A bicycle odometer (which measures distance traveled) is attached near to+1( kv ,/ ozwj,-qyu5xlahpthe wheel hub and is designed for 27-inch wheels. What happens if you use it on a bvozl+ya5q wu,1kpt oj/x, (h-icycle with 24-inch wheels?

Suppose a disk rotates at constant angularjnhv2/ nk;b7f velocity. Does a point on the rim have radial and/or tangentia 2hnvb/k7; fnjl acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the 8ntk dq v;8n0rangular velocity $\omega$ Explain.

Can a small force ever exert a greab07av:gp3 8cvyp v51p potgw/fed ,(t ter 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 w gk tvy-:w*rf+hen yt: +r w-vyk*gfour arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets alvk(q+ -co2 wat the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sl vac(+-ow q2kprocket 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 being able to run fast have slender lui se+x(4z2ugl8 cf9lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34).zucx 9fi lse +(ulg284 On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bea il8 se c6p x9p3j6bbtna/,,klu3q5ham?

If the net force on a system is zero, i:j9knnu1x e q7 v6nsho l z77q*/pxvo6s the net torque also zero? If the net torque on a system is zero, j7s7 nz nop61vkxe*9ovl6xqu: qh7 /nis the net force zero?

Two inclines have the same height but make different angub-0ck+) s5wy5n7 l ,uyzydtx. sq7chles with the horizontal. The same steel ball is rolled down each incline. On which ihxyl.+7 kzy )sc50s5uyct dub qn,w-7 ncline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from :7 ax4ywm/yzcgxy5i5 rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline z/m5:5yw7agyxi c y4x first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the sa wk. c1jx:njw)me radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greaterj1wk:x )ncw. j 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 conss56i7rmke yv:iw 4wod uew4 ;jfq38d9erved. Yet most moving or rotating objects eventually slow down and stop. Explain.rdev k5i ms;y9qdu4:6 83ji7ew fw4wo

If there were a great migration of people fy(.ggalpk/a :i n x/;toward the Earth’s equator, how would this af; aylfia g/g :nx/(.pkfect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any inmjk nd8g4g.qh y5o1l59nv5 i6jv ( cjpitial rotation when she leaves vqc g(5d 91lv o64jnij gn85m. 5pkyjhthe board?

The moment of inertia of a rotating solid disk about an axis through its centerepkxp7/pz9 6vu v v3+vhi6p z- of mass+pz6v / pp hzpe3ux6i9 k7v-vv 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 holdinhta-.v v : (rc2ln6qqng a 2-kg mass in each outstretchet:vl.vc (rq 26qa-nnh d hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the sams csam6b0 lo):e mass. However, one is hollow and the other imas c osb0l:)6s solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on13 9gqh fv wasmj;4w kp s*8;oib5j/oe a horizontal axle points west. In what direction is theo9ig*p owfevb5;s 8a;kqjh41s m3 wj/ 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 decreasing?

Suppose you are stand19.ygdg r9b,hsg 5ld ping on the edge of a large freely rotating turntable. What happens drl5g9dg1 g9yp,s.hbif you walk toward the center?

A shortstop may leap into the air to catch a ball and throw ilcah; l* + gajddo(-/.fc4 b)+xqwasit 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 rota/j.wl c+x*bdlqg )+fad c-4o; ahsa (ite in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss wh(hjbh w 9b53vjj xdwd788 +kpyy a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller 95k hb +7hyjwv8xb j(dp38wd jcan operate to keep the helicopter stable.

  Express the following a tlfj(rt;8/ ocngles 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 coin ztepj) f,+-srcidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Su+zj) etpr,s- fn and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from E:oh2jo; f 14 3e,h hw:azm2+ rbkp1osoug-j ckarth. The beam diverges at a -f2e;uj z1oba+ ohkj2,:orksgh:hcp 34m1o wn 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 thejl -kkpt0 2 4+bfbq:tt motor is turned off during operation, the blades slow to rest in 3.t 2jkqb+b-tpt0 :klf40 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(tc* y+v1xk vo to another child. If the ball makes 15.0 revolutions, what it 1c*(oky+v vxs its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.sty9 )7dlrj 5 jqv:1rx5hm1v y(qz1ra)9w hro0 km. How many revolutions do the wheels mak yh5)zv1 m j(j ar)hw9dro5 v 91tsqyxr:lrq17e?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its anbtb , h,-vh nrm, 9v93hv3rgjpgula tv,-r 33 g nbmv9pv,hrhb9jh,r velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 9ujesxiyhyw f,3 si. qz09,8e8–38). (a) What is the linear eq3w0jsif us8.yiy9 ,,z h9xe 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 ve); :-jc 2gp2 nkilnqt.wcucp iu3)) ejlocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed-2i ib,rb/nu4 ymth;w 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 cq+-nkewwk n+ /entrifuge rotate if a particle 7.0 cm from the axis of rotation is to experie w+nw/eq -+nkknce an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerar0 0hbu+hd4,hngtt w +tes uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Dete,hwhb+4nr0 tu 0hgd t+rmine
(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 radiul g*7-u skme;hs $R_1$ 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, astronaut-u*( ng.2 fr-jxtxmt cs 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 cylin-mxcu- gfr 2x(t.j* tnder 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. Through howwgl1s 66n+kdp4 2n ykg many revolutions did it t2 k4l + wp6g1nkn6gysdurn in this time?    $rev$

  An automobile engine slowsyo rja)j,6c f pnj347 1dnk6ze down from 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for t.xd;j 5ykgm 1rhe stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revo15xrj my dkg;.lutions 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 diamet+ s67bwq x0r fo3o s56dqrtu(mer accelerates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the obmds(w6qtur r 30q6 57+ ofxsedge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it71 oe z99s)epgklcyl 9wio *(w is running at 850rev/min It turns 1500 revolutions before it comes to a stopo1 9*ekyw l c9 wigloesp(z)79.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformly f vgcncf yjemm9,72 p a8fip,)3rom 95km/h to 45km/h The tirf3c y p j9anp8gfce2i)v m,,7mes 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 abfdj0c 2vq. ya elo//6w4 7bg:qi lfo3s the car reduces its speed uniformly from 95km/h to 45km/h The tires haveb/ /:j2g 0yvw 6e a.ioo7lqfb f34dcql a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when cl.)k:kk gnc-5ot2izuy ; l cu5aimbing a hill. The pedals rotate in a circle of radius 17 c 255.o:tk -kz uc;lkiunag)cym.
(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 wide. Whatdrns04 tj709zwz+6yl2tt so/ z r emk: is the magnitude of the torq6n79rlr2/d szmtz: 40 0 t koe+zytwjsue 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 tor.;u9 tg+sofoxu4 i1n;s zbgw: que about the axle of the wheel shown in Fig. 8–39. Assume that a .sfn; 9oi+w g :x;u4utgs1bzofriction 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 c5,0co hgj no9-h8.fmxom,rd to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque o8,d,m9o0-hxg j 5.ncohrmo fcn this system.

  The bolts on the cylinder head of an engine re d;lh12d 2fl2-t4jdf(rc eodhquire tightening to a torque of 38 hrd dh ec2dfll14f(t2od2;-j$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.mjo9*bft3a3u2:x u1pd w vq 1 i2q+akq648 m when the axis of u39fdk qv21 ou2pqta3b :imx+*jaqw1 rotation is through its center.    $kg \cdot m^2$

  Calculate the moment 5)-f*j yo;j)r13avcu zvpu cnof inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have1jj)c;vfv z cnu)uopa3 -5*ry a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rf6+eho ltv k1 f9+0yclod is rotated in a horizontal circle of ra +k+c1 0tfle hof96lvydius 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 rotahfu, rx/g,y2j ou30d 2o( ,m d*ziwpjhting at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N toodg3uu pjr*2, ( 2x0 yf/jdz,,hwimhotal.
(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 pohpvs.5c i*0o: hdkr6oint objects shown in Fig. 8–43 abour :o0* sckvdp6o5hh.it
(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 isgzy)/z zk geu7so:bo r )rj8)0 $5.3 \times10^{ -26}$ 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-9w l1tbv q: 3p5otpvc8(kgzs bpakx9+(fub8 satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius oc9+ ap bt o8w stk59u:(8b1 lvgzp-vqkx 3(bfpf 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 8.50 cm and a mass kao8h;-r*w,n d; l+n f;hpe klof 0.580 hlh;or*+ nd;, k-ak8f pe;w lnkg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings y 3k/(;xxlr.qrp3za h 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 lsya(nzl:*2 p-cjx- khand-driven 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 (ea -(:lpjlknzs2 -xac y*ch with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventw(0/9kc .j yrk9mrs8r mldu(iually brought uniformly to rest by a frict9yki wl8jr . 9ru0rk(s(d /mmcional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 71st(e bklxbci8 5-1 re $m/s^2$ 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 the forearm, whi d/yj429syv,yfe c w7qch rotates ab/9w 4efy jd,sqvyyc27 out the elbow 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 bld pz ,k6uc5r)vade can be considered a long thin rod, as shown in Fig. 8–46.k vu,r6dz) c5p
(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;bzxdvmp23 k dgpi)62 89iwg wnsists 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 rest within fqz8)xt ++/zsx w mkq9iour full turns (revolutions) and releases it8)z 9+sxwm k qxitqz/+ at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of in ;y0uaufd t9b.ertia 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 developmga ,c cfcz2u7cf9b0 6hn66yb s 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 7ysp3 o,k(:nc e.3 kg and radius 9.0 cm rolls without slipping down a lane atoy(kpe 3 ns:,c 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum ofq zh-n5,csjwa *bgf/6 two terms, f6cqh *zj,5ngb-a/ws
(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 oghs1i cc0/0e4;kutsof 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.0 c0/i4th01eo kg;c sus0 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts wjs2baog v;8 3from rest and rolls without slipping down a 3 gowvb;82j3sa0.0 $^{\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 7.wixom5c7*ggtzng4 to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it txzg w7ci 7*g4.5 nmgohits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.20 lu1d*lou *7vm;pjur10-kg ball rotating on the end of a thin string in a circle of radiul vp 7ol 0*rud1umu*j;s 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momenhc q 2vv-f 3pqqs us)k*jt,b70tum of a 2.8-kg uniform cylindrical grinding wheel of radius 1f q b2s 7quqhpk0vsjt*)3cv ,-8 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 d qr 5a:hl:mu( -tn5vj 21hh/gh91x) ytozdlithat is rotating at a rate of 1.3rev/s If he raises his arms vni-:5/lq 9jm2hxgydl zt: 1u1htar h)(5hdo to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can re 0ql jfg0fbf8:duce her moment of inertia by a factor of about 3.5 wh f0lg8:jf0 qfben 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 speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin bcw)k;cu*sa 2rotation rate from an initial rate of 1.0 rev every 2.0 s to a fin sba2 kuc*)w;cal 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 aroundbsu2wv,iy,8x- a9 a zk a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotati8 vszb w-u9akya2x,, ing wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spi(h0;nbfztb 5e t2etw 7nning 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/m1)wkgbrtd 2n/ gl0x 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 onth8g*jkng 7 4jqo an identical disk rot g7j*k nh8gqj4ating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2t9qtqev -r0x)01 yybe .4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round p1efjb6u. m*n: chdbcbdx955r latform of radius 3.0 m and moment of inertia 6eudhbj r1xmc 9bc.*5bd:n5f 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-round66b;bfxlv+15aeno 6lwjr:s2ck (z1at mk ht 7 is rotating freely with an angular velocity of 0.8zef 6obax6t;jk7h+a 2bv(6ln5s k: mw1c1r tl $rad/s$ 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 wh pcv*n/3q 5)q,zi+d evj egax1ite dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what woulp1e* az+35 /) cdi,xvenv gqqjd 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 excess os 2;, 5wiimkraf 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 x lkvx oku62gfd*p)*4 $ 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, inpk3a2h;y8 qw yitially at rest, that can rotate freely without friction. The moment of inerakqp38hw2 y;y tia 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 stand3-w.br5g fiy vs at the edge of a 6.5-m diameter merry-go-round turntable that-bf yvr.iw53 g is mounted on frictionless 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 the8 ru(-la5+adu8 atpe:olm -hy 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( l 5ypa +-ul88heu:m-radota 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:i-na y c1- 64zxgbwyg faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) b16 g4nix:-yzwycg -a to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from res: uvph6w70 ufy5-:5dtwvg rmt 7p,uckt at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acquire cd,gxh z) 48jttv1ea -fksq:3s a rdeh)1 3sqkj8 tg, -cfa:4vtx zotational 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 solid o/6oz06pna * 1;kjxt erkl( necylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (lj/k6(o1neo anz*60 kt xep;rconcentric) 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 e1qn+ idxd5n.iykres 66 4qxqv hk5 -fav6l+9the 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 t(/*qjavprzm 4/ykc d +imes as great, were rotating at a speed of 1.0 revolution every 12 daysr*vy4qcmp k (j//+daz. 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 the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use5psv(nhmj7 xcwzsif2- 8j f6. energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform c(s2 jjc5h spfi. 78-fmxwzn6v ylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrag*6mncmqykmf * v 94o-tes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v=3.3;lr+zo.j ,g c 10bydwx $m/s$ 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 ypyml( du- -*zM and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as i l*-u(ypdy-z mn 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 the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, and xawfl z16o)m-tpd 1 1wwe want to exert a horizontal force F atw f1zomp- xt)a61 wdl1 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 sr6 vc 9ib.hdoa+ps;8fpeed v=4.2m/s on a flat road is making a turn with a radius The for9bc8a;h6 so rvf.pdi+ces 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 length 1.5 myt a+ m(21 hzd0id(lua and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a 0tiya (mhz1ud la d(+2rate 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 r7p)+uy9prqqf dw-q 2cy9 bnq2ods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skat9pwu+7pcry) qqy2q-q fbn d92 er with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists k, 2deha+8yez;l.omjn. jpp) of two cylindrical plates, of mass h8ed;e a.p+zo.)ymk2j jpln , $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls alo*rr6g;m7yaicu dp+if7 mp up*7.h du6 ng the looped rough track of Fig. 8–58. What is the miniu.purr*yc7di+ h;g fpm*dia7mpu 6 6 7mum 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 h xp 4qf hn.vx iax8(s* +j 3(g(kcefdaa3n9p1assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions 7mg1yncup)j9 a4c2cj as the car reduces its speed uniformly from 90km/h to 60km/h The tirjcpcju2m)7c1y 4 9gna es 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