53:of 1.3rev/s I kq o.yzj, 3cj54:qctxf 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 shown1;h mendfs;wh.ib 749ngy rd/ in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck 1e i;s ;n4gf.r9ydhwn /7mdbh 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 rotation rate from an i-4esoem j,/ta:igr 4wnitial rate of 1.0 rev every 2.0 s to a finali4mej 4 :,t/aswgeo -r 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 its center at a freq:hq8o te x dn+5/mg(-omeuyf:uency 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 then5:xogmey( q: 8 f-o+/htduem clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skate 0w+0zy ctms6gn u28gvr spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular mom. j/l19k;mm iz1t bphuentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped 4e 9 e+7-w;.gacrjsrh,cj e moonto an identical disk rotars;e.r9g j4,w-e+com7 hcejating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4rk*+wmb 9/hdx $rev/s$ 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 standsecr* e)/e a vaf-ipdb9rx:*k4 at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inert/ *vix *rbc)4a a-ree kefd9:pia 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-rounhx:tf(yf uy:fx:anfwx4x 8y 49z);s kd is rotating freely with an angular velocity of 0.8 4k yw:;):xyxxh(ft4y:afunx f 9fzs 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 coll s/4rq d0oe j/vycy9lnm92(ppapses into a white dwarf, losing about half its mass in the process, 9 r9n/s ev jo/pm(c 2l0dy4yqpand winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to 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 inxzci (w1e bz ry in98yc07t3p- 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 tc k6jf rurm-x4r5l5 *$ 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,rqc yh-l5lz ,( initially at rest, that can rotate freely without frictio ,qhcl5lryz(-n. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stanugwo / om6c.xx45c;-vn xhl7x ds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frcx5xg6m o xxv;nou 4. /hl-cw7ictionless 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 t4xsw +bd8*k1q+1fqk 9ujdf) e yeg4edhe 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. The spool rku4 d9 q+1y qebs w8ge+fd)d1 jf*4exkolls 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 wy:ckmrz8l;wilc6 yv+c3l ;+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 case, treat the Moon 3:llr+;cclvwk6 wy ;y +czm i8as a particle orbiting the Earth.)    $\times10^{ -6}$

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

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius k8pf vn6 92kkmy -4nku0.20 m acquires kk9py-u 62vmn8 fk nk4a rotational rate of from rest over 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 y4ne4: u5-gpv8jhztasolid cylindrical 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 and diameter 0.010 m. Use conservation of energy to calculate the linear speed n8jg yvpz-ue 445ath: 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 wheof4w7 sw 178:soxg riuel ($\omega_R$) 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 Szbf1-gx ;q-qrc1:i:qge4 pqiun, but with 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 the star is a unifo-qiep -;1zcgqbr ::q fg1 4qxirm 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 tyoqpp sj 1eao-ds; *)gya8. k6o use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a fly1p k gaodas)6;*.oq-yjyse p8wheel “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 illustratemo .pk8:q 8 c-r n/1rp+nfjnnms 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 om7d*t :/r4b,-i.i0pbb/ h mwhoomqhpd e/4oon 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 pivot freely (i, o1(agf uhd-p5 v8oghrv*3lg.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the oh g5a rpvd-8og g*vhfu ,3l(1force 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 vertio7 slb3 ixrd7:cally on the floor, and we want to exert a horizontal forcdx s l73o:7brie 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.),zyn, pm:(ytsa 5s 0r ywi5dm2m/s on a flat road is making a turn with a radius The f,ys(wsy )dm m5:ai5znr typ0,orces 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 sling of sv.jd75 cm)w6 g*vnbv h b8)sckc*.djlength 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a j chb.b v7)8nd*m6s cvg *kcjsv.5w)drate 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 cyln/* 58fm kcylux mm-7binder and her arms as thin rods, making reasonable estimates forxm-cu5mb kfnl7* /8y m the dimensions. Then calculate 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 consists of two cylindrical x(5igj5w7jndp0p key2 zkj 4( n 4aa)vz9xy7uplates, of a 0kdxpei njwzyg ( y4xj9n7(j74 z5v5ukp )2amass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radvaba9x:f aiuoz z-d2y;5z)o7ius 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 witv; dx5foa27z o :9baya) iuzz-hout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assumtnl2k7.iogy 3 e $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spee54a19- sd s bu2qts4t 9ciqikfd uniformly from 90km/h to 60km/h biku sda9t415q 4siq2cf -t9sThe tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s