A bicycle odometer (which measures distance traveled) is attached near the wheelibl4w*w 6vcazomss3 2l( :(ol hub and3wlo(z s:vi4 cbm2 a 6slw*lo( is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constalpe fk(2f6+5n xn48q hpum/w bnt angular velocity. Does a point on the rim have radial and/or tangential acceleration? If theqxnkbe 4w2 p6lf5um8f (hp/+n 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 g0j*t a-d8u 5ztt g+odok al(9single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater t1inhg ;4lc60lg 2cyv horque 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 diffics-z v/zz3q/zy ult to do a sit-up with your hands behind your head than when your arm3 /zz-z/yzvq ss 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 a(1o 0v4m:mmbyjkblh3a, k7 gct the pedal cranks. In which gear is it h0 bhagcom4 3lb:kym1v k7(jm,arder 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 r:iz.d kxj6q3 yun fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mas3d 6x:i.jy kzqs is advantageous.

Why do tightrope walkers (Fiejs 8q x 7i53he6u7fzyg. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zer;pl+k3invs)g o? If the net torque on a)gi; p 3s+lnkv system is zero, is the net force zero?

Two inclines have the same height but make different angles with atl 1lt/1 dgqe h:wi0n .b3bn8the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the q e whn/t81 b:.il0glnabt 3d1bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) down an inclinea/4y bpv xl6f *.58va8v ywptp. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottomvp v5av x/pbl*aw 8fy48yp.t6?

A sphere and a cylinder have the same radius and the same masqf2 n;kobifua y9h(3)s. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which hkfyb2; noua(3qh 9)ifas the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum jsqyh,tadj xa.60:t: and angular momentum are conserved. Yet most moving or rotating objects eventually slow down and stopjtt jdyq::,h6 .0saxa . Explain.

If there were a great migration of pqm5 l*+lfk8c 5orl 9n wuw-pp4eople toward the Earth’s equator, how would this 9ml5orn5w8 pkc*p-l+ql4w u faffect the length of the day?

Can the diver of Fig. 8–29 do a somersault without havi*yzka6r+ y4u g;la -zung any initial rotation when she le;k6u- y*zzagy +l4aruaves the board?

The moment of inertia of a rotating solid disk abouh ,a,+ cwaxfk,t an axis through its center of mass isakc+af, wx,,h $\frac{1}{2}WR^2$ (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 stool holding 4q +u.xscyb)r a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity inc x)sybq4ur.+ crease, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. Ho3cc:cbb,+cs iy7ya3 pq2 z/i cwever, one is hollow and the other is solid. Describe an expec :yiqc3ps bc a,+73 /ycbcz2iriment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west.o,q/x10ufnih;ox87i5e l cef,cn5v b In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the ta;xnbv5nu 1h/ ile i,f8e5c0 f7c x,qoongential 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 freely rotating turntable(xvik f:-w8qcz8b;gj. What happens if you walk towarq; -ivb8kw:8gjfc(z xd the center?

A shortstop may leap into the air to catch a ball and ehmz1z8- +ars oma+si6x 3a l)a7+t gfthrow it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will slagt)me+h izar86a z137-a+xf+s mo notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the la.2fytd7i-dmi8 hssyg+:p - l d9 wvra2w of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discusshgydsi i wpd2m9f 8 -2yda+-l:7r t.vs one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: q eus)+qg/ ( yo/jez 7eylm/-z(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 ax6dr1 ujsar/h)a gc,aeq 0r(*mazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the g 16ru/(axjha *s0) q erc,rdaSun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is diredo/e, j,pl gp(cted at the Moon, 380,000 km from Earth. The beam diverges at an p, dg/ o,(epjlangle $\theta$ (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 motor isoi bk4)0vw ;zrxy.a6x turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelav.0 b;)4xzoik6rw xy eration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anotfqbgx at9o/ //her child. If the ball makes 15.0 revolutionsfq/t/9bgx /o a, what is its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many re b yxjf;gi dh*g4+w)dwj+f/+uz+kzs- volutions do the wheels make?iz hdfw -;++jjdkw /s*)fug+xgzy4b +    $rev$

  (a) A grinding wheel 0.35 m in dir2,jqw8rl xvz ws5s- (ameter rotates at 2500 rpm. Calculate its angular velocity izv,q-ss5wl r 8jr xw(2n $rad/s$ $\omega$ =    $rad/sec$
(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 comple mgid:cvg-3a- te revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m3 vgagicd- 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 zbgvrko ,1x 3p3 p9cru+i1b5x the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a;delm71 a-tvnp; 3ad7p:xy fa 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 centrifus z/i.hxa p3piepf+. 7 ayiv,,ge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration oahpx7yeps+,.3v.ifz ,p iia /f 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerate-mjnq 9kdl4 5xs uniformly about its center from 130 rpm to 280 rpm j5d mx-nl 94kqin 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 ; i0,16xsdhmqd ej3uh$R_1$ 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 Apo x d5:dnxtg-i2jygk08llo 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 revolution every minute during knd25 jyit-80dx gg:xa 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 r2dxd j.s),zy-d5y ye15,000 rpm in 220 s. Through how many revolutionysy, d2ejd zd- 5)x.yrs did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 12:qa4sl0c ;,ugeqb h5.8 qeqet 00 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whirling “h-6hlihr.g -mu uman centrifug-gri lh. u6-hme,” which takes 1.0 min to 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 accelerates uniformly from h vgcmep6q 0-mia09kc4 1g8 ql240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have t cea6vhm k-m819lgpcg0q 0iq4raveled in this time?    m

  A cooling fan is turned off when it is running ar(r,b9h -j qsst 850rev/min It turns 1500 revolutio,-sjqs9(rb hr ns before it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 repn)h) : of1txwvolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires hav wn1h) po):txfe 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 car rea p- z ul5gn *7-8hr20twichraduces its speed uniformly from 95km/h to 45km/h The tires have a dihit0 8pnu 7 ahrlgza-2c*5 wr-ameter 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 on94waxtx8iypkx b5 2r : each pedal when climbing a hill kiwxx 8y4par:t9b5x2. 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. Whf 0 y0g 8qfyhz 85ncrkoohq-44at is the magnitude4k 540r-hn yqo0oc8qgh f fzy8 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 about the axle of the wheel +hlsg;*gi m98zk6maj shown in Fig. 8–39. Assume that a friction torque of a*mhgl69jm 8zg s;ik+ 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mas8oq5l1ela9 l ds m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net l qlod9e18al5 torque on this system.

  The bolts on the cylinder +vxd+x1 rx7i jc4 cl0rhead of an engine require tightening to a torque of 38vrxxc1xic+ 7r+ dlj40 $m \cdot N$ 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 0.6418r 16;0u;(hqxwo2nee7b k hkcrqu n i0c,ijg 8 m when the axis of rqxbhu0 0qih ,1girc7eju(k ;62c1r8; e nknow otation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. The rim :i2*usmew0/((bs 2xyo uzsm;r1ur knand tire have a c;ue 2w*b i(ums2s m(uz1rs/y no0r:xkombined 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, light rod is rotated in a horiz v/ g4-v4iuudb+bbzv4ontal circle of radius 1v4u/db4uvi-4b bv +gz.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 onlrffk2g6 3 jm2tnq7/m a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N m73 kfqm l/n6gr2jf2ttotal.
(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 o:; cb1 lm56srw,sk:zoy/b;hky )jqsm f the array of point objects shown in Fig. 8–43 aboutclr1oys/ k:5y kj ;6 mqbs)m:;hwb,sz
(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 oxg+0 f1; x ea5qx:,ld cnco-vbgygen 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 sat2 b igdqqt 7g:veo13z2ellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required stgibqt:oz22 1 vd g7qe3eady 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 ulf sng4m)6w3 vniform cylinder with a radius of 8.50 cm and a mass of 0.580 kgms4l)w3 vf6ng . 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 swinr rf ekip/75 x,26aeiqgs 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 on a small kn1lva z2o+h w;o b.b*hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of bhkanw 2 ob *;1lz.v+o760 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 rotatia/*8+arr81jo-wqy qdlb 7 vping at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque qr/ a+ 8vaoi *8 71bwr-dlypqjof 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 3.6-1k i8kxhg 7f(ikg 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-kgalc fe0v:f+d/ ball is thrown solely by the action of the forearm, which rotates e+f0vcd alf/:about 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 7 wnji+y4l*qjq7:/g3g nviur rod, as shown in Fig. 8–4 4/* j7gvninq7yrqg+jwu:i3l 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 -dt3,iol4jye (d ja,vconsists 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 accelera i+ tk.7f5 b drm79 xvpegy7yyafe0,8dtes the hammer from rest within four full turns (revolu70af7tdrdyvx 5 i pee8 y9yb.+m k,7gftions) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of ine;r0 b1:(twdo66shik*mx(qxh q*u ewl rtia 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 torque of m cxo-u t-.k-9 kjpek,280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of ma;k jtyw6lgl ) bg4kx 9.v4ff3*n,umklss 7.3 kg and radius 9.0 cm rolls without slipping down a lane w 9 *.llkxlg fg4j;mvt36y,k k) un4bfat 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respec5upcx5jt1 n7j t to the Sun as the sum of two ter1j ucpjtx7 5n5ms,
(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 y)8bf-v up6irmuch net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? 6- fry)uvp8ib Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest anp e2+h7dfo)n90 jdoxs f wj95ud rolls without slipping down a 30.0 0+92fwsjnx djedf7 )o5 op9hu$^{\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 verticucvea,c;4h2ij ;iw8g ally on its tip. It starts to fall and its lower end does not slip. What will be the speed v ea2 u hwc,i;c;j8i4gof 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 a7.b abur , w/pjbm1vxfqn-/ 5mgjo3y+ 0.210-kg ball rotating on the end of a thin string in a circle ofoj g/mva3/ux+ w .jq7-,bbmf 5yb1 nrp radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8lk8azp;yl .0 s-kg uniform cylindrical grinding wheel of radiuz8plsk0 ;yl .as 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 hi aie;c.3v6a rle y0yxab8i-*js side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decra xjb;8a*ey ivy6la 0i cr.3-eeases 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-.- h9 fz 1cj7execcgi Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straighteex c-chf.cij g7z -19 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 spi/*c* -emuczk*t)y zj z)hysfnew0.r( n rotation rate from an initial rate of 1.0 rev every 2.0 s to sk-r /ty0myh**f nzez.))cjw e(uc*z 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 rotati+bo;am, b 4:dl5bo de/1kodoz ng around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk 4d;e b,ooo5b:1dkl baodmz /+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 moment7 -gpg:3t r 50cdr5s1 yeihlw noz0.42e silhnum 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 momentp m*.h+gyfoj4thqf5-jc4+10t xew 5us give5 um 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 ont* wa jpcpt6)6to an identical disk rotpa 6jptwt)*c6 ating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns 94o khae93;hzimh ;rkat 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the 6 vt dj)(mhk.hcenter of a rotating merry-go-round platform of .h)6dvkt( hjm radius 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 frep6 /abr1px p9 7c2d)lnpwew) er b.9ri+rr v+fely with an angular velocity of 0. p+r.d9r )bwapen)r ce/ir6rb1lpf92pxvw+ 7 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about hal yf, 1sdz25)/utz cbvw/ice(zy al6:vf its mass inuv2czvly c e/)syz6 /bi5tda: ,w(z1f 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)$\approx$    $rad/s$ (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 /adp e2k 2cig: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 xgnalav u8 *u4va+(/ u$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can 3tu37gxi( yti1s b m5orotate freely without friction. T xgi3i7om b3tu(1yst5he moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-g4wy v-pxved0zj.4i 3 vo-round turntable that is mounted on frictionless bearings and has a momew3 vd p4i.v0e4vj xyz-nt 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 end of the rope lyihrdw 0q1qq mn e,a,68png on the top edge of the spool. A person grabs the end of the rope and walks a diap ,qre nhd68mqw1q 0,stance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the cez b hugwx;u*g.64z0same side always faces the Earth. Determine the r.ecgzuw; g 6zb0xu 4*hatio 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 rest at a qi,b2w+4 l b a)(nswcbrate 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 uniakdg p6yg:50 j n6e3xkform cylinder of radius 0.20 m acquires a rotational rate of 6 6a jnykkg0edxp3g:5from rest over a 6.0-s interval 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 ma .nt/soi mv 8qdb:3spti96+vsss 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. Useiisd6 3sv /tpm: bqv98ots.n+ 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 angular speed of 7x;89 p6ps mdsoqufo0 bzt54 nthe 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 witi y/rok;l(-e) w oxf;kh mass 8.0 times as great, were rotating at a spee k)ewr xl(yk /i;f-oo;d 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 ak 7kxc/tbya5 9 low-pollution 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 uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be abla ky/95tbk7xce to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates anr710eap 5t-p kv jcb+l $H_2O$ 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 horizonta8sfhy( elst3*ah./ url 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 (is, jgj+zr:na+a ,mh +c.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular accelerationhm+:zac+ j,sn r +ja,g 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 ha k10lmecqq v8qrg p/2(7:clpr s radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it wi 07 crp2pq1q:mvc8gl qle(/ rkll 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 on16f7fl.cyi vqau4vwid18 0 t i a flat road is making a turn with a radius The forces acting on the cyclistif61a0w1.yvu 4 c i7vdt q8ifl 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 )thj oqt 11wof2;;af oa sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle ft) awf12o;j qoh1;t oabove 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 asfw)s(f,tdo gwg( z ;-jf3c6yu a solid 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, gc,y)w-z( (j;6 ft3owgfdfsuand with arms held tightly against her body.   

  You are designing a clutch assembly which c;ahdfdzmp0 9bo*i5 ap46jbv:- al hy7onsists of two cylindrical plates, of mass; aal-6 ap049hdhofbd7m yz5bpj: i*v $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 loemz ( *nq2h*y/-ybrom g 4l7cooped 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 of the loop withmc oeg*zbyo2*4r q(l-7/yhn mout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not zspoh(q: bgg bd5b 8;,assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unifor-rr 0qsf+4yx)qiv0;zawu s ;pmly fraqi p0wsz;u0 4r fs+;yvx) -qrom 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s