A bicycle odometer (wln tm4u 5zjg, 8z.,6rq(yhlydhich measures distance traveled) is attached near the wheel hub a6hdy(5j,8 l,n gz.r 4qtym zulnd is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant an 6c-o.cm 8iabidw,g p(iq9ht-gular velocity. Does a point on the rim have 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 of either component of l- pi(g -c,bawc6omiq ti9h 8d.inear acceleration change?

Could a nonrigid body be described by a single value of the angular 2k jw* sc0(x;lqa( nlovelocity $\omega$ Explain.

Can a small force ever exert a greater torqu (j s.w/ krk--bu(zgewl+hyu 9e 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-upa:dw(vm:u9ugrk wj-xi3 i 6m- with your hands behind your head than when your arms are stretched out3 9 wim:a(iukgvdwr-:x6 uj-m in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the t4(d by /oql3lrear 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 harder to pedal, a small front sprocket or /(b qlolydt43a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with flesh kae/dy8i0 nt15m)*t yfr*qej and muscle concentrated high, close to the body (8ett*na dyk)ij5 * em 1/q0fryFig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkec7 cr46hxb9gjrs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is -;vfqcl 0byz 9f7:qmq zero, is the net torque also zero? If the net torque on a 7 :vm90cqyff;-qz bql system is zero, is the net force zero?

Two inclines have the same height but make different angles wo;5230fxye f2a lurb( xw4myn ith the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gmo; lu52 n 24r3(e yfb0xxfwayreater? Explain.

Two solid spheres simultaneously start rolling (from reke6v .k1odpvj 2e -/yvst) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of1kj6e okv2-v/ . vdepy the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same masfujgg ;rckv e:7t.j9*s. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at tht jce.uj:k gvgr*7f 9;e bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum fap0x4 3r-i j7f+a8 traq k5ajare conserved. Yet most moving or rotating objects eventually slow down and stop.i5jp jff 7rtax+ 3q-kr a8a0a4 Explain.

If there were a greatf ,c7vut1aor8 migration of people toward the Earth’s equator, how would this affect the l7auv to c1f,8rength of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial xo 8skb:d(ouvko;9b 2e rb:z9rotation when 8o k9;(2brzobu::vsk9 obxed she leaves the board?

The moment of inertia of a rotating solid disk about an axis through(d(r 8*w;ghizwpdnf-8ef 8ro its center of mass (g e (whr *zopw8-infr8dd;8f 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 stoolb554cxjp ume5 holding a 2-kg mass in each outstretched hand. If you 55m 5ju be4cpxsuddenly 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 itgett2 7n (j;kcj2 xrk7f8o)e s hollow and the other is solid. Describe an experjgje2e7 tr ( n k;tc7xok8t)f2iment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle pofp e0rg f5:utro v.f90ints west. In what direction is theff9.ptrv r o5f:u0 0eg 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 standing on the edge of a large freely rotating turntable.o r8fja4/-l hk What happens if you walk aj/ro l-f4kh 8toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As u)vyx nyg 8,d, xc9r)uhe throws the ball, the upper part of his body royncv,8 ,rxx9u ))g duytates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of co6-pfu* 2s f+tgt62f 0wlsva3/ hypununservation of angular momentum, discuss why a helicopterup60wpf fhnfvtu u+ t-3y sl2/2g6*as must 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 anglebtk.hv+gmvka u/i. 0 (s 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. C uhs; qr9z38v:;l )dko(dpbaxalculate, using the information inside the Frontpb;xo;ha8)dzdu s: vkr9(3lq 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 Earth. The beam divergesw/8gdjc 3 ;)p80q-v c4dnhxp( vejaz p at anvdc0x3w) ep8;napj z jc(8p/vgh-q4 d 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 motor is ivsu;/;g pc(* vz xs(dturned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bla sup/(zv gvi;(dc*; sxdes slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anoth5exwn ;orb3,x er child. If the ball makes 15.0 revolutionbnoxe;3 ,wx r5s, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0t irnr84el/7yvxb/k* km. How many revolutions do the wheels ma ln47 v8irrek//yxb*t ke?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calc acx7b9ar 3)pohm-c :k1ggj 8z8c08ftvfnj5bulate its angular velgag 8z9 ffmp 7 h31ck0x8- cjrn:85obaj)tvbcocity 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. 8–38).iap: .ka 44xx).cm a)wqxmjy;q )et+c (a) Whcm)x)mi4aq t+ jc : .px4x.a; y)qkaewat is the 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 (bv 5-5vw*shwc.p/kar 2 /d(acll f3pwa) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear sp**ey beoi mfsk6;f7e0,9jftzeed 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 rotate if a particle 7.0 cm from the 8+,jh z6et+w edt(zy ccy.hl 8axis of rotation is to experience an acceleration of 100t h6zy +ty(.dwc,lz 8ece8jh+ ,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates unifr fbhlzi4m3m0 n b8,vq tgjr;7wq;o)*ormly about its center from 130 rpm to 280 rpm il n)84r,*fqm;rq 3zw ;ijbgot7m0 bhvn 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiuste*ag v7 e3teov3am8( $R_1$ 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, astro43 ixfx;nob0xy zfv4ael6;z +7 ptm j7nauts 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 al4t6 mo+penxzv3 j;74f7ai0y fxz ;x bs 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 uniformlyi:vr7vt*jkg+ ippqta;f 52/ b from rest to 15,000 rpm in 220 s. Through how many revolutions did ba:q*rf+tp vtkii;2/7p5 v gjit turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 je+ 7blnak a )ewlg;2:s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highs ips*l ycf9+e+peed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 comples 9e+cif+py* lte 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 unifuzpw3 40 izwd4ormly from 240 rpm to 360 rpm in 6.5 s. H4dw0iu 4w3pz zow far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is runnin-p:a ni:d hsc/g at 850rev/min It turns 1500 revolus hc dpn-/:i:ations before 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 a12y 2gk77czqzw1m yx revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have 1 w17qz x2ma2kgy7z cya 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 make2;ik1mp * obt/ha0ute 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.ho /tubt akm*i0 1ep2;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 her1,:p9q rzouhf weight on each pedal when climbing a hill. The pedals rotate in qur: ho9 ,1zfpa 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 wide. Whatnc-kvuemu 5y(c- f3n7 ud t*u7 is the magnitude of the torque iv-*(u-c7ue d 5ftyunn 7u3kmcf 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 tpz8esqz09 w*h+ fi3 rfhe wheel shown in Fig. 8–39. Assume that a friction to iws+peh09 8zrf *3fzqrque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached i/as3u6.0b9mwsa2k/ mtv d 77n lywvkto the ends of a massless rod which pivots as shown in Fig. 8–40. Initially thk v72a7mwv ak.w/0y3/6l it9bdnsmsu e rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requg peom+y2t(*s.sqkg,of q0(4xaus f , ire tightening to a torque of 38 ,o gfos2p *se(( gq4uys, m+qtxka0. f$m \cdot N$ 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 0.9llek+d 6dw4jv x :a6g648 m when the a6vga:4w96dk + ejlxdl xis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diamt*p*b w3k svq,-rpxq 4eter. The rim and tire have a combined ma*p -v,b43kq*rsqp wtx ss of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on(m:f 8 ltu)/hp0hm1 cjm9dcaj the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calcjpm8dl:ha 1m m/0(fc tjh)u9culate
(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 bo1x08nsc p t6/l 9rn+kmd,xigmwl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N tx6p0/ n1k inmstrdlc,xm98g + otal.
(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 ar7b f-*hhp*nvp8u 3tn 2fz,zf jray of point objects shown in Fig. 8–43 abo fv7z-tf 28pnbpf h3**j,zuhnut
(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 m)hrwthn.8 i+ rp(vb+ 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 satejyik- l kp61:kllite 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 k16p klky: ji-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 8.50 cm and a mass o6 wcrm juwry))f:/br-f 0.580 kg. Caycb6)r/ w u)rrmwf:- jlculate
(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 fd(k5j rdjh/f1f xl/1h d,e.sbat, 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-drih /p)0byitu.z-srheax 1if4*ven 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 kgbaph)hi suyer -41t* 0fi/x .z) 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 rn;d wgw30x:o:bgi7 qopm is shut off and is eventually brought uniformly to rest by a frictional tgdwi ox:bn oq;w07g:3 orque 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 xa/sot6 03nped/och7 cm: 0wq 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 im bw:+6-nr7yb.jbwf action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to wr -6bjw+ifm7b.b ny:10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long t(k9cqbgy .zc-t-z.x x7vn e)r9jcqg.hin rod, as shown in Fig. 8–4tqj 7) kexcnqcg.z .xbc-.(z9rv gy-96.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses, ve1bgih n8yd8( s +ild;zs32e $m_1$ 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 rescjp j+-45 8o( zjcnuru wl)qa3t within four full turns (revolutions) and releases it at a speed of ac wp)r8nuoz- j 53 qj(u+4clj28 $m/s$ 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 mom rjctzt*6sn: 2 1viie4,vodc9 ent 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 m5,7kd. 3mmt,v upwodof 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 radi5j p5se5yx 0ivus 9.0 cm rolls without slipping down a lan50vs5jxeiy p5e at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect t+5u 1pvq 2z9,xegabgc o the Sun as the sum of tw+xcbu1g2g p9q ,5evazo 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 a)gvl m1-gpjaz p9 u/sz +,ql4knd 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 8.00 s? Assume it is a solid c/ggl-u9,qazj4p zpvs+kl) 1 mylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls with:llms, /3zc cfout slipping dcm,cl/f z3s l:own a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to fall and itgx*cxjcg.b/ sfh g08 4s lower end does not slip. What will be the speed of the upper end of the pole just before it hits the gr xcc0 *xgbg4g8/f. jshound? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum rc pwvs2:);9nj hg1 4;: jmpg/myuvxcof a 0.210-kg ball rotating on the end of a thin string inp4 :9s ngm vhywc)1x prm:c/;vu;jjg2 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 grind/ ra;bjz+b h4xing wheel of radius 18 cm when rotating at 1500 r/zrh + ja;bb4xpm?    $kg \cdot m^2$
(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 rotatu* c c0jbe8o8ping at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotatioop*c 08jc8 buen 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 redu2 +v,z5vsfya.kw8poq2 wmye . ka5 zb2ce her moment 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 2wvy+k.p5a85b. qfa,sez w omyk2z2v 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 rotationh 5bi/g ; hvf)plfbjrdb; 73g5 rate from an initial rate of 1.0 rev every 2.0 s to a final rate ofbh5g)d/l 7;3 jfbv rf;gi5bhp 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis throjm5ve /2tc7gxugh its center at a frequency of 1.5rev/s The wheel cancmj7 2txevg5 / 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 momentum of a figure skater spinning a8 tygt,0)z c2dfq* dpct 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 Earthhf :d if x3.vd;3tbyq:
(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 inertim,h j,p(w +d l;6uebb 8sncrmqb56tw 4a I is dropped onto an identical +t( pbb,486umdh 6elwsnwjmc, ;5q brdisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 8./ge3j ktql8aqyg ;rat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating )) , myeco*kbgmerry-go-round platform of)eo)*,ycmbg k radius 3.0 m 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 merry-go-round ) /vht4 ycibw2is rotating freely with an angular velocity of 0 4t2/)cyvwh ib.8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, lvpk-y2 rdm..fg:gap 0 osing about half its mass in the process, and winding up with a radius 1.0% of its existing radius.dgvp-k.g: rf0a2y m.p 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 ;nr /nkl2ikg81i f(e uwinds 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 4 ck )smo.v*+pi4vus k$ 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 arr:z(j v)su71jidnfbq- kl /6t rest, that can rotate freely without friction. The moment of inertia of the perqu j1r-zsvl6 )(:/nkbfdr ji7son 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 of a 6.5-m diameter merruc(oe1q2:3bgni y jvtce4--g y-go-round turntave y j(u n-q23c4gcg:1be-ito ble that 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 the ground w1d qpdjzne1- 2e9.pbx ith 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 witho1ejq ep-d .pzn 291bxdut slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth sc(jp88 d ix8a2iixm9euch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its 98(8 xi2aei x c8mijdporbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at yl;qwp6kw( o.s p s4/:rk byx;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 un)n /b h c )h6sec;0*pnqed1yzkiform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered byyse/ )n b hzc0nq*1c;pk6)dhe the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cyli/qa9*l il9gxv nop563jc4vr andrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and dq9p9 gvcnaal 6i* rvjol/ 53x4iameter 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 te4ed1kumr ot7 ;02tdj5a:scbhe 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 timcva4ok3vor 1:es as great, were rotating at a speed of 1.0 revolution eavk o1c4 3rov:very 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 the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutionnnzhs u;+5ri7 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 needing a flywheel “spinupu5hir;s7 zn+n .”
(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 b* h8mbs,s*(pt,xwpran $H_2O$ 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 slx y4vvrl,k)vgle1w.4- oc ltsw13 *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 f q(2txpqyu*b 9.bn-/n jh ;kmw6 x;bitriction) 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.uhxxy- .9 b(n/t2 wibjnkq6;*mt q;pb 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 verticac 3n +5darcwo 60rl,kklly on the floor, and we want to exert a hdan6rc3+ol, r0 wk kc5orizontal 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 spif2w u9ikta//; jsx 3teed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle ajkifs/a 2;it3 /9tu xwre 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 qpb *3t2dts4 vm and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of qtbp342d tsv* 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 t +g5r8klr5q ithin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, a5+ ktirlq rg85nd with arms held tightly against her body.   

  You are designing a clutch asses9fm-*p me*c1 rxnu-tmbly which consists of two cylindrical plates, of mass n9 ur*s-* cmefx-mpt1$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 radiuslo5i1y:m.j d g r rolls along the looped rough track of Fig. 8–58. What is tiyd51 l jo:g.mhe minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do nothn2(oce/t mx - assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed i;70ij (rh wriuniformly from 90km/h to 60km/h The tires hw ;7i0r jiir(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