A bicycle odometer (which measw,mglsd.dof,zj8 5i2 ures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle w8f m. 2dd,,ozjwg ils5ith 24-inch wheels?

Suppose a disk rotates at constant angularmwltlrh23x -a6 q(p ,j velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either comp( w,-rpxlmah2 6q t3jlonent of linear acceleration change?

Could a nonrigid body be described by a single value of the angular veloci*jovhe 0peka km. e1mve +;3s 6e.sb,bty $\omega$ Explain.

Can a small force ever exert a greater torque than a largereopgd25o :,1 bjooxh +sbc5bo -(tl7d 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 you8 hwoyhsbp22n;p 9sh6 r head than when your arms are stretched out in front of you? A diagram may help you to p h sbyonhw928;s p62hanswer this.

A 21-speed bicycle has sevp92 rur.h2l 84wseq pjen sprockets at the rear wheel and three at the pedal cranks. In whice.qjsp28 r 94lpr hu2wh gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs withebl.: ms rbh)x(yllusq *cx(4. lip .8 flesh and muscle eb x( cshsl8pyq:r4)l miuxb*.(.ll.concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow beam 7 yuu10ec9 zn x6olfy,lwf03/ytfh*h?

If the net force on a system is zero, is the net torque also zero? If the 4dubdb14; q: pem 4elbnet torque on a system is zero, is the net force zero?lpb4u 4 d:1edb4me;bq

Two inclines have the same height but make different angles with th:l hvn: o3kwm1e horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottomlk1: mnhw:vo3 be greater? Explain.

Two solid spheres simultaneously start rolling (from rest)tj746xerph0mxe0nrv( 4f j t/ 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 tn04p7j60et rjx4r/f (hex mvt otal kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They startn5b7i-l oharb7)(q pmct6 ;di from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which 7 5 pb)hd;bl( 6mct-naqr i7oihas the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular myjtd 8d/1y l0jiw7a:womentum are conserved. Yet most moving or rotating objects eventually slow down and stld: 1yw/dw8 ajiy t0j7op. Explain.

If there were a great migration of peoaaxp51eh3uj +t;7 qyj ple toward the Earth’s equator, how would this affect the leq7+x3 ypat uaej5jh;1ngth of the day?

Can the diver of Fig. 8–29 do a somersault without h7lz)4*vptcf e)ce8*y8 oit jsl2m e;qaving any initial rotation when she leav2iq 78ecyttlc s)* ofvm4e*)zp l; ej8es the board?

The moment of inertia of a rotating solid disk about an axis through itsnqnrx )l3ff)vt 6.f z6 center of mas r.6z63nv f tf)n)lqfxs 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 sittingevrt ocwq e( 2(pvqf0qcmm ;k*a**v), on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, e,*q t oq*cmvk(qav )wv2 fc ;0r(ep*mor stay the same? Explain.

Two spheres look identical and hav6ad4a(a avf 5we the same mass. However, one is hollow and the other is solid. Des64va af aaw(d5cribe an experiment to determine which is which.

The angular velocity of a wheel rotatc - 1k/eoa;sy(x :petzing on a horizontal axle points west. 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(epy;ze-s/1kc x aot:. Is the angular speed increasing or decreasing?

Suppose you are standing ounn5;0ve 8e zxn the edge of a large freely rotating turntable. What happens if you walk toward the cezn;5xv8 enu 0enter?

A shortstop may leap into the air to catch a ball and thr ,8si5li3x9gi hz ,wyu-h a0sfow it quickly. As he throws the ball,0sluxhza5h,y3w fig- ,i s8i9 the upper part of his body rotates. 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 conservati ur9umc68z 5ueon of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep th6 85 u9uucerzme helicopter stable.

  Express the following angles in radians: (a) 3l9+z,ou- :pcl gxcod-81ds q z0 $^{\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 becagon5:f6s7u dh *d dtvkv83k,yuse of an amazing coincidence. Calculate, using the information inside the ,yn8s* :k6do5hdg3t fdvvu7kFront Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam do *: okea:ti6aiverges at an *o a:eo i:tk6aangle $\theta$ (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 6 veuc:(8i4ja i500 rpm. When the motor is turned off during operation, the blades sia 8(vi :jue4clow 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 to fpkxst 6xx9340xx0 qdanother child. If the ball makes 15.0 revolutions, what is its diameter? qf4xp6s3tx xdxx009 k   m

  A bicycle with tires 68 cm in diamet o4n8-::liz ystviwy,er travels 8.0 km. How many revolutions do th v:8w:o,y4 ii n-ytlsze wheels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter a5 t97* +uu l i/wfcbjmyb3p3trotates at 2500 rpm. Calculate its angular velocitia3 +lw u7yujt9 * c/btpb5m3fy 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 cq3yggj9t k r(keeviglv49+ 11omplete revolution in 4.0 s (Fig. 8–38). (a) What is the line+vr 4g3vgekqe 919yt1 jkg li(ar 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 around the Sun (2g jx-a4qlfp    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear spee2(fzt(b-htt4c e8zfm d of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axis o4zkh. k9jpaowc :mv/ 1f rotation is to experience vc/k .aho41pwj k:9m zan acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acc.l99nrzp o .mhelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 snh9 zm 9lp.ro.. 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 radiu/9 i/tcg f;sfis $R_1$ 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, astronauu5h y :am+gg:h(/x ehets aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of th5g:ye g(+mxa /uh:he heir 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. 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 acceleratee-secgw z6mjc6r264 ys uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in6-4 cszc em26g6ywerj this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. 0/pfqtom+-egpop/mo/ s9 3nq 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 jetsrf0n/5 ,)dtefu qliv2 in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutioru vqd2i )f,e nl5/0tfns 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 uniforjtnmgbxv1qc5b ;g5pq*. nd0: mly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveleq b j1g.qd0 ; v5mgcnbxn*pt5:d in this time?    m

  A cooling fan is turned off when it f8j.da12fyl ekbx 6 3pnks6s9is running at 850rev/min It turns 1500 revolutions before it comes to a stopj b3e9x2p fkyd6.l8s kfs6na1.
(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 fchaf5l)bkw*bs t7+ 7the car reduces its speed uniformly from 95km/h to 45km/bcfftsh)7abk+7* w l5 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 m xp)27 wpf/ks97zaeuolutions as the car reduces its speed uniformly from 95km/h to 45km/9 pupx) zk7/7ws2m faeh 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 a4pjle8 lv6 jf9byi0. pedal when climbing a hill. The pa9fy le vj64i.8lbj0 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.qhr8ds 1cs.ou vy1j./ js; o/a What is the magnituo;c rdvs1su.o1/a8.q jh/ j syde of 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 ab; j*. gu)p/ye/ys,eu n8tg qkvout the axle of the wheel shown in Fig. 8–39. Assume thn* tpy,v ugeqjk 8ey;/s )/g.uat a friction 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 ends of a massless rod which p3e3 aj1t+o etpivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on to j133 ea+eptthis system.

  The bolts on the cylinder heaa sb1h9ej u8e-d of an engine require tightening to a torque of 38 usje-h b819ea $m \cdot N$ 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 24 8 iugerba13lq utx0of radius 0.648 m when the axis of rotation is throtu0 4xqu2g8ria31bl eugh its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bic 5jiub2ph aj 7f0tlkq 4p+wq31ycle wheel 66.7 cm in diameter. The rim and tire have a combifqw2lk5uaq3+ 7it 0jbj1 ph p4ned mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, e3g 4gl;0qq0frq+0v ufb0 c lolight rod is rotated in a horizontal fq +uq3b0 04oe0lvrc0; qgflgcircle 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 bowb9 2c 3qh8rnwx2)nmlyhn ,3u dl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force9n, y2)32n x cbq nwd3lh8umhr 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 ofe(u+l/g-v 0w+v ojmynu /;x.+esrjbk inertia of the array of point objects shown in Fig. 8–43 aboe-(ng ro/v+; x/j+vby0j.u+kmsleu wut
(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 tl l;)6a.z9iw0vl3r cvgkn+g;r) fr udwo 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, uniform cylindrical satellite spinning at the corrn;cb pauqv(i6yx0/,s ect rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius ofiv n;qx/( c0b6yp ua,s 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniforx 1qv0)zb muks*6xp(sl7eb m2 yq8 4stvu z*-um cylinder with a radius of 8.50 cm and a mass of 0.5qu01q vx2- *ubs * lz4tu) mms6v87by kxpse(z80 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 swing.a*6sovwdg 5vs a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially 0f0ewog9tzn0 ,0upix on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency0wng ftip00o z9e0x, u 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 g /h rs2+)-)u-prtxbm/kx.6noyv xparpm is shut off and is eventually brought uniformly to rest trhsm+-.xyvo )r 2p p -u6xg nb/ak)/xby 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 pxlrh(o jd1a :b5jwf f)ix)/f -re+ 3eat 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 sf)ak p/zhng+) o4d8dgolely by the action of the forearm, which rotates aboutk fhnzg/)84a+p do g)d the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown in Fig. 8 :b6m neq2 8i kqb2.xjqv+pl3r–46:.i26pbxk+ rleqq b2vq n m38j.
(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 massck-ru)yf8o.np uwz*s (t*:r 8 bsr c tz0x:hd4es, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within fo5:1ddou5yf8 z qk;zku ur full turns (revolutions) and releases z1 ud;y:dk5 qk8ofuz5 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 has a moment of inerti0yu2peln0xw-yju2oc. y 3-zpbm; h c5wj0b3a a 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) hwh 0e *ekk9kgcgi;l+kwe,3 develops 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 j laf wlc5km*(80g1pw slipping down a lane at 3.3wf(5 l8gja c mk1*lpw0 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy ofz;2att8 s-bc en fva(* the Earth with respect to the Sun as the sum of two terms,82ba tt (z;*facn-sv e
(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 r .s(b0gqf j9xbadius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinde0gjb fbq9s x(.r.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and yx ptlri9q807,n w:dj rolls without slip n9:0 j7,twypr iqx8ldping 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 balabo -c-da0tis6 p:,put4z-f k, eghdm0 nced vertically on its tip. It starts to fall and its lower end does not slip. What will be the sh,-6 tp gmd -ik t-40,p:zoas 0fduebcpeed 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 the end of a thi5w4o4)qij d.l ;. imzcnepq4+*zd lnln string in a circle of radius 1.1i*..4e; i5l lj cqo+zddwzq44mnnl p) 0 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical gri16ykma30rvcnkd9lsv5e+ - 7gn u q)e0t 7xstw nding wheel of radius 18 cm when rotating at 1500 rpm?temnw7 09kud +segnvx-1q70al6 r5 tv3ks ) yc    $kg \cdot m^2$
(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 rotat79 aoqz hn oj785ebt.ping at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decre5 n qoo8teap.b 7j7h9zases 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 momena3lmup8 ysf g c(,tg86ar-rs :t 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 as: crpa( g-m8 ly,8sf3gtr6uis her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate frhp v.nt :p j:f)q4bs8oom an initial rate of 1.0 rev every 2.0 s to a fbnf:t osh vp:j.4q)8pinal 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 vertical axis throughu/ vu 9 o9zakxwm3i*nk4vyc */ its center at a frequency of 1.5rev/s The wheelzkk3x*i9/w u/vuon*cam9yv 4 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 after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skatertj:e btpv2t x v5q4 47w f05ofrxkq6n: 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 momevz :8x9d g0kyintum 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 I is dropped onto an xj; ojtpb*m ):t pc21pidentical disk rotatio: ;p1mj2 px)tc tbjp*ng 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;,b6ljtz3t j+x o-dofaw 3q 9z $rev/s$ 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 stb3zkj pp904rmd 1 *lqzands at the center of a rotating merry-go-round platform of radius 4 dljzb prk3z0pq1 m9*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 rotatif.qdjz t05zdjz ywf1 48pj 03qng freely with an angular velocity of 0 3z 8jfzjj0yz1.t5pqwq0d4fd .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 half itvq5k)sde0manpo. t92 s 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 integer)o2t0v dq5)apmn9 ks.e$\approx$    $rad/s$ (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 wi6l-b- oz7fw +wprv 6md3h5egvnds 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 -16ts9w5znj jstnn .j$ 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; p.m q6qcn fka)kw65k, that can rotate freely without friction. The moment of inertia of the person plus the platform ispk;qk56 mcqf6 ankw.) $I_P$ 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-rouwq fuecr.r x,1a3x+i :nd turntable that 1i :x fu.e+rxcr3q,w ais 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 tj3 p8*o2;zauaw+ o1p-lqp uvdhe 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 spool’s center of mass move?ozua +l wu 2jp8*-v1aqp;op 3d

  The Moon orbits the Earth such that the same side always faces the Earth. Det*laeprrb : 53jsm)j)i ermine the ratio of the Moon’s spin a:rspj*a ljbr5mei ) 3)ngular momentum (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 rest at a rate of 1 opr g.;(i f.yrm/$s^2$ 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 ih-tx4xaw s69q5c65bmc3jb ydn the shape 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. Calculate the torque deliver6sy6bj5 tmx39hdc cqw45b-xa ed by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cy;1hut 57db3 tuv8o oirlindrical 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 the linea 8vdt3;oiorubtu 15h 7r 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 angula pkv.er9pf+42w xj)b ir 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, we+n1 5bl/ mebifre rotating at a speed of 1.0 revolution every+l /n1 bbiemf5 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 automobile is for it to usja.m+hyp 2qwq / 1ixqh7p(ce 0e energy stored in a heavy rotatin xe.h1paw qq0y( 2p+jq7/ ihcmg flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “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 illustraunv1g-t y z1v+wb2dhf4a(jx:tes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at sp -i ;e*izb210pd chvwdeed 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: hu/tavm03a :az; enm +vam,l.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizu30;mtmv:l e +an /amvz,ha:a ontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing verticallu ttf0+cv7s. jk.c*7,pymp tb:zu6 u inbh68t y on the floor, and we want to exert a horizontal force F at its axle so that it will climb tbn *:yz,8u0cp+6 .7sfikbu7 6hc ptju.tm vta 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 fr0 k-o*cm hm*tr6gyg ;lat road is making a turn with a radius The forces acting on the cyclist ant0g*mh; *6rrm y-k cogd 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 :a8uk1yi+ av/ok5gv df;mz rzo,7 b/sinto a sling of length 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 required to ach fayk s;d:k,g m/7oivbv1u5a/zr +o8zieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solidqt:*v75 mpg (in)wy*i8sk nic cylinder and her 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 with arms held tightly 8iy n(wsii:gp *mckn t q5)*v7against her body.   

  You are designing a clutch assembly which consists of t* +kzgabg+jof x3w7 v/rf*cj y46*quctw2rs+ wo cylindrical plates, of mass c3+ c+fo7u wb *r kzyj gf2w* r*jgs/v4at+qx6$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alpzl (u-: vf8a j:ud7m 9aou5czong the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point a:5m7p-f:z u vj9u 8zdolu(caof the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu71unbo sk1d(jt)uu07 y-qli jme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions ased+z0x 5r3q;uf m(ao b 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 of eachqmxu(f 0d b5e3;ra+oz 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