A bicycle odometer (which measures distance traveled) is attached near the w(upr ekep7tm 7tw-l s:(6vu,fheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wh,e6(ut7:s -m k e7r(wfvp lutpeels?

Suppose a disk rotates at constant an3ctsj.nyt)ak -+ )qz, f/bnx ngular velocity. Does a point on the rim have radial and/or tangential ac.fz-n/)bnt nxykaq +3)j,stcceleration? 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?

Could a nonrigid body be described by a sing rk1gxi44qh9w+ bcy2r le value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater :bn(h udxotrhp)rqc j4* 4v.x) 5uc8z torque 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 head than wzw2(p2b i:9p3nr bloy1 y5rochen your arms are stretched out in front of you? A diagram may help you to lr5bbw2pyz: r9 ( y3np oi12ocanswer this.

A 21-speed bicycle has seven sprockets at the re) cyfk-gl.x(d ar wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal,d ( )fgxylk-c. a small front sprocket or a large front sprocket? Why?

Mammals that depend on beinp, w(-tyz8u fbg able to run fast have slender lower legs with flesh and ( b-yfwzp8tu,muscle 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 lk3/xlp y*0 ql)j veh+oe 4vmm)ong, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net +u5s9i/b/dsq )b wxcgtorque dsq9bx/ /iwsc)+ ug5bon a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontaufz)()pqz5m7lnz5t 3,gyv j c-ferx5l. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain,zq5(-ff))j zznvytxc mr el37g5u5 p.

Two solid spheres simultaneouslplxa 1pdv0ok 0.vk2 w1gp/f7g y start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which og 2dgp11v7lk0/x kf .pwpva0has 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 mass. Thocup8g7c/z1 9ybdt8t)p6 wg cey start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Whcu gy/ b698zpcp7o 8gdt 1w)ctich has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and anguiknkzr* s2b g kss387*lar momentum are conserved. Yet most moving or rotating objects eventually slow down and stop. Exp **gk7s28z3isrs nkk blain.

If there were a great migration of people toward theopce04 )a7ef:g2iic t Earth’s equator, how would this affect the length of thegta0cpfi oe4i 7c:)2e day?

Can the diver of Fig. 8–29 12s :xm6xr inmiw5n,to so7;xdo a somersault without having any initial rotation when she leaves the boardmwo15m6oix , s 7ns2;t:xnixr ?

The moment of inertia of a rotating solid disk about an axis thro tkz.: )elyl6dugh its center of mass ily.t lkedz):6 s $\frac{1}{2}WR^2$ (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 sivm,d.k2o ysu4l p3 3qtool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your anvdyqks4.m3o il32u, p gular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow anl(*s ts7l e3qud the other is solid. Describe an experiment to determisqlst3e u l(*7ne which is which.

The angular velocity of a wheel rot+:umppnz +h2p amo7d (;tcf 6zating 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 potpha+pf ;7 zcmmzn u+:d62(points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large 9h6(b+1aat:dqgnc mm freely rotating turntable. What happens if you walk g:h+ab9qtncm6 d(m1atoward the center?

A shortstop may leap into the air to catch a ba5u z;2yqyub 7;uoz1 +p km)tnmll and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and leg;b nuz;q)myuz p2um 7+ko1yt 5s rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a helo0r e)1rddc ;p3bi-qw icopter must have more than one rotor (or propeller). Discuss one or more -;3db)cro dp0rw qi1e ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radian ttk*+ kaa.vh6.c dhv9g)hl ,j*vuqc.s: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, uxv 3 epqnw( xp9*d;fha60mq1gxp7 8 iising the information inside the Front Cover, the angulari0q1 wg3ip*(67dxnvhpm q pexa89fx ; 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 bea rp1l1f ba5-1b xh.4uqelne6j m diverges at56el1n 4lfj. e1hbuab1r q-px an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motork bdtyf,hh - uw)h,g;-1tcph*s 4:xqu is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blat ,htf;u* dhp, 4xyhq)s:gchu1-k - bwdes slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to any0 8fnml,z q+wh- +jcq71i; a neovwz2/ekp e8other child. If the ball makes 15.0 revolu+im whyvp0 ;8n zeq1c-n8e7+ j2wkaz/oel ,qftions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. H(xs62cl5.a*v0ei 3 h gpwlqik ow many revolutions do t6wl2 c pklvghxe3q.i 50asi*(he wheels make?    $rev$

  (a) A grinding wheel 0iv;ab, nw;a)f.35 m in diameter rotates at 2500 rpm. Calculate its angular vel ,w ;a)bvfa;inocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.0 s (Fig. 8–38). lm,49djqlu w1;ah2b)vzh8 eu (a,h )hjm81;wuua zqlle492 bd v) What is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular v bjjh bh g:)uc uf4g8jdm9)j,-yd8:tlelocity of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point n ) 2+ zwwqf:iy) d,ayo(bl4jd
(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 theqq00ojbtp -knr7 kn+/ axis of rotation is to experience an acceleration of 10k0tkbnqor/ 0p-+7 jnq0,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about itsp-qm:6sg+ f5w 98p fghjrq n3r center from 130 rpm to 280 rpm in 4.0 s.-gqg5smf pq+fnw38r :pj9rh6 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 radiuslknnai9 9 5lq* qyiao46l l02g $R_1$ 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 spacecra 9(aj fmk/sv.rft 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 revo.mj 9v/arf(sk lution 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 to 15,00v0) mh8p4agck064f k ; vic iyk31reouibzp650 rpm in 220 s. Through how many rev68crp i ak4v0h3 vc6kkoi g0e) y15ip;bumfz4olutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm tpaus24 h )qk( iwfmh04 w)/tbao 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 stre. (0tjw,fzj ddsses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its fina,w0 z.d jfjd(tl 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 fqkh2l*0u;oprpm to 360 rpm in 6.5 s. How fa* h o2;0puflqkr will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running ( nd q1fas2zu1at 850rev/min It turns 1500 revolutions before it comsa1z fn(u12d qes 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 wz8:ln1od4gi)zfi4j c- e x-qreduces its speed uniformly from 95km/h to 45km/h The :4jzl o8)qw4z dnecif gxi-1-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 revolutions as the;dws 7f8:u25 +n ybwbk ej9rhq car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80hf2 r7;8wjyw+5e9 s bnqu:dkb 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 n sevj245s)w gg+* otaweight on each pedal when climbing a hill. The pedals ro+oev*4s 2ns5jg)t g watate 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 q6v msq8x.rkdd 4t5w e.uwj,bv1o, f *x+t* qn55 N on the end of a door 74 cm wide. What is the magnitude of the torxb8wsnd+ mo *t ,tqefk j ,q4 *15dwqxv..rvu6que 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 wh:ge4 ii ek7.a hf7rxu.eel shown in Fig. 8–39. Assume that a friction rfk7 7.x:e4iaigu eh.torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, ftyn7g)-/ sx xare attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal pxnf)/7tx gy-s osition and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head ofy ))qwwxhnoq7 ugs/)l;5a z+p an engine require tightening to a torque of 38 h;wqng)olsz wp x 7u)5y) q/+a$m \cdot N$ 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 radius9xxg9 m ,slv;ka*caw-6ws, av 0.648 m when the axis of rotation is 6wc*;w a,x99,xav-l s v gaksmthrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66. *un73,raico ;-abhu9qn0 wye 7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be,- noh cuae0rw3u9iyb *q7a;n ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is r 0v mhgk ccp8iix*.90yotated in a horizontal circle of radius 1.2 m. kip0i0g.9 hxyc*cv m8 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 - ag*+.eb6 k,1fmdjcrop*vo r a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force betweenmoocvfa-+.g*dr,b1jp ek* 6 r her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown incxvy; ncs5is*e( 7p -a Fig. 8–43 about ieans-y( c5s *7p v;cx
(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 twr5i0,8zcf :-tarxg/kt c j7wm o 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 correct rap3s9:afuv du wb::l,dzhe6d0( wy 5ymte, 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 fo y h3:9baz0 wds6,l:de5v( :uwmfduyprce of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cyl+8-uk9j qcn oninder with a radius of 8.50 cm and a mass of 0.u- 9o+8nqjn ck580 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 to 3fksg0oib tjo;xw 8. c9hd 3;d* $rev/s$ 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 tange/3p ascbm,1f*(zpl zpntially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and hz 3ppac( l1fbm,p s*/zas 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 isk9/ ilv+t(dgo eventually brought uniformly to rest by a friction g( d+i/kolvt9al 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 w5 :nxq0lh2bbc)yh*qa e 4re8a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the fo t7ehakpmr62-mx+o,e ej x *w5rearm, which rotates about the rxoxe m,+2tk6e5pe -wj7h*am 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 bemv 4ggbcx; ,p((e5cd r (qsrf9 considered a long thin rod, as shown in Fig. 8–46dsqxr5; p, gb(9v4( egc(fcr m.
(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 consists4dlcs- :44v3lm )qxir-lzszj 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 hammer from res-w 0ua2n 1ba */mlmxhevjyx;3t within four full turns (revolutions) and releases it at a sly1w2xv*e/ 03hx m-a ujn;mabpeed 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 m *h3uevq,xghsj 44e ;joment 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 devel5 u,tln6jirq -ops 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 rollsni994dnr9m p he (bcj9l,9 k( jvvl6ci without slipping down a lane at 3.3 9,viie c9nblj(4jm96 vpr(kcl99 h nd$m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to t,7f tm /,iibnmhe Sun as the sum of two tb i/,m,fmi7nterms,
(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;8dof.rg8 ( v+lrs ( esfvqxg..50 m. How much net work is required to accelerate it from resf(rfvqex8g s.8.rogl; +(dv st to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg sd*uw16* ix- u hek.pl)ok n*ubtarts from rest and rolls without slipping down b**ui1xlokn -k u)he6w.p*du a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to f lz1avlr7,tsrq8l53n wti. v;all and its lower end does not slip. What willtvs5rw1z;.8lvt iq,n3r7la l 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-kg5ypp8 ;vsstlcp 7z2 j: ball rotating on the end of a thin string in a circle of radiusp yjpp728lv: ssct5z; 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindricaf 1qjn 6j8kjk o,syr(0l grinding wheel of radius 18yk0,js nfj1oq 6k (8rj 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, o- px+ief 59dx.yd aao4n a platform that is rotating at a rate of 1.3rev/s o-xp9id.e4a 5xd + yfaIf he raises his arms to a horizontal 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–e(kip4 7 0rkm ghqp87j29) 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 ikiqjmg 8rh 7 4p(70pkes her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotatio j.ta i6d7kh-5aqx,thn rate from an initial rate of 1.0 rev ehhktd a5i7.t-j, qxa 6very 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 vef17pd4e7bqk0bc pc 8dsgo2y1rtical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wfscb812p qg1ebp77cd4do 0y k heel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a fi;kgn)8ts1c -4* aeo .tknegkigure 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 momentum oj*oz ench u, xjh8 j6g68br5h6f 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 momenarmrs*w dj2x;k;mz o10be,6 m t of inertia I is dropped onto an identical disk rotating atxa1d r,k;;s2j rwzm6e m*0omb angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at .i:/ ad9. f7r9qzr/lab 303w iqxeknepvkls02.4 $rev/s$ 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 tu(lg e6ktczv + 27o4br9,ixto.jc s6 the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 926cijcotog.(l9 sttxb2k6re4 u z 7,+ v0 $kg \cdot m^2$ 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 anga(b 3pupxi -x ;uu0+tfk)rbux a0iv7 6ular velocity of 0.8 0u 3 (u-pxb tf7kii0+raabuux;px)6v $rad/s$ 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 coloi / mf+x-3 o*hom5gsx3 fjyr.lapses into a white dwarf, 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 momenti r3 xfo5y+ x.-gj m*oo/3smfhum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in n-q3bvdsb+65 hod yu, 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 hgf:do62z 3zbley c;4 $ 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, ini l9mwxh9sjqt6 g 7t86wtially at rest, that can rotate freely without friction. The moment of inertia of the personmhqtx8g 9j tl7 wsw966 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 )26rk92r3z ketdh3 oadlb -wu diameter merry-go-round turntable that is mounted on frictioz - tdw2b)r2ulkod9 3re3ha6 knless 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 the((md*h kgcd 0 kg)7*7xp5r hzvoqsas, 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*mkg*705( vdh paqgsrx dzcs (7,hok) unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that trs h50.:icbme:t dn g*he same side always faces the Earth. Determine t nedg*b .:shcr 0:5mithe 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 orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rd6o; d:ah.x fjest 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 shape of a uniform cylinbht9; gzk4iwn:+m b(o der of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intw(+ b: bkio9;tnh mzg4erval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg as: *dnml xz ee43n5n0-sg8k)d5w z imond diamezddm0-*s)l4ne 3m5zo n5i8xsg : nek wter 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 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 angulfhc: qvc+2 4bsw8n*-qab1fj nar 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 masu221tbbd,kx( nb. cj/ jna8lss 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarjajt/cbxknd 2b.8 s( 21blnu,ters 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-pollutio rgqnp ap )4l xm4*me/;(,x-tdah7du an automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a unifo4 -lu pp*am d ana,tx dx7r);gmqeh/4(rm 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 illustratehy+lil9ls,pny oyh m;5 (5n/as 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 t+gr*j w3n 7kqon a horizontal 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 ignore friction)7peqlr-hov3 * about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment ofeovrl7p-*hq3 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 stan6 wwve 3b z)x3t5ft4vwding vertically on the floor, and we want to exert a horizontal force F at its axle so that wbv34)zev6 5ftw3xwt 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 x)v/-fa5ur8p a;z digis making a turn with a radius The fu r/z ;i-xadf 85v)agporces acting on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rod+ hp;jcr6oq:)9hp jfck into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal ci cpro:q9)f+h;hjdjp 6 rcle 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 + qawm/8xr+libody as a solid cylinder and her arms as thin rods, making reasonable estimates fo/wil+ +qarm8xr the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical )k*9cwkqnk fn1xt.jg1nx;u q:t. +gzplates, of mass*k;wkf :txz19x +n1 t.ggjnn q)kq .uc $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 ro.z75n;xhfkpslfe qw + elw -)9ugh 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 of the loop withoux79)p-;w 5elfwfn .selk z+q ht leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu+b2 8fq4b3te jwxohk7me $r\ll R$ h =    (R-r)

  The tires of a car make 85 d01hqg4m a 7,jqrdd/:l)jkiv 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 accelerat, kd/ vm7041jdgljqiqa )d:h rion 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