A bicycle odometer (which measures distance traveled) is attached near the whee;r hl( bbu:hntc4 ,s vf/i43rbl hub and is designed for 27-inch wheels. What happens if you use it on a bicyc3nb,r4buc h;fhr t :(livs/4 ble with 24-inch wheels?

Suppose a disk rotates atu ,ep+6u4x8 sfn4b, mnib tye. constant angular 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,t.4,ie6e 4+ y sx fbunmupnb8? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single i8*cc y0d3sqgdi.m )p/zj3 l kvalue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torquibinpk4g+rz f* 8k3q . ll*4xie 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 withfz)-tz3p;.cjar 63w0s pqy ww your hands behind your head than when your arms are stretched out in fsrzfz 33a)qw6t.w c;0w yp-jpront of you? A diagram may help you to answer this.

A 21-speed bicycle has seven spbquq33da k7. brockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Whyabkuq7d3. bq3? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being abyqi 7pt *2 7vygx0codo 0lg0y2le to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass iy oqg gli2d0770vyco *p0y2xt s advantageous.

Why do tightrope walkers (Fig. 8–35t h)vrdxu:4:7ca1(v hf-tt0o4kqo kq ) carry a long, narrow beam?

If the net force on a /xzjd0 hp.i * bnmsgdql9y:(9system is zero, is the net torque also zero? If the net to/.:jn dmb xqsp * dgl(99hizy0rque on a system is zero, is the net force zero?

Two inclines have the scxbxzkq8 n)i8 76z qq j.a);obame height but make different angles with the horizontal. The same steel ball is rolled down each inclineq;o7a.xjz8n 8kzc bqqi)b)6x . On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simulta9wmah. d,n oy6neously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the n6 ,ow9dmyh. abottom?

A sphere and a cylinder have the same radius ;8zdeyzd z;jp8xwq. :r8zho5 and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Whz;yd;e5r 8hq8j.x pzz 8z w:odich has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum area8qm t v:sa-3+bhkccq) .r: iy conserved. Yet most moving or rotating objects evqt k:qvmhyrbsc-). +38ia: acentually slow down and stop. Explain.

If there were a great migration of people toward t mnj:s7pjko 89he Earth’s equator, how would this affect the length of 7jmpnjs 8o9k: the day?

Can the diver of Fig. 8–29 do a somersault without having any initialjr ,e b/n//jt-j bheu: rotation whenbh/eb tj,j/u :ej /r-n she leaves the board?

The moment of inertia of a rotating solid disk about an axis through its centej 0bcn97g7lgxv vf 4n/r of ma 0cgfb7g nl 4/vx9j7nvss 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 onp.bklin/.tj 0 a rotating stool holding a 2-kg mass in each outstretched hand. If you sudde.ki 0pjlt.b/n nly 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 is holloc7y9cex+ ea3ya t6hh ,w and the other is solid. Describe an experiment to axc hc 93+e6eay7hy,tdetermine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. rt7rbm+em5a )In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasi5e+ rm7b mra)tng or decreasing?

Suppose you are standingkr qgl- .so;nl9ac8tn2u -u(e on the edge of a large freely rotating turntable. What happens if k ec un2(rq lo8na.;u-gt9- lsyou walk toward the center?

A shortstop may leap into the air to catccgh 95406zmwu)tn.y balq.l r h a ball and throw 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 legsnl6)z54 m wlhr9.u0 qtb.gyc a rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mo bcs p(,jwa+.o5wovt. mentum, discuss why a helicooa wc(.so v5 wjpbt.,+pter 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 followinhpskz4ea s z, -p6y25wg angles in radians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on E;o5uvg5 l r k y1:gfufyo 8mq1wy-81vjarth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular -18gov; 18ym1uyrufo vyq5wkf: jg5l diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed9zkhp7mv p )2p at the Moon, 380,000 km from Earth. The beam diverges at anmz h7p92pk vp) 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 rozo4syqc (h; h75p1 ity,bgfz0zj ,s;rtate at a rate of 6500 rpm. When the motor is turned off during operation, the bls,y;1 r s,hpht7zqy;5( 4oz0gcb ji zfades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m) si+m/ lfw 2e6n1uiep to another child. If the ball makes 15.0 revolutions, what is its diafw)1 /ls26 miie ue+pnmeter?    m

  A bicycle with tires 68 cm in diameter traga2k*6 x-y0tk;ar chn vels 8.0 km. How many revolutions do the wheels0xa6 ky-t2cra;hk *g n make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Clx3,x 6qyny+t alculate its angular velol3 yqy n,x6xt+city 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.o 1uwgei-a*b8at0 yv+*j5q v a 8–38). (a) Wha*wabq-avv+uoea1 it g5 *j y80t 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 (a) in its orbit fbpp:kh9:pj 4va(yk,gs;*xt around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed 67,,s:-uttjgt) odg9k jak cy 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 7.08 1t :qc .-wpmpasab-k cm from the axis of rotation is to experience an accelerat - bakcp-s .8mtwpqa1:ion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center f k:5 d0;;,eyybvmuphmv6 oh3krom 130 rpm to 280 rpm in 4.0 s. Determ:uyyhk;o v3hpe5m6m b0,kv; dine
(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 3uoprj, t.k +)6rdvmc$R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard thj+yz-2(tk z*ex7b ;ezux bpb: q8c z.xe Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they acceleraup2yz;-8xcx .z: k+eqbtb ezzx*jb7( ted 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 c jye/wb t:5-(vidwez56 qhd2from rest to 15,000 rpm in 220 s. Through how many revolutions diwhv eq 5d /y:tjbc5w(e2z-d6id it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. ub 9sul30+u z1frm 9xyCalculate
(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)ms hl36hu 8rh.vzid . of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 compler zhumsh)6il.vh.d 83te 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 unifon*c:iz/ b b/amcgn;wnw2k17c rmly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel havza 1/nc:c7w2b cm*nb k/nw ;gie traveled in this time?    m

  A cooling fan is turned oap i;wd3 smn 6*ovq+s:ff when it is running at 850rev/min It turns 1500 revolutions before it coq6n vao3s:p;d* s+w immes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car nmsz:qx +lk (*reduces its speed uniformly from 95x :s(n+zk mlq*km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 rev/w zjn 50b2kdoolutions as the car reduces its speed uniformly from 95km/h to z2d0 jo5wbk/n 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbingv0v4s n0 ,q4lyq3b;v vs s/3sztdhbm2ox;5oe a hill. The pedals rotate in a circle of radiux4 q ve3 2ovs4 ;b bo/ss0nydl5sm0 ;vzq,3tvhs 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. What is tb20byopzu um4e bl2t4+*t-uthe magnitude of the torque if the force is exe -b u*tbpl4ozu0uty 2b4+ m2etrted
(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-mp /ijbpb 0 ;orw7xydq.9+ gj the axle of the wheel shown in Fig. 8–39. Assume that a friction torque owpy rq 7obpj9x.i/dj0m ;gb+-f 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 .i )3x cwkkcxb0*s7:s ,y iutkbr- v+sof a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal positik c y*,t7.0 xbs skv:-)xrbic3 +wuiskon and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylin*va rqykr4 lv43, cz1gder head of an engine require tightening to a torque of 38vc z*ry,v a1gl r3qk44 $m \cdot N$ 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 spherehk 3zud.i 56ac of radius 0.648 m when the axis of rotation is t.36i uczdahk5 hrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of lrbk s2 a7r)z)j hw/x280uzja a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass ow8u l27jrar/ z)k0sbxaz )2j hf 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 rod is rotated ir5yjnkly p t-1j 72c0mn a horizontal cirjkyc15j0p-7tlm yn r2cle of radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angfi+bb.5 ev(d qular speed (Fig. 8–42). The fi5 qf+v .dbeb(riction 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 objectsuwvo lj (zz;/e4*wy- c shown in Fig. 8–43 abou;zlczv(eyuw/w -j o 4*t
(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 conson g,rt e;q)b1nm /j /ts6x4gaists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform8x8o / )n.8ftmx nkkpk cylindrical 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 of 4.0 m, what is the required steady force of )oxx.8/kkkm8nt8 pn feach 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 cylihpu, /o3 )recender with a radius of 8.50 cm and a mass of 0.580 kg. Ca3ruphco)/ , eelculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from resot x4* lryfkj+ ri;)f9t 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 tange7qfidaz86 p ,c jway.+ntially on a small hand-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 (eawfqd76 y iz,aj a+8c.pch 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 o1b+l-llu3q. zhr; ap mff and is eventually brought uni; pul.ah+1lml z q3br-formly 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 accelerm aflm-jeh/2i)wp (s+ates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by t bu4lqug7k;. vhe action of the forearm, which rotates about the elbow joint under the action of the triu4v7uq ;bl kg.ceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be vw3j.k mflsth:,35cwconsidered a long thin rod, as shown in Fig. 8–46jk3w. m3ws,v 5lhf:tc .
(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 consist-l nc9mqe --a qn:zr.ss 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 9gssvu0llbd 4:2io)ahbp/9w juu g0 4 hammer from rest within four full turns (revolutiu090)bs:vpsh 4laub2g4udow glji/ 9 ons) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor hargt au,c2gq7pv1+/ dv s 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 deve5dlp cu0rmi -8lops 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 mh+c 7k6m o(chrf hz+;cm rolls without slipping down a lane f(;hkmrc+oc6+ 7z mhh at 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 of a(vuufop q 2b zu1e)2 irg)j,.two terms,u zuav.g ()rp u j1),qb2eiof2
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How muchke *sml(05 w:grrvk)o net work is reqvrk)rl*w(km g o0s: e5uired to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg sw0 60gx:xella7f5rwk js 8o4atarts from rest and rolls without slipping down a 0sel0r7w k6wx:8xgoa a5 jl4f 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 an1fwzs,yfx n4ox5/ m 2ad its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conserva2 omy 5n1f,4wsfa /zxxtion of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ba0 wq, g:2nqgqjll rotating on the end of a thin string in q,0:nq ggw j2qa 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 ofwu24 2ml bryiv* 4j,wl a 2.8-kg uniform cylindrical grinding wheel of radius 18 yi4 bjl4uv2rw2* , wlmcm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rar.f ;lkdr f5v,te of 1.3rev/s If he raises his arms to a horizontal5 d;rvlkfrf, . 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 moment ov4srpd bi ;;kj*m5t+m f 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, wha*rjd4pmb ;;tvi ms5+kt is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rl )wub;vf+e2mxkfe(7 otation rate from an initial rate of 1.0 rev every 2.0 s to a final rate of 3bx7 )2 (eve +lff;kuwm $rev/s$ 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 h4w ypw2 uv1-cmtd(f4 2lm)pbrotating around 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 centeptm1d2p (2v wf4uw-lb 4)mhc yr 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 spinnino wf osjbd4z589wrf30 g 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 moy:z,d- j7 l bsr+aulu7mentum of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylind3r7 wx w2k*kmqrical disk of moment of inertia I is dropped onto an identical di r2kqmkw w*37xsk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 i n-ls5c+rso, $rev/s$ 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 platfofab/xj9c(:n/ jo -ig mrm of radiusn-xmb( cjg: i/ afjo9/ 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 is rotating freely wxo 3 o+im6ae;4rgiyd+23 yx crith an angular velocity of 0 e3d+4xi2 3gom;riyxcy6ro+ a .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 eventualx-o(ezito p2n)2gr ,z ly collapses into a white dwarf, losing about half its mass in the process, and w) poizg(22z- ,enx otrinding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve 44mpl :aaed4;lhdt(vwinds 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 z vrno;ra l a-,xa,/p+$ 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 lm+2ta9i 9r og,ue2l apn+ tq0platform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platft rg292aml9q+ie, aunlt p0o+ orm 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 merry-go-round tulz7 -zc:8kbql q7aqxe+ei9 ;krntable that ila7bk ec+lzqzx-;897 kq e:qis 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: e)m1k 8oxnof 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 of rope unwinds from the spool? How far does the soomef n 1)8:kxpool’s center of mass move?

  The Moon orbits the Earth such ek 77o bju.hmm+t 4wk+8f6zjxthat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a parti 6jkzo7tu h+m xw4 .78jmeb+kfcle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 t(kb*fhso, m9m/$s^2$ 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 x t3k1)rao m9wm p;,sswg9;a uuniform 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 by the motorm wu 9m kx;),;19tpa3orga wss.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of maobb n/45s 96 tor1vnfgss 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 calculgo /9nnrvb154 bt sfo6ate 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, hp(5u a *9mqc hq(ah:,ch4d fisow is the 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 ma22qy0lqvyfrcx/- p tn8*2gxo . u)verss 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 tgx0u/2. nl) r*qyfr vp-2tqyevx2oc8hree-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 use ener6t0+fa xul32d ( jtbt6s cbt2rgy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindricad tt0b+2 c( bs6 tj6t2lfuarx3l 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 illustrates /ln juckfg9v0),bb+n u7dlb,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 surfac0( ,ahivbd/uag b 6t21z rdsy;e 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 fk87veaxg60m - uzu b9pcth.ym,9n sx a/g+fk5reely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. As zp96xut.fmc,7u gv9a x/kb n5semka -g0 8+yhsume 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 vertica5fdjgbqi*- kp)pzw, 8lly on the floor, and we want to 8q*f pbk zgjd,)5pi w-exert a horizontal 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 speed v=4.2m/s on a fb q- q4/o. /r4+lsfcxq 1zoqj5p7nrmi lat road is making a turn with a radius The /.rro1s q-cbon 5 l 4pi4qjfz7+q/mqxforces 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 f 0laza59jwm) :ndyj: 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 reqdfz5: my )9jal0janw:uired 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 herf *:ln uu8 .qq.i0zafr arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and wit ulqu8. r f.zanf*0q:ih arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindricc i(4kwjyx0 u5 w.o6uaal plates, of .kyi5o4c6xjua( u0wwmass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 6hsoub9(jz(5/m q9 sx(vw ryy radius r rolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marb 9vw(m5sb(y 9/u6hozyj( qxrsle 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 ass41jzwu b1 //zdd21*mg3gjw1 glzh ctoume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as t 8qb;8t ay)cqjfygj( /he car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) W c)qf;8y(/jjgqay bt 8hat 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