A bicycle odometer (which measures dirw;9 t*b(smbhntk 0 h9stance traveled) is attached near the wheel hub and is designed for rbb9 kn9hm*w;t s0 th(27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates atwd pd4vg 3zs;g*3v/ib constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases d3v/ z3gsip v;*w4b dguniformly, 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 sim2f+yb .dg6zrg 1 kqj,ngle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torquex8u 3b7 +iaxvgx .v-5lmti/z h 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 difficunv sr.gip+ u1xgy3 q7-lt to do a sit-up with your hands behind your head than when your arms are stretched out in front of i+17u pr ygn3qsx-g.v you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and threb r9e2;lr4 u2*z)qklp b jwq,ce at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? Inlkcjz,ub2 p qb);er24w *q9l r which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on be7ms,chegyb s. cg5 .a8ing able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). 7c y.mb,e.sahgc58gsOn the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkerb+b /kf)f 9cqp. p9z;qgm -woqs (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net ,7e0koj,j +6jss xcf ptorquej,cfj 7oxpe,s+j0k6 s on a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the hzpm.rih1w:2(uf9yxg / r y1kborizontal. The same steel ball is rolled down/2zb.1f w9xgm y :1h rpryiu(k each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start r i5 +ypzbqx1q3vz,u8lcq7 p(iolling (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 kiy5ip7 lz (8qbx3u1p+ c ,qqizvnetic energy at the bottom?

A sphere and a cylinde8040 miuk.pcoiz k2umr have the same radius and the same mass. They start from resuczkmu04.p i m8o20 kit 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 the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are cons u(0qgyl y bvha15y2u4erved. Yet most moving or rotating objects eventually slow down l b4 uvq(yh 0uy1y5ga2and stop. Explain.

If there were a great migratiovf++(n p 6vwggn of people toward the Earth’s equator, how would this affect the lengthv(6 fp v+gng+w of the day?

Can the diver of Fig. 8–29 do a someru/nbmre q9+5h ;o e9j sy,h/qesault without having any initial rotation when she leaves the boar hs e9jn+,eyo/e q5h q9;u/bmrd?

The moment of inertia of d9 khjwy(ysjtu ))l .y/o2he+ a rotating solid disk about an axis through its center yj)h/+es9ojd t )khyl(w2 yu.of mass 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 rota,g)pue, 8xt w2e2zddfsq8ezwuj5p . -ting stool holding a 2-kg mass in each outstretched hand. If yod f2p5 wtup8zj. )d2sze ,qw e-x8eug,u suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identiuq7eapoow8:pqc1 5xw::sp xc( m8d;x cal and have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine whwpe::18xx(o5: 78;mq c pawodsq xc puich is which.

The angular velocity of a wheel rotating on a horizontal axg3libt:.2 iob zpw8p9le points west. In what direction is the p32bilzow:g i8 9btp .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 ,d.) 2u,j q;*4kbcirbz gcpb7 yi;izeedge of a large freely rotating turntable. What happens if you walk yc,eg7 4 bu*;2pbizkjr; b.z)ciq, di toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly. As hpyzx 0ups65osyb 9v,zvc2v*-e throws the ball, the upper part of his body rotates.yb6cs 5vvzp0uv-2oy pz * ,x9s 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 conservation of angular momentum, discuss why a helicoeofum0vq*2:p u(5 p4gia( vp*y8z c zopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stabl(o*:gv8p v2iu4(pyeo q*uz5zpa mcf0e.

  Express the following angles in radians: (a) 30 dnbau 3 r 390+c h++6tdpapyqv$^{\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 coincidenqej)xhiw:2cdf80bx7 9mz q 2 tce. Calculate, using the information inside the Front Cover, the angular diameters (in radian:wt2xex0jf28diqc qz )hm79b s) 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 diverges :kur staza6h21.h/ ncat an anglckh/h2s.6zrta u1n :ae $\theta$ (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 mov + mzz-fefnwi-nuy* 7c qc3:+78-eqjfie q/d tor is turned off during operation, the blades slow to rest in 3.0 s. What is the angulaqv*/n q z-7ef-idj cc8iufen7+3fzmyw +:q e- r acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball mme,ml 5d8*uaon a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what islm memd 8u,5a* its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutions do+lnx2aqry5r9s :i5p ky9 ds t6l/g xn5 the wheels makiay 2 rn5r :/qdngxsyplk95stxl 96 5+e?    $rev$

  (a) A grinding wheel 0.35 m in diameter 2e es,w.eesws h2c5c3 rotates at 2500 rpm. Calculate its angular velocity2sehws e3es,c2.e 5wc 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 co:-e mmp2azje( mplete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed zjme:2eap (- mof 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 around the Sun 2l sa0-x8mp or   $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poi y pgy.bb-dc3iza ,k)vtn) (3gnt
(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 ae ugow5lmljz0: xdr s40o+r+*xis of rotation is to experience an acceleration of 1l0 +wz+rol:g jxu0*5es4rodm00,000 $g’s$?    $rpm$

  A 70-cm-diameter whej: y ,pjnm9 7ai6kfelxngow 783i d6x0el accelerates uniformly about its center from 130 rpm to 280 rpm inely9nm i 66no8p:0d x fg7wk 3xaj,7ij 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 radiust sz6n0k(ed:+ xzoia* $R_1$ 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 the Apollo spa 9yk h-aru,sv(cecraft 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 cylinder with a diameter of 8.5 m. Determi (s9ayuhk -,vrne
(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 e-qk9ny +8:xe)rusv ry 1vs31sm )lazfrom rest to 15,000 rpm in 220 s. Through howy)una x:l v1-8 3es+vy1srk)m9 rsezq many revolutions did it turn in this time?    $rev$

  An automobile engine slows dow7v.8w hdy jd-4ilbad 2apu):vn 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 the stresses o nk*z hgkk1: 2ovq)hd-zg8v,t8pb :f of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn thro1,b tvzkqk :kfgvgzn 2:hh8d* )8o-op ugh 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpmko2+ mr +fy3ta in 6.5 s. How far will a point on the edge of3o+t2 kayfmr+ the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min/ te3yv6/ e-hwmulie7 h94-hsq grcb: It turns 1500 revolutionshhm4i v-e-/ t r:w/y 93 chee7lqb6usg 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 revolutions as the car reduces its speeupzxp j/w3)o2 8qvuu:d uniformly from 95km/h to 45km/h The tij/ x3q2uwo:8zup) puvres 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 qp /jng 9iwf2ue:cp*6revolutions as the car reduces its speed uniformly from 95km/h to 4e* /npq j9pfui w2c:g65km/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 bihjx2m/p1au 87s ihf z-ke puts all her weight on each pedal when climbing a hill. The pedals rotate in a circlh-hj za/f2xmis1u8p7e 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 j( sf81dem+ucend of a door 74 cm wide. What is the magnitude of the torque if them + cje18sfd(u force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–3t f/k- g4hliw99. Assume that a fric/-fkglw4i th9tion 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 ju 6f 2sbhacq3zbk./+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 directionahsbuj f/ 2kqc3z.b+ 6 of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening toc738f;y4.h +bx1ppkc tjvcws a torque of 38 c xkv 8bt 3ws.pjh7fc 4yc;p1+$m \cdot N$ 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 injv r u6f*-ahb4ertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation is through its cena6 u*f-v4bjrhter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Tb)d/nzk hj e66he rim and tire have a combined massjz) 6khnbed/6 of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the5 8jx6 8kmtueu end of a thin, light rod is rotated in a horizontal circle t8 6u 58ekmuxjof 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 atx-isa cu 9k8;k constant angular speed (Fig. 8–42). The friction force between her hands and the -98ik c kxa;usclay 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 yi. /0iqft9vy 1 y*mzdpoint objects shown in Fig. 8–43 about iy y/yi z1tq9d*0mfv.
(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 aw+5g3i mnii3 utoms 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 satellite spi7 c,drjkl .u-ws,v .ojnning 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 each ro vs .c-j,u,od. jkrl7wcket 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 8.50cvdhh:t05 sgh2md9 4( ti-l ab cm and a mass of 0.580 kg. Calcu9dahb42 iv(d5 h0gmls :thtc- late
(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 frokn8 2g7c:p8gp n8x);xiq nlxam rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-round gq6kdh;1l6 n:ur ifu220mcab and is able to accelerate it from kh12:6fmgil u0rdb 6nuq2a c;rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the 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 a7*m i7p. zixpzew r.lb/t ;b/s,n vc2und is eventually brought unifl vs bwzz.7;u/i7/cip*.p mb2rxte n,ormly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg ball at 7 re t lh7j hu6r7m49 *pmb:wwse8it,g2$m/s^2$ 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 th -6on9 rk/nevwe forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated unifore /-n69rkwno vmly 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 cons/nhu6 zons73l ;ym)nmidered a long thin rod, as shown in Fig. 8–46. oumm slz h ;3/67nn)ny
(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 ci ii s8i8try- tx93nm7pcto9* onsists 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 hamm0ucx vw35x w;ekwgatg9b 0by7j-x9a. er from rest within four full turns (revolutions) and releases it at a speed of 5ev- b 9xax;xtw9ag uj. b073cwkwg 0y28 $m/s$ 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 inertia of vuoi u2b;2p: u$3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine developsyk1,f 4 t /r.btaljq,p9p:eln a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping doxrlyd ol 52eyg/ ;f8u6wn a lane at 3.3 2f; rx5doy/guy 6l le8$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of/.cmn /dg5paipn q5m7 two ter7agmnp/5dni p./cqm 5ms,
(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 -e)v2c),an y/*dxecho sxp /wm. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? - yxa)c c)e / hon2/xdvwe,*psAssume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls withouw ;ta o(w67xvdt slipping down a 30.0 ;dtv6xao ww (7$^{\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 gun6vtvy6s: k-wy3,:;)c)q z nhrqw kstarts to fall and its lower end does not slip. What will be the speed of the upper3v;r k,t) ) 6hnc s:-wqkygn6:uqyzvw end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular dw u4i3vq,c1+u;smps i7lu 5vwpu-0y momentum of a 0.210-kg ball rotating on the end of a thin string in a ;5yvwuu0w1d m- 3,cp+u7l upvissiq 4circle 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 ;q zqp2uu:f+gf7. v17oq zrcyuniform cylindrical grinding wheel of radius7:7qc 2 ;uqgqr+zp1fu o f.zvy 18 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 u ,l5lb wp0cna7gc4g9f0vle ypf 0*l0that is rotating at a rate of 1.3rev/s If he raises his arms to a h cl7c0b0p gg4anlf*l0 lw u f,59yp0veorizontal 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. 8by5sp uu(4 m iel3n-o+–29) can reduce 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 s when in the tuck position, what is hyep bms +45-ou(l3inuer angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spiv7p 0 l -eta5zw+7 jz68escrkin rotation rate from an initial rate of 1.0 rekc zvea-68s+jre7 5p 07 wztliv every 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a ,( +)x4d3qiuaxnfn*c cffb-overtical 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 diametc)*,qbu fo-+d3n cx4aixf ( nfer 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 sqq :6i;hfx()b k4b3zl qsh: zzkater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular mom1/of0 ow7p-v0 j4s ,irjrsgsqentum 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 cylindrical disk of momey2o- kzy7;elu;bw 8 q)7o crebbms--lnt of inertia I is dropped onto an identical disr7)eb;c;bz b-m-o u-qe yslyol 8k2 w7k rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns alp2ots6 8396u iwv (+idh ogcut 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 t9j /oixvh a4 tgir-4ldo)0h6of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 92t0a/)t4oxoil-9 hg4 hrvj6id 0 $kg \cdot m^2$ 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-gop590i ocdx +iy-round is rotating freely with an angular velocity of 0ypod0i c+i 59x.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, losing about hal/:ufnt7qw4t b f its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(rounbnuw4t:f/q 7td 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 invol gt60j3nh/ xe, jvm rer8m/fo4ve winds 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 *x7 il*1 gzrqt1(us zh$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freely wiw+6x:.haary bt88lio o vg7 i(thout friction. The moment of inertar8 l v6:xtoo 8i 7w(bi+.ayghia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-1n;btrz38p zuj uqp/3i,n7 blgo-round turnta/ piqpnzt,r8u3ub7n ;zjb31 lble 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 with th 8n 0ghg;asye-6 whywl 1k(k)de end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a di(d61w )eka 0wk -hy8;lnh ggysstance 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 Er, bir q q7:-(o.r)vf6.f+iheaso ooqarth such that 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 particle orbi.f+o6 a sio,rqf.)vqrb ero-(hi:o q7ting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest a q:ijd(5 (aqupt 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 ;vci 8oq; ypv5-b4rdvxe bh*-of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calcby-- *evvor 8i;b 4 pdqchx;5vulate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two sow;bxk -jv2/peneeb,798 jv vglid cylindrical 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 diameter 0.010 m. Use conservation of energy to calculate t g;e8 n/v eebvkvwp2j x9j,-b7he 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 the angular sp )84mw+ch3h1v i npqnweed 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 t5ma;c0t34qv 7awwsu l imes as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass tcu v3 75lmq4w0;wasa 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 qh(ion ai 468y 38vupqis for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, usp3no 68 qih(aiu8vq4yes 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 “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 al2o cswoq)75;gy1z5)v*c y, tnutv jxn $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface a/ xxpq.n1uw/ ot 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 fra2 .o uitjx2m0iction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.].2oj2uita x 0m

A wheel of mass M has radius R. Id,fcny52 rjgo/:,goc t is standing vertically on the floor, and we want to exert a horizontdgo: c,, jy2ngf o5rc/al 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 flat road is making a turn witi ahm 3.gfbv8bvu8.quj 77p1dh a radius The forces acting on the cyclist and cycle are the a8ud7v1 pibmj3q8fh guv ..7 bnormal 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.ar4kl +epui*( yr8b g65 m and begins whirling the rock in a nearly hybl4egra86 *rku(+i p orizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s,mf4+ek6kekft/ odv2y d6a3n body as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the anf6 62mv+a 3o,ed kkkye4tn/dfgular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

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

  A marble of mass m and radius r rolls along the looped rough track of t cxxtcs2zwjkabm 6f/,kgu2: 3pb*5 (Fig. 8–58. What is the minimum value of the vertical heigf tgm bjwk:2,(xab c6z 3u*2pkt5cs/xht 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 nvk68j6xvy nu3+ p pw.fot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifora/ *vx6yqt78 ej-qmhxmly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleratetjq */h7vqmx6xy a 8-ion 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