A bicycle odometer (which measures distance traveled) is attached near the whe+7fq. gzpor k2el hub and is designed for 27-inch wheels. What of+7pqg r2k.zhappens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim hav) vmo 0vs/eg4 f:/jsai:y-z tke radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude ogki f/z4y-):vs0te/ vos: j amf either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular velocvw0+pqpd8 1:tp8u s1 ,srlo9bx u0su eity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Exp4)vaa7r if k(qlain.

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 yo h)/:whgem0e jpnb-i: ur head than when your arms are stretchedw: hnpem:j 0e-gih)/b out in front of you? A diagram may help you to answer this.

A 21-speed bicycle haya-t,s ;r/.o;qvuek 36njbcxs seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedalk ua ;yq,/tc -6o.vr;enbs3xj, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on bead)xv.9 rl-hu8ty s ( . ac2zl5dauq2ring able to run fast have slender lower legs with flesh and muscrd q9c8d z x.2a(la2url stuya- v.h)5le 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 lo)u;1dx ho20pqj7k bjqmb8i/ eng, narrow beam?

If the net force on a system is zero, is the net torque also z.i mu0djwc1 /hero? If the net torque on a system is zero, is the net/uwmij dch.1 0 force zero?

Two inclines have the same height but make different angleap(/x r)l( n dmcg3+m5bvemv1s with the horizontal. The same steel ball isrm5mv1( l pb)x+(gv ecd/amn 3 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 (frot/fz a8g ha6y,m 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 totag,ah8tyz/f a 6l kinetic energy at the bottom?

A sphere and a cylinder have t ,p6brl fcf/y;he same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greatepl6 , f/bcf;ryr 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 amq0; * 9cgwclgngular momentum are conserved. Yet most moving or ro gmcq 90lc*wg;tating objects eventually slow down and stop. Explain.

If there were a great migration of peopl*v;y *6co fodz 1jos*iy)/bls e toward the Earth’s equator, how would this affect the length of /*yi*; lossb) ofo16vyd*jcz the day?

Can the diver of Fig. 8–29 do a somersault without hav.dbek3 au 1-ee uszvzr x:1z;+ing any initial rotation when she leaves the bx ez3;1a1 z.+vdbure:-ukeszoard?

The moment of inertia of a rotatingcbenl ai t.:*+ solid disk about an axis through its center of mass i+b:*l .ctianes $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each u6-:/ hbfoqk coutstretched hand. If you suddenly drop the masses, will your afk:/hob-c qu6 ngular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow qoksv 4u 1b4zqt5s5uol 5ve 0)and the other is solid. Describe an ex0te 5 z q5)b4vqu4os1s 5uvkolperiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle b9 zrby10fb6f :9llev points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describ1fb9v 0lzb rl 6yfb9e:e 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 *tu)yh;j8 tq ye*gs-dof a large freely rotating turntable. What happe; ue)-gy8htdqjy t *s*ns if you walk toward the center?

A shortstop may leap into the air to catch a ball and th 1fa7tsjiq/+q 6;p q-vbh or4drow it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposa4t dq1bs r6q/v+7-op;qjihf ite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angu;462gjzcup 6 4wyqy yslar momentum, discuss why a helicopter ug y4yc6qys2z 4p6 ;jwmust have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following anglezi5lqdxvn em9 l6 n2)a/ijk99s 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, using ; ,a/eqxuk, ):sii xwrthe information u,iqx/i)kawr:sx e; ,inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from E8og 9l;n biak/mkq;zgbe:u/-arth. The beam diverges at m-;;aklgonz9b e/i/ q k:bu8g an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the moto:p8y zm xk6vx,r is turned off during operati:zxmx86 y ,vkpon, 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 floora)buiowh3 lj2uno cw, 3b:t-- 3.5 m to another child. If the ball makes 15.0 revolutions, what is its di)-3ibc-2w ubojhnu3, aow:ltameter?    m

  A bicycle with tiresc 4kq 1mq 6kiosnzk2/m5p(+pe 68 cm in diameter travels 8.0 km. How many revolutions do tm6pz cqqpm+i51 kkeso4(2 kn/he wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcub3xvw 2h r1agfmk+ 1.xbd p:t7late its angular velocity i.1xmh b12kd: x3fatwv7 pr+bgn $rad/s$ $\omega$ =    $rad/sec$
(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 revon mqo11ez )2gmyd1)i q6cbe)p lution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m f1)nbmed6iz qq 1m1 )g ec)2opyrom 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 orbhn/0tpk8 fe w2it around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spz glwb/ )0,kcmeed 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 centrifuge rotaqu8g,buzl3q* 0n-v.dihz d k0te if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 10u*u,vdlq g0zk hd38 qbn0z-i.0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unif7 bmsg+)cbcso-q(.bm* gacwj (d/ ts/ormly about its center from 130 rpm to 280 rpm in 4.0 s. qm.sacm-b+w/bt /o(j *)c gg7d ss(bcDetermine
(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 u-s -tys8h yq:wome 0e s(4x +8dyib,u$R_1$ 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, astronaucgyuew1p(c s;1*:cgv ts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip,c :u*ccpsweg1;(g 1v y they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm in 220 s. Throu ny,bs q/k6t ;:eyg pxq env((9y(rmj4gh howp/m;(rejkn, 9((by e vtgqysy 6q: xn4 many revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to mizr.. 7(inujj g5wy.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 highspeed)1qvh ayj awjv8ikef ev-h.j. qfc5::,,yfu 1 jets in a whirling “human ce,uj)fkh:-ey . hj,5awjq.8 qcy1:evv fif v1antrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.95p6c9jhusf/e sga-,n;b gni 5 s. How far will a point on the edge of thei95-;ebucgn9g /f hs sp 6,ajn wheel have traveled in this time?    m

  A cooling fan is turned w ldxgzv1+u )7off when it is running at 850rev/min It turns 1500 revolutions before it comxvl7 )1z wdu+ges 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 a*vab ;mgo9zul m 1,bc/ je:*urs the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamemavg le zu*bcmbj,/* 19r:ou;ter 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 revolutg 9 l yc8z*6vwu v2pu2vpqs9fb-n)0fxions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diamet9)yv9 f02w nqfglx -u2* 6zvcs8vpb uper 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 put 8:9ct/dgh lh,l x(vxos all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radvg(8x , hthlxd9:cl/oius 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 o/s dt)trb13 pjf 55 N on the end of a door 74 cm wide. What is the magnitude ptb1 d t3srj/)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 wheel shown in Fig. 8–39. 4tf8f,f yhq:+ej ,c*q xp:x loAssume that a friction torque of yh:eqo,l p*x4 jcx,8:qfff t+ 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 0n-ag*xfz6a :2gne/nf.t x sdi,y7v smassless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude andx2 v xzsent ,:0f6sai/gdgf- n.7y*na direction of the net torque on this system.

  The bolts on the cylinder he*0b6drolf v3 zdp2kfv z8/ 4diad of an engine require tightening to a torque of 38 kb p 0 fovfdzzi648l/vr3*2dd $m \cdot N$ 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.f ;aluie*s ov s jaw5w.85b7k68-kg sphere of radius 0.648 m when the axis of rotation *8au ;oek.lbsaj5f7wv65 w isis through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 yuz9ns u4 65v5x3pwx)ht,b4hi3p owh cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ix5 p yxz,)u5nht4b iw43 hwpvs39u6 ohgnored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in ac13a *i fhgjzu1 dg(nmieolgf6;+*r/ horizontal circle of radius 1.e 1 cu3 (* i6fm1gdhgrjnif/+glo*;za 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 rotatin+.xzhry59yje f l 9c1og at constant angular speed (Fig. 8–42). The frictio5o9 fr z.+91lcjeyhyxn 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 array of point objects showgcod:: 387v ul/ ltcibn in Fig. 8–43b: c3d vgoi7/8llc ut: about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass i fj5 v m;z71e3we8qmsws $5.3 \times10^{ -26}$ 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 thecb8;(sjdi e4x kn3 *75sqlfo9b-q zsz correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite hj 3lz 8kdqzssfs59oxicq e- * 4b;n(7bas a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8 eit6lv7a n:b: abei86.50 cm and a mass of 0.580 kg. Calculanib e8: t7l6 :abei6avte
(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 swi ww4*od6):egnagy 3fs,k n1yings a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-dez2wa03hk6 sc q5 ymh9riven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the m2qy59h z3cawe60kh s torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating5z m/zoi z9x 4y(/sr tex2f9ss at 10,300 rpm is shut off and is eventually brought unz /rf9/xs(9 o sm 2zs5teyzix4iformly 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 ba+uasghqxed/x0b b *z w81+u,nll 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 th. 7jpfiz8c6ak*-)csf+ lfout rown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45ju +-af8 7fi)*s 6pcfclzto.k . 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 b+elq2mcuwaix cqr6 ;mk ,ejd3r 49d 1sa,gm9-e considered a long thin rod, as shown in Fig. 8–46.m,l ur1-scj2+3 ;ge9kae6ad9cwqi, mmxq4rd
(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 co ;/+pak,1 6ckbfr9br.pu-ykxk gnez-nsists 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 g 1gu4oc1o:d u3wrk.ythe hammer from rest within four full turns (revolutions) and releases it at a speed of 28c3g1ouo.ru:g yw41k d $m/s$ 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 pi)y hj1 b:nh+a moment 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 d8:(q, rpplppfevelops a torque 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 rollr ehyv05j9w6hti /w, ms without slipping down a lane a6w5t0h/r yh ,ji mev9wt 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the 0 r-6fjed:1e m*chmso Earth with respect to the Sun as the sum of twoe-: desh m6*oj0 fr1cm 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 16461go a)bh u0 g:ix ppc+z2d:rb0 kg and a radius of 7.50 m. How much net work is required to aca i: 1)uzbh+pg 6g:dc b0xpro2celerate 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 w y4b1p. 9fb-ereo*k vsithout slipping down a 30.re*op-s 9fvb4ybe k1.0 $^{\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 starts jl lsz p)k28/js3ur2k to fall and its lower end does not slip. What will be/srl)jsl 8 j2upk z3k2 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-;txlp+d(, uz .eboa 1fkg ball rotating on the end of a thin string ,zpa;1(d .xuteof +lbin 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-rxj-*ds p 4u/7zip6y yad*yz;kg uniform cylindrical grinding wheel of radius 18 cm when rotatin y ;/d7jsyuiz46 p* p*yrzadx-g 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 rochet3u+ u9 y3ate of 1.3rev/s If he raises his arms to a horiz+ych9o 3 ut3euontal 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 mo5d+t. fzxg18d ou i+ h)jinsw-ment 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 in the tuck position, what is her angular s. 5 8s-+)fdwh 1gujdzixot +inpeed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase h:a- j,qc1elhspk;r:qz8b )7nx p) ivier spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final pja-x7n8p;r:z)1qshcliqv:k b)e, i 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 atgjm *5eitw :/p* n)kpp j52ap 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 ofpt*tj: pj)pw*2i a 5 /p5nekgm the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angul83sh3wce5ws vl5c 4ktar momentum 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 vdwx)tl d71m /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 bt*9 fbd,h4uo I is dropped onto an identical disk rotating at to ud9*bhb,f4angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at ydm6ppngu ti.nkwx:4zj7m 2( :7+wqc2.4 $rev/s$ 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 kmi; 3v6ppd3-jh0 syg mg stands at the center of a rotating merry-go-round platform of radius 3.0 m6s0;vg p- ijymd3ph3m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merryk/:bkggbke tja/1ule 5) 8/ gv-go-round is rotating freely with an angular velocity of 0.8 kgk/ek1 /j:l5tg)vb8euab/g $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losl k0fakg4,wd n4-mkv* ing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integem- f 0g akwdk4n,l*4vkr)$\approx$    $rad/s$ (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 windsp8/ 7wm ax:lysi5u8a i in 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 g ,5(6s+v 4pkwfa qrhf;zv8ud $ 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 rjaf/3mx6waa,. kaki/trpd * 8est, that can rotate freely without friction. Ttj8aka im6f,x a.p/dk3 /r*wa he 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 edge y xx/.kee./ iqt1: ti;l4bg usof a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bea/4lq;:kbiy t.u .x/xes e1ig trings 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 ro xer sd2*ga52mlls on 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. The spool rolls behind the person without slipping. What length r2 ed2 *gxams5of 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 Earth. Det1bs4.kb1r f bnermine the ratio of the Moon’s spin angular momentum (abou.fb1 r nbs41bkt its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratel+48jbw kn t8imi*gw7 s from rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder o2h -kyuy/tc)js6 ev37( ppwih f radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate thpvc (ytuhspy3w6eh 7)k2j/-ie torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical diske(ibj0dmg m*gp0 vm/.qf ue72s, 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 of the yo-yo when it reaches the end of its 1.0-m-long string, if ipe7 (fem2mdq j0gb/uv. * ig0mt is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the an 2nazr4 3cwh: e kmec42ujh5.r. wmtfg09r+hcgular 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 massco)6h mx5c6 mzngq99s 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 h69 6)mmnccs5zx9oqg process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutiomq2s.c( ebyb fya868bbg7gc j6+ 0s orn automobile 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 ness8(eygb b0g cac78 fmb.oy+r6 2j6qbeding 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 illustrateadbo 4y3+y g*bs an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface a. -nsq l/lv;e)ipixt; +m gnj)t 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 fric, q+ apxw8l uqyh(ge51tion) 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 force of gravity acts at the center of mass of thegh1x yq5,w(lpu a+q8e rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the flh7tcm3z zdk k,5fpnj7yp ;ezip4)9o 6oor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55)j ;7c ,k)p5t7ezn kz4zyhp od3fpi m96. The step has height h, where h

  A bicyclist traveling with speed tdl9(m/)wkj w+2blz5 4ecywqt8,avuv=4.2m/s on a flat road is making a turn with a radius The fov2+t9cwwa( dbkt5ql m uy/e)8,l 4jwzrces 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 gg52myttu*ro ( h2m.uw r4)bilength 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat2m)g4(m hoty*r tw.iubu 5rg2, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body ace5kr8l kr :o9m9,u9cv2 dsyos a solid cylinder and her arms as thin rods, making reasonable estimatec ,v9859k92oruske r:co dy lms for 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 consiu .54, ztzyzqs8kp 2jksts of two cylindrical plates, of k,z. s kt48 52zuqzjpymass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped rough thpy(k (tai 3d/t 6s0hcrack of Fig. 8–58. What is the mds ph (t(y/ck0ta36hi inimum 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 assuz d(o4uye*),z c/.4ebjtizng me $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its spe,7c5n/ofe elto ,msz 3a87juwed uniformly from 90km/hj sn,5walfc, o o87/e7e 3uzmt to 60km/h The 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