A bicycle odometer (which measures distance traveled) is attached near the wvag z3amg(+sny: 1.hvb :opn;heel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-in .yasv(abg ;:opvn3 1n:+zhgm ch wheels?

Suppose a disk rotates at constant angular velocity. Does a poinynm: h5mxb *9g3rcz4 nt on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have rn9mczhb* m5n: ry34gxadial 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 valuer)9pad bk4.c e of the angular velocity $\omega$ Explain.

Can a small force ever exert a greate2 :2 yh6kflkvp)zbj5tr torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your hands behind your head than whx wm ch530. -yoohm-sgen your arms are stretched out in front of you? A diagram may help you to answer thxhm c 0ohw5-3mgy.o-sis.

A 21-speed bicycle has seven sprocketf.vojvlb +f e.aj1:3ps 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 har3b j .p a+o.f:e1ljvvfder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run gd*n i1ycwg w jy6o(bylx;d /h95e3k+fast have slender lower legs with flesh andbkw5cdy ng(;lyew xo1+369gy *ij/hd muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narr*shf i7gau jc,r oof79 yd6w(3ow beam?

If the net force on a m di0 )g;c6p pud+yh9lsystem is zero, is the net torque also zero? If the net torque on a systemh+mg6d)0i9y pludpc ; is zero, is the net force zero?

Two inclines have the same height but make different angles 7jdf:9pg79cr1xtgik e 9 i;tvn.k ;gnwith the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the b7 t9vg 9xk jd:7nfn1ip;c tgg.; 9rekiall at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (frow zptvxvs3ova0/)a g1,n 2q3z cu 3/gwm rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the b/xga/31wtau3 3 n2oc,gz)zvv pw s0vqottom?

A sphere and a cylinder have the same radiusn7a9mpfg gvc :5vbz28 and the same mass. They start from rest at the top of an incline. Which reaches th: vgagp 29 bnvm87cz5fe 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 momentum are conserved. Yet mz3d +rwufrqedlsgkg+-9/35ah dg 5 f9ost moving or rotating objects uqd3fgh +esgkg9 f-3 l5rdw a95dz+r/eventually slow down and stop. Explain.

If there were a great migration of people toward the 3 81s sqoevu,ve9hiy+ qmr5d4Earth’s equator, how would this affect the length of the daq5, 3s91hr4eosvy8diu qvem+y?

Can the diver of Fig. 8–29 do a somer,n*qefc war39(5dd*xx-e9khrkf1 hu sault without having any initial rotation when df*f-a nd(rh 1r xue9w,9e 3k5ch*qxkshe leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centero-alg 32e ,v3 brcoyzk ak+.o, of macbg,-kalk2.y r eo3+z, o3o avss 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 (gy q()so-xpxcu4ug 3 holding a 2-kg mass in each outstretched hand. If youo- 3(ucp (x)qsguxgy4 suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one isjyb3 9bw 3p;y+sleut m);le4z hollow and the other is solid. Describe an experiment to determine which ipwtjby4l3 ue3;+lz b;sme9 )ys which.

The angular velocity of a wheel rotating on a horizontal axle points t8b+xt, p;llpwest. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasi+ bt;lpl xt8p,ng?

Suppose you are standin5h ab4x(9 g.1axwz rbtg on the edge of a large freely rotating turntable. What happens if you wbxga9w41b( 5a zxh t.ralk toward the center?

A shortstop may leap into the air to catch a ball and throw itsq+:lnhkfbd tabky9qabu- 54 :c; m; q6h2s6x quickly. As he throws the ball, tb;kk2a+ h9c6bymhu:n qq l-q a:x s4;d 5ts6bfhe upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the la jhws w)(ac+0yw of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or (scwwha+j)y0 propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following :lvmg4wtw-k 1u1ep2r 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, c94 tq)n:t4a7pooixfz ,zm8vusing the information inside the Front Cover, the angular diapnvxozm,4t:t c9q8 i7f a )oz4meters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beajl2 5r9rimss54zca )n m diverges at anl5sa4im 9)rrz 2ncj 5s 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 s 3f5bn-ks u,id r-6et-7 vj-xo klb-cof 6500 rpm. When the motor is turned ofiu,k 5b-6-7ljv d r-ckxesf3t-sbn-of during operation, the blades slow 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 another child. If thnk(;*2 t uovkwe ball makes 15k t;k(nwo2v *u.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions bxn1 e+ral+g7jx nbi :mbo(*1 do the wheels make? n m r*1+b jng:bibolax(7x+e1   $rev$

  (a) A grinding wheel 0.35 m in diameter ir9thvq/,d -zrotates at 2500 rpm. Calculate its angular velocity in 9/q i,zhtrv- d$rad/s$ $\omega$ =    $rad/sec$
(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-r-uu55 mubcchapqot18;.f2rx ound makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is ;mfr.5a uo2bx1 qpcu8- th5ucthe linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit yy bu-c 08lg yfs8qghrer9; +6around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a pz(ueq6e4 rna ,v.9a yuc-st.f oint
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm frooa()3nsbfj3s ur j(4pm the axis of rotation is to experience an accelera bassur(pj)4fj n( o33tion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acce7/di b t;jkk)kqh. lq8lerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Deter)q .qhitl dkkkj7; 8b/mine
(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 ;a2 5r1yqh2ugffr w. x4iwlr 6$R_1$ 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 aboarm )ujlmo* 97,i 5j bbjxg6fn)xty5iyw7r2 -iud 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 revolutix uj92rbmj, b7*)ifo7gyi)mjy w5xluin 6t5 - on every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest t ):5zg.i* za+lj yyzafru 9k;mo 15,000 rpm in 220 s. Through how many revolutions did it turn in this time?zf*uzza.ykalj+m rgi 5;y9:)    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm ik,xlz 2 0;xtnen 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 highspe lnctwif *:)b-ed jets in a whirling “human centrifuge,” which takew ic)-nl*t bf:s 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 to1x 0vnrr/zx* c 360 rpm in 6.5 s. How far will a point on the edge of the wheel have travv*1 rx/ n0rxczeled in this time?    m

  A cooling fan is turned off when 35 r 9awi9z9ry-zjxv;8 y)p9l dncjee it is running at 850rev/min It turns 1500 revolutions befo98 zyej-vp3)ly9r; w j59in9 decxrazre 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 zcm o/( /gzfm3c)4skq as the car reduces its speed uniformly from 95km/h to 45c qmg/k4sf mzoz c3)/(km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces itsehtjjcgs j:q7 /(0; ak speed uniformly from 95km/h to 45km/h The tires have a d/ egj(jcsq:0th7; jkaiameter 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 when k ;zfdu)l* +i.p:3nzd1hr mbl climbing a hill. The pedals 1d. u:i);zhz3rl*mnk + fpdblrotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm w: (, *8kvvdsgmnq g1efide. What is the magnitude ofk8vgfnqv gm( :d,*e1s 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 wheel sho.x 4vzk*ctb2wsk4 p:h7yk l y(wn in Fig. 8–39. Assume that s4l*x yy(kb zkv k4 ct72p.h:wa friction 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 the ends of a massless rod which pil21y6 n3g1r9glm o npvvots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction llromg21yvng9 31n6 pof the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a tt *c w5n0bgkt/orque of 38 b*twk0 g5t/nc$m \cdot N$ 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-kns 8to3jeh- cb 7*auaf2k8f r6g sphere of radius 0.648 m when the axis of rotation is through 8ks62neroc-t3fa8u bjh f*7 aits center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicin7a(/tcq1 ):oeb ilpycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of th p17/i )(al :iobtnqcee hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thc1 66n(:.h-xytp seadk 8jbe hin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculat- ky6nah.x p6 c8thjeb(:1sdee
(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 rot8tl- rq,(opjw ating at constant angular speed8l(orwj q -pt, (Fig. 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 aa1; d+r; wf7t(uy:b tvj0uydinertia of the array of point objects shown in Fig. 8–43y:b;faj1yt d ; 0d+truv (7uaw 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 tw6;5xp9*m9czdth th:zhpcx3; dj p q0bo 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 bia5d1:vsqkp;b0iyb-o 2fsm 6.h1 ydsatellite spinning at the correct rate, engineers fire four tangential rockets as;i . :q -0bbi1 1dsy2kfoa6y5dphmsb v 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 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder w uyrzh) .+8 sgh23mfyvith a radius of 8.50 cm and a mass of 0.580 kg. Calv yzg2 3)hu8+sym.fh rculate
(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, t,zgjlmesxj++4t6;x accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry2 j+t/lt ;eigf-go-round and is able to accelerate it from rest to a frequency of itg2le t;jf+/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 10,31smog;l -w,+yd9t m ns94sbys00 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1dm 9-y,nw9gls4 s+ bssmy1o;t.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 accelerate0wq+e;bhl ucp0/ :i gxs 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 by the action of thefv338oljd tv:c0k(c 1svl 3jf forearm, which rotates about the elbojtd8 ljsc(13ov vkf3lv3c:0fw joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered aa p,w6icdkkegw m5h16ycg7 + , long thin rod, as shown in Fig. 8–46.pi5,a, k16 wyh wecg+76mgcdk
(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 conx.s *zd l6kq1;1j1a;epxdmor sists of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from o eijfow 3/k5,rest within four full turns (revolutions) and releases it at a speed ,io3 / 5kfwoejof 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 mo6djay v+nw5i+3 71a qvzebxy:ment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque of 28g6l1vw,ta22:7 tsqk sn n8qci 0 $m \cdot N$ 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.)dquupj+i/ 4*i4kii x 0 cm rolls without slipping down a lane at 3i4 4iu*q pj)/xui ik+d.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy a.-qnoidd8x 8h a1u.ry8xn z9of the Earth with respect to the Sun as the sum of t8y..9-ux8 hrqx dan i 1o8zadnwo 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 kg and a radius of 7.50 m. H+u6b /yo2o rrvow much net work is required to accelerate it from rest to a rotation rate of 1.00 reor2/ o +y6urbvvolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.*ej4l1v zmeg:5u7: ataat4jm 0 cm and mass 1.80 kg starts from rest and rolls without slipping downmt :tg*jaa5ajv47e:4e uz1 lm a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on its tip. It s0f)-*+. guv2re d0 yfjv ygkiltarts to fall and its lower end does not slip. What will be the speed f*kv+fy )rd e2j gviy0.-g ul0of 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 rxleoag qwj8b0hx0 j (dr4. d35otating on the end of a thin strind34q .0xaob8g5 ed j xh(rwl0jg in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical x6ebf9pak+lo1ckg36r 8w ja 4grinding wheel of radius 18 cm when rotating aa3wjb4 f o+6xp96 1agrkl8 eckt 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, han2 h,ll yqq725pnf +pguds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.87y,2 npqhql p2+fg 5lu $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8h;.i)8 v1yyh xc cs(nh–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight posit8vhyh xnyi;(c)s.1h cion to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from1uf p*y6ya:k:m9s l kw an initial rate of 1.0 rev every 2.0 s to a f:s :y9wma*61ulkpy k 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 ax,+ sy8hst cpv-is through its center at a frequency of 1.5rev/s The wheel ca 8+yh ctv,sp-sn 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 clay sticks to it?    $rev/s$

  (a) What is the angular moa8h ;-o6--cfjip q-g dhjem(omentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the Earom f0oz 7wzc8:5)vz/ vbor0mrth
(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 1,m cknhxm86jdropped onto an identical disk rotating axj6m m,1kh8c nt angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns afm*1f9 ikpz k/)ob2r 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 k9o5,6xwahi yat the center of a rotating merry-go-round platform of radius 3.0 m and moment of inerti 6o9hi ax,5wyka 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 angulaolfg8;ij1, d tr velocity of 0.8 ,tofj id;81lg $rad/s$ 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 dwa3lm,h8 zvwknsx6c*21eyvi .rrf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radi2 k3s wme.r1y*h nl6vzx,v8cius. 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 in efjot/ 408m4 mfl-vw nqxcess 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 x5 d3tw+lp7o i$ 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 re a2xub,gy;hn-st, that can rotate freely without frictio un a2-;yhxg,bn. 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 stands at the edgegzxq1:ji3 .q8f*0t qxwz,lhg of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and hasqq130hwf.g: ixx z jt8lqz,g* 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 the ground with the end of the rope lying on th8 grulc -.lf i5jsv08ee top edge of the spov80 selg5 c-8fijrl .uol. 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 same side always faces the Eart7t4,+ a eljwrvh. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat7jw+a tr,vle 4 the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at x-l z, j5no1sva 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 radius 0hh 6mkxm ;b+i)xvma(8 .20 m acquires a rotational rate of from rest mk6ha bm;mhx )(+xv 8iover 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 cwv.5aocq4 c3,m;dizjylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric)3.z cmiq 4, cd;v5jowa thin solid cylindrical 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 th2.s+0 jsvz pkpgio;p7l;q;g n e angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 5m8/iyh3qvbl 5b i,xy 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 uniform sphere at all times, and that t,5hyb3 x8m /liq5ibvyhe lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobxh5ok q(gs rl1wki 2l9-c:f rw2*;g )5ohapbnile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel 1bqlk2 ron(9oilwfh:h;g*x 5a- wsc gkr)5p2“spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates ovz- qxrk* eaud lc.hx/0p59;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 horizontrwlguor66j*4hk t4l0 9 qjo *hal 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.e., we ignore g 6y (hm*chf6r,/eyfo 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 thecyer/,(fmfoh yh6 * 6g 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 on the fl.qlol dyd nos1k0/9og t+i-) ioor, and we want to exert a horizontal )10o.9og/l yko tlisid+-ndq 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 spee 2ersijp0*3 wpd v=4.2m/s on a flat road is making a turn with a radius The forces acting on p0i*2 3wpr ejsthe 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 length 1x-y8o 6x rswuvd(a5v4 .5 m and begins whirling the rock in a nearly horizontal circle above his head, acx- x5vy wvuso 8a46(rdcelerating 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 and her arms as thin rods, mak(zun:2a .a yi4g;mvp l5yjvd;ing reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds dy;m4jg (.u : vvaa5 ;y2znilpfor a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists ofc xeto 9f47br5 two cylindrical plates, of 4rxefbo79t5 c mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the lo hr wzx36 oa+m*s8y(ijoped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is tw+hx m8*i3or6yz(jsa o 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 assume yg9-c8*j :uvze lza /d$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces1las u ppwxiq+sy e3u,t+. ddls/9 a:3 its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular accel/9tl+,adaexd i s3 ssp.1q:u+up3y wleration 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