A bicycle odometer (which measuresno5oj,ik)v 8ew3v /ai-53rslx2 ld x l distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you u5al x 3/ ,e 8w 5k3rl)vxnsjvidl2-ooise it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rih5t23,cg9 jd8 namzk bm 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 linear acceleration change?,htzkbc8a 5md ng2j93

Could a nonrigid body be described by a sin cc(3;a8pzdtd om7n3hgle value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torquep/nq4 c51c rxmu3o/ud than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behind your head7lod-8gj z ;gn than when your arm-z;ngd gjo7l8 s are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three at/1d a) m 7ysz kkp) gp:+wr-dlf1eid/w the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear ipf)7awskdd 1+dwykr1 - :ezp/li )g/ ms it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able 4)h,op esa+gtto 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 distribution4ag+p)ths, oe of mass is advantageous.

Why do tightrope walkers (Fig. 8–n/x-4. w(x5qdtnhlu u35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net th(qi 9( t29eyts y v6;mvd-ooqorque on a system is zero, is the net force zero?tqvveqi26 htod9 9yy;s( (-mo

Two inclines have the sg l neqv9a1p7.ame height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incq e97a vlgn.p1line will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an q i.- n6o: emxu)*y/ mtux3/hofv)bkpincline. One f//mhx*uovm n.3btyq x)u:i k-6 )o pesphere 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 bottom?

A sphere and a cylinder have the same radius and the same mao,g*)ue /cjfwasjn67t,du (ass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bo ut6 edj( ) a,ojf/g7asw,u*cnttom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conv31ahs o f*bc0served. Yet most moving or rotating objects eventoh* fbvcas 013ually slow down and stop. Explain.

If there were a great migration of people toward the Earth’s equato5abvo,ko qi 27r, how would this a o,5qkbo av27iffect the length of the day?

Can the diver of Fig. 8–29 do a somersault wi3o +edbrfie*g d*8(o bthout having any initial rotation when she leaves +( beg8o*d* erodfbi3the board?

The moment of inertia of a rotating solid disk about an axiszry9yo7q(f fax afw3+6, u1za through its center o, u(ayz61oy r3wqfax7f azf+ 9f 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 rotating stog(tnh8 3 )rr.zbkuvx0fs) a0zol holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular vel8au.3hb v 0 nrzfzx(st0)gk r)ocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the sa8 ue rb z3b2d:gz2y/beme mass. However, one is hollow and the other is solid. Dze/u yd 8brgb23bz2e:escribe an experiment to determine which is which.

The angular velocity of a wheel rotating on ytec*26gufl/2 0r cyxa horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If f u2y*6 gxtyecr/2l0c 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 largy2r9fa (ignf1 e freely rotating turntable. What happens if you walk toward the center(ni2yfg9 r 1af?

A shortstop may leap into the air to catch a ball and throw it quickly. As h4+fzzwe d+ 7k)lrgie- e throws the ball, the upper part of his body rotdzz)ef +k- +4 liewrg7ates. 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 h 9tj:mje. 7i ryj8ng6xw9kk +a helicopter must have more than one rotor (or propeller). Discuss onkjg.n eikt 7x6 9m89jr: whjy+e or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radia(5cscid sg *8h u.ji5cns: (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 ofa.o)qvs4sb8 u an amazing coincidence. Calculate, using the infbav84 q.s) suoormation inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is dire,b:xclrh-b;b m-sax;,m( ;zo tekv 2rcted at the Moon, 380,000 km from Earth. The beam diverges at an an;xba (2mxs ;-zk:c-o b tlmbhe,vr,;rgle $\theta$ (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.,yp2 xxbg 6p*cvq b,9i pm3jd rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angulac 6ib,,3gv.bpx p2* 9mpdyxqj r acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m t,6ggzr(td etak487dzo another child. If the ball makes 15.0 revolur4z t87g ed,zk(gtad6tions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutj)oilvz:iyh1s/k r9 * ions do t j)shyoliir/v *k9 1z:he wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Cal.dedug* 8u h vdg65ee:culate its angular velocity 6eeug hv.5:du* d8dgein $rad/s$ $\omega$ =    $rad/sec$
(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 3l/g, km pjin9makes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m frli /pg3knj,9mom 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) i rs:rh)q )*6e :3nwgjr f)ipq dgc(d5hn its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poft xv6gx0 cewi)l 27o4o 4xa5mint
(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 r7hvjv9/s n5s cotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,hcv5s9sj /7 vn000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 13)b1eicz u2m gd4tf*hdm. n 4.d0 rpm to 2804em.2f)cd*d z udnt1bm. 4ihg rpm in 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 radius(7j3rli 2gz.jjr g2*,k dfxns $R_1$ 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, astrow )-cbv l.nlz1nauts 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 revol wnlc.l- vb1)zution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest tosui30xc o8:h e 15,000 rpm in 220 s. Through how many revolution8ox3s cu :i0hes did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm i;ertjl:9x h -,e3k ojin 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in axixsr7n4q)-fnzq.upny8gu 3dzu i8 ep) 64z+ whirling “human centrifuge,” which takes 1.0 min t 7 q8uzif gun64 q uzyp-))8xrxz3 .nndpse4i+o turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter acceley7furr v(7p *otc4w+mrates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in thiorcy7t7v+f r4(puw * ms time?    m

  A cooling fan is turned off when it is runn ql+q /p bq3li 2c94qwyi,)yuzing at 850rev/min It turns 1500 revolutions before it comes to a stop.py,c4 q) lquii /w93l+bz2qyq
(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 sp*a/h5s7vvj bl6g;1e6 jk dx9)fhyg uaeed uniformly from 95km/h tguhj*d6yv)g7h ba /v ak9 jl5e1f 6x;so 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 revg3ocagc( qv3 b c6gb;i8:j2psa.fi-zolutions as the car reduces its speed uniformly from 95km/h gc az f gv3.q26bb(gpji3io-s8;cca : 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

  A 55-kg person riding a bike puts all her weight on each pedau24 scs /r*xnhl when climbing a h x/sh24ur *csnill. The pedals rotate in a 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. What is tht oi+( (btzdly)gqx ,u;(shd49s2tb:fi fuo 2e magnitude of b9h, f+( (dfz :)lgtb22us4u ioyqs ;(itdxto the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wh1my6- 9n-/ vfensawl aeel shown in Fig. 8–39. Assume that a f /w1elayvm s-n6na-9friction 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 to the e6pf z8iw-brx.ho h/7onds of a massless rod which pivots as shown in Fig. 8–40. Inw6ph hf./ -7oxbor8i zitially the 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 ofgm2a8e -xg9w0u h3zu q an engine require tightening to a torque of 38 z qmxueggu0a8392wh -$m \cdot N$ 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 0.648 fa5fi f-rl h,.m when the ar fi,a.fhl 5f-xis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a4p pnr bg+,l2s bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass4 +n lpprb2s,g of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the 43n f3uy 1wfciend of a thin, light rod is rotated in a horizontal ci3c 3 uf4f1niywrcle 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 angular speqh30fm c,gdgw+ :hd (bw) l bhz2r4ge,ed (Fig. 8–42). rf 4dw hqm,,bz:dbc3(g ggl hwh)+0e2The friction 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 ine1d5c*k4.fixyk+scpev sa+ip7+xmdwl.y5 . b rtia of the array of point objects shown in Fig. 8–43 abo lfx75 v+ . +kxya bpmiiwcsyp15sd.k.*+d4ceut
(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 o f 3(v(/ikivlkxygen 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, uniform cylindrical satellite spinning at thej h* hp pi9z)+g(3pg43awymgw 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 rocket if the satellite i9 hzw gmpgg+ya3j4w)ph*3(p 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 .ic*: 0dr:(z 4nquao gqz )ogf8.50 cm and a mass of 0. *zg :n.f:iuaooc) zrg(q0d4q580 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest npj ba(j9,vlb70 * qkr 34lcecto 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 tangentj-tr+pm y8ay6u mwu1h ku).;8 c2wsfxially on a small hand-driven merry-go-round and is able yay.w261h fu;8t)j mu8srx -+upwmkc to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually b.x km7 t9kass:rought uniformly to rest by 7xkmst9ka .s: 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 accelf7,yfkwbm/ 5lerates 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 t-+3rkw srt h0bg+on,ohrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle,+k3twr +o o,0rnsh bg- 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 considereddpre)o f.kd9mch9c t9 17(wjp a long thin rod, as shown in Fig. 8–49k1( oddcp.e)9h7wt9fpj c rm 6.
(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 masseg)b0qemcf1 4ms, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest wd0 q n)xo sj5vm34ov)zithin four full turns (revolutions) and releases it at o 5)qvxs4j vzdo n0m3)a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a0mg9p) cq/bx5 ;b tn 3mievzgp4 a1jq6 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 develops a torquee;3b4y *h gusexll;q2 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 slipgv 7mb27:ovha jls 71cping down a lane at 3 s77ob7 agvm1:c2l jvh.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ooxcghp 5w6; aa-(kixn/3 f5 zmf the Earth with respect to the Sun as the sum of twgh -m/a56x5 ixz3wakn op cf;(o 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 and a radius of 7.50 m. How much net work.f-987abe:d:e hbhp r o5rvqp is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.0 rp:edbq .-h9 br75vfohap8:e0 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg stayus9 .omgit0 1qzo); krts from rest and rolls without slipping oz0qok1 t9mi;ugys) .down 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 balc81rnuvixe:69;2 c qfvw;j bx anced vertically on its tip. It starts to fall and its lower end does not slip. What wiqc 6v 2jr;e8 xxcvb91:fwn u;ill be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on tvn 0gaq-5:f cou x2g2jhe end of a thin string in a circle of radius 1.10 m at 2uo5 g:xjvcgf20qan -an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular mom z s*k0x+z4l3gwk 0yjpnh9rv4entum of a 2.8-kg uniform cylindrical grinding wheel of j +zs w*gphn4z 4k00vx39lryk radius 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 platfo 5kr8wfeze +d3rm that is rotating at a rate of 1.3rev/s If he raises his arms to a horw+z8k red3f e5izontal 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 , 6r3hdlnrvb5wttc: :of inertia by a factor of about 3.5 when changing from the stra3td ::5t hwvr,b 6rnlcight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spihglj1 1jfmm9 02b81+hyn anz sn rotation rate from an initial rate of 1.0 rev every 2.0 s to a final rat1nfh1m 0ghjb+z8l a12yjmns 9e 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 vertical axis through its cerslufm y(7:,8vgm26qn jku) j nter at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel a,)q8f yk7uu jrvj6 gn2mms( l:fter the clay sticks to it?    $rev/s$

  (a) What is the angular mome i iisdge9el8x3(b2h: ntum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum8wm d)wy)plt 4 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 moment of inertia If)r7zdv5 xp9vleee-+ is dropped onto an identical disk rotating at angular spvezldxr+ep5- 9 7vfe)eed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at tw* 6,q7 xhv/awa2r 9n m1mi9erm1 jkj2.4 $rev/s$ 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 2zi1 jc i66gdnx cw5g4(:tuemkg stands at the center of a rotating merry-go-round platform of wg:j( ceizg tx4 u6icm12n5d 6radius 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 with an angular velocoag/1k),(ypj ;mfv pyv t00 vcity of 0.ym gya f0 vcv ,)01/(kotp;vpj8 $rad/s$ 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 ; 8wv qrlar 4f/i(b2zmdwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integefbl4rmr/ q2 avzi ;8(wr)$\approx$    $rad/s$ (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 windsmd+y b8(rja sz 5k;nf6 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 q e81z0:o0gri j9gc-8gth fcp +irz0 q$ 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, th 6z4e)cp4 dkfy lja+v*at can rotate freely without friction. The moment of inertia of the person plus thky6+czdvj4 a 4lep) *fe 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-go-round t/p+y scbdyp fq)11v3n urntable that is mounted on frictionless bearinpp3qy+nsyf )cdv 1/1 bgs 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 ryn7 n( ardk1oe pdpqr050l0:yolls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of05 kl 1err7nqndyp00 (o :dayp rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always f: fy2cjoun61k sg/0wi4vkkg,n :il 6naces the Earth. Determine the ratio of the Moon’s spin angular momentkc0g1l:/ k,n 62 snovk4i n:y ifj6wugum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from res)y,m 3yl)qsgut at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the +v0qcv h,x 0vrshape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constv x+0q0v,cr hvant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solim6w g8nz5ln1 hd cylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thi5h mnnwz6lg 18n solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angr)q;+ 0ujbrgtzyl5 9s ular 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 times as great, were ros5;)uim zit6sa3fo8c y/zphbb/ .b 8etating atuz/ pb)3 bi ifm/st8;bascoyhe5.8 6z a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the 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 automobaashv 9ug80ujk gr5,.ile 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 kr.9 0su g8aa5 j,vugkhg, 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 illustrateyvc1op(8f c g-s 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 horigbc0se jnw-52zontal surface 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 ig h1 b)kzatt5sd +1ud bm4i*pg,nore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment o,st1udbz 4*ha)gdb 5mpit1 k +f release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radiukvudl-voc(*f 1k b ;ay5o0v8u aq:kh6s R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it r5v *uk-ykb1akdvuv:6 h;( 0la ooqc8fests (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 with ahmm.ue p4tmzaa ++ +p. radius The forces actin tm pe.++m+.m pzu4aahg 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): 03mx2/yk:l m;d8 qczw89erdsgd utir mv1 m of length 1.5 m and begins whirling the rock in a nearly :1u;y)srdk 9dxei:/dt mgmm2 c8zql rw vm380 horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this 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 thvua 4e3 :v th)x6yqr/nt lvh*0in rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her bodh63xvu4lv *t ntq/ y )hva0re:y.   

  You are designing a cxp6oau ,ea5+8 h9wridlutch assembly which consists of two cylindrical plates, of mass a59aw exihr8 d6 op+u,$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loolsu) vbqav83r/.2ixsc1e :rz 0dtec2ped rough track of Fig. 8–58. What is the minimum value of the verti:2.2q1tu8cas0verzdcx rei)v3/ bs l cal height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assum k o, 73.e/uysqar7bv b5 etm6rzqc:9:2f fiewe $r\ll R$ h =    (R-r)

  The tires of a car make 85f0d c8 ba/p0;q eff(kl revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration kb a(dqpfl/e;8 00ffcof 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