A bicycle odometer (which measures distance trb0hy , nwtdm(;l2e/s caveled) is attached near the wheel hub and is designed for 27-inch wheels. cw,hdb/0(etlyn2s m; What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on thl7 uwnb e xxqpg/.jaupx+(;5 9e rim have radial and/or tangential acceleration? If the disk’s angular;a9p bnu.l /ejx(xpwx7q 5+ ug 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 sinu+ e+q1mtoj+pklr1o9x49 idlgle value of the angular velocity $\omega$ Explain.

Can a small force ever exer1yc u(g+( bcyit a greater 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 yourxrz12w9 ;ra nx hands behind your head than when your arms are stretched out in front of x19 2rwanzr x;you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear :qp4ri9ikhqis6ov.noq .* g3wheel 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 ih 9 3o6vqpgq:4r ii.sn.kq*ogear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on zv.f uj:ktd5jfv,,yg: 3/ya mbeing able to run fast have slender lower legs with flesh andutj3a .y kmg/:d:fj5v f yzv,, 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 walk yrb,c t:57lhrers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is the net torque also zerocj hrdlcb;/w *etw -0 o al5 -i(.9mdwwn59dup? If the net torque w.bco r5 u5j-mtewd90c9d-w ip al;d*/(l nwhon a system is zero, is the net force zero?

Two inclines have the same height but make different angles with the horizontalcc5) m4qhm )hh. The same steel ball is rolled down each incline. mh5c))mqh4 ch On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from afhew1+3 mh 06f-dh s.pc3xcy rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bm3cfeh-p3c s1ax6h wf d0.y+h ottom?

A sphere and a cylinder have the same radius 1q y7qr6,+dnrrha 0ah4z8h ppand the same mass. They start from rest at the top of an incline. Which reaches the botto,4a h0+ qprhnayqzhr867p d1r m first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular to1;*a-6w sfa t-kj fgmomentum are conserved. Yet most moving or rotating objects eventually slow down an -j a*fkotw6-s;1 gtafd stop. Explain.

If there were a great migrahwf( c8et + s20l.n(-imrzcyktion of people toward the Earth’s equator, how would this affect t(e .rn2h f+-kymsw(ct 0z 8ilche length of the day?

Can the diver of Fig. 8–29 do a somersault without ha*3..cj puyy ;*q zxzewving any initial rotation when she leaves the boe. ; zc*jwy*.qpz3yxuard?

The moment of inertia of a rotating solid disk about an axis through i lbe4)p(5jgwzi ,b;ah ts center o5bj (ha)ei, zpbg;wl4 f mass is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating s5o3 xwe2 - ,2.ghqesfwcwpe.utool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrea ,5uwc- 32wg.fe.x2ewospe hq se, or stay the same? Explain.

Two spheres look identical and have the saslfd*i.z b bk)m. 5bt l8c17wlme mass. However, one is hollow and the other is sdlb i7wc.zll8m.f)b tk 1s b*5olid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points we92;m ik -53 syrwvuauast. 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. Is the angular speed incre2kv s u;uiw3am5y 9-raasing or decreasing?

Suppose you are standing on the edge of a larg)b;; paew bb;dhb) hx-e freely rotating turntable. What happens if - b; ))bhhep b;;xbadwyou walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quickly.yhn4opec 52+ df fpi80jqdp 2, As he throws the ball, 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). Exf,cy2hqn 5 8p2e dfp d4po0+jiplain.

On the basis of the law of conservation of angular momentum, discuss whml+t -e /4quxyyxj) sf:7t kw(y a helicopter must have more than one rotoxfwl)y tk:e+u-t 7x4 sj(/myqr (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 30*p, nipk(j9 oz $^{\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, using the 5(sl(zzu fnc3mx.vbv;,v3wk information inside the Front Cover, the angulawb u(,kfzmsv3;3c .(zvnx lv5r 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 fromew0;/ nxguye)i+ 9 vfr Earth. The beam diverges at an an+x fewe 9;)u /rvngy0igle $\theta$ (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 mop8 dnvm ejm*+5tor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelernm v+85pejmd* ation as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level kzuw+)k4ftnni/t*zmiof ez 7m.3/9 hfloor 3.5 m to another child. If the ball makes 15.0 revol4 umnmzf/i+k /w9o kz*7eh)i3ttznf.utions, what is its diameter?    m

  A bicycle with tires 68 cm in diameter t iif523ju6 nytdqy j3/ravels 8.0 km. How many revolutions do the wheels makef yunj yd2ti6 /3j5i3q?    $rev$

  (a) A grinding wheel 0.35 m in diameter rh0bs).m ,;0xlp pe l4 +nmyqvwotates at 2500 rpm. Calculate its angular ve l,qv ); .0y0x+l4mnembpwhp slocity 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). r kik4a*sj:0:*efo:)cpc p y ln,yva4u x2d/ e(a) What is the linear speed of acpdkpaavr*ey0s*fk u,jolix y 4)e:2n/4::c 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 velociqfmr mim1, zx)fu4/j0ml m):hty 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 v h:v79vfp5dsa 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) musv qjy n/mtj:61t a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to nj6t 1m/q:yjvexperience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceleraten ;pu1eilie 39nv q5l1s uniformly about its center from 130 rpm to 280 rpm in 4.1nvl ;9 ueienp1li3 q50 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 radiuv /wt :nxko(c9q6h we5be-3rqs $R_1$ 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 Moonwf9.s pr:;lgs7us5 (hasw5ulps4 a y*, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time in:l s57uls .5ss(aswg*9uypraf; p4 hwterval. 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 15,000 rpm in 2zzrs ejqfl,3 f;u1rl+4zh* g9 20 s. Through how many revolutions did it turn iezzq*jz+h f3 l,4lr1s9r u;fgn this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 8ruvzd-ocvn z7z 3x-rz ;(l2cs. 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 sx ; rx1 bekkutz7h/u4/.s .w7jfmpq*stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 comp sb; u/ze. 1m.uhp4w q/ *rtk7jsxfk7xlete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.5 zpd99w)v6 ,ro9) qntbqex,b ks. How far will a point on q wexn)9bo ,pbqkzdv6,t)9r9the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 8o6gcl e pnwde5zykzg *301(u9 50rev/min It turns 1500 revolutions before it comesw gy9d l*0 (6nzoe3e 1kup5zcg 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 +mj. ubqf1f/w car reduces its speed uniformly from 95km/h to 4 j+/.fwfqmbu15km/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 revolution6m2 )uon 7z(b*s bfzuznjc,l; s as the car reduces its speed uniformly from 95km/h to 45km/h The tires ha c2* ub u6m (;nb7j)zznzs,lofve 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 pedal when climbin y8bu3xuqcqh325e 0 w7llg w99s:kvssg a hill. The pedals rotate in a ci3yg053 9 cw7h vl uu: lws2bq8seskxq9rcle 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 w(aw ig)e 0vcl/3lasb3ide. What is the magnitude3 s bvl0alw)3a /giec( 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 whe:* snhcn-xwzhx9:v 7 zel shown in Fig. 8–39. Assume that a friv :cw *n:xz9hn-7 xzshction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of maskg+k4r;xsgd3 p 4b ,xws m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rogk ,x+prg; 44skxwb3dd is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engk a4w equl;97c4+ndbiine require tightening to a torque of 38kuq;+ w l4n7ei9d b4ca $m \cdot N$ 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-kgf*)/:varo fi k sphere of radius 0.648 m when the axis of rotation is through:)vk/ra*if of its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. Th0x+xt8pngg ; ( 5lhvopi. )inpe rim and tire have a combined max.n p5p ov (gxi8+t)n ;gph0liss of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on mljhshu cg(.,:: m.vpthe end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculate :cvlh gj,mu. :(p.hms
(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 bo)1eyx l585pzr;pra-dtk 13v kd8 bbzkwl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction fozzkkb rpt v;d 51- pe)1 rlba58x3yd8krce between her hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of poi5o3 j vh,4nhnbnt objects shown in Fig. 8–43 a3jnvob, 5nh4hbout
(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 t,)ig t b*tbfg6yrnnm1) a -i7two 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 spinniz6y 1; sa(xlizng at the correct rate, engineers fire four tangential rocketixl(sz61 za; ys as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radiunm(b+u(-q. mfw +qxnqs of 8.50 cm and a mass of 0.580 kg. Calc+ -(mubx.+mwnqq qn(f ulate
(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 reslh3kbm 7 /w1kyt 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 tangentit05:y:axj hy,z mye;e ally 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 has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate ty x5zyy ea;:m,: 0ehjthe 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 10net ;3pix4+r8x yk3gr ,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.t4n +ir;xe 3 p8rgk3xy2 $m \cdot N$ 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 acce n1:hyo(dab a*lerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forearm, whic 0mma ff7iej5 ;kdzh24h rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is famh0ef7mz 4i ;2kjd 5accelerated 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 r9) j)aen *evgw-m 3mkwod, as shown in Fig. 8–4m-a) e vwk*w mn3j)ge96.
(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 consi) 0+f*0ztkbp *v0 j2j ccuamtyiw2vfw;q7i x:sts 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 rest wl8goqroc:bh2-n4 3f q. fcgo 1ithin four full turns (revolutions) and releases it at a speed ofolof. c:1q bgc3ho-q28g4nr f 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; s i1(ie q ymf4a6-bp9tvcyg8 inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque ofib5;ufe5 o5r p 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping do zgf4fnlm -x ck8utz*cu2y/ :2wn a lane at 3.kgu2l8cfu4 xz ynfc/ *-:2tmz3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic e/;5qy*t1mtjae ope-c+ xd eu2 nergy of the Earth with respect to the Sun as the sum of two te;etu1 m* q+dexytc2ja-op /5erms,
(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.ofuh6p 3 m.vfjumle:px ;(58o How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00u3ml; h5oe8(u f p.v6oxf:m pj s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls ,6f ae onjr76mwithout slipping down aojnmr6 ,ae6f7 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 onv 6vjt.s i)uf+ipt6: g/w a.wz its tip. It starts to fall and its lower end dti vtvw +w .ijz): 6.f/psaug6oes not slip. What will 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-kxqfy*v*fi 2k 9g ball rotating on the end of a thin string in a circle of radius 1.1f v9y*qfix*k 20 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 grika) 0sjgsdc) va 3ln61nding wheel of radius 18 cm when rotatingl)6k a)dn sas 1cv0j3g at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform thatdhpzb,5a 0(1;pot( x cdj ,gbx is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the sx;,ph5gt0,oxd((dbj c zb1 appeed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her moment of ine,shn2d7+qpp.vgbm; d rtia 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 id., ;h 7sp+pbgdvqn 2ms her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can inn 3/pd 1zu/rgm)jnjp/crease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final m z 3) 1gdjj/nu/pnrp/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 through its center at a rn:mbzz f e)16c9)tv gfrequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. Tz6c)1: fgmnve9 )tzrbhe 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 skater spinning at 3.5u4, .i/qhv4k nsz ggo83 txuj5 $rev/s$ 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 lx(o0fzm/wga,aes ,n:3 3tba9fr ;prmomentum 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 identicy12bk0-ulon)c nhwy 7 al discknwh unyo)721 lb-0yk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

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

  A person of mass 75 kg stands at the center of a rotating merry-gg+4erpb eem+ cc9-g (ho-round platform of rr +ch(g p b-mgec+9ee4adius 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-roun dh99wq:mzk (r(min,cd is rotating freely with an angular velocity of 0.8 mihzk 99 drcn :((q,mw$rad/s$ 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 ;ausb28lymu2 bhw/,ed1p vn ,white dwarf, losing about half its mass in uelb ,b 2u1n/8sm2dp;v,h waythe 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 in excess ofx*g*a lv p+c hge tv)+thd357a 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 )dz-*pg 8rz5sj6w okv$ 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 lw fm6 0inv 7*n4vw*ahrotate freely without friction. The moment of inertia of the person plus the platformimwn7l* hv*n0fa w6 4v 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 stannyrfs*;gka1ur-6 d 3rtzz1o5 ds at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a momenzugsd- 56ro f;1na*1r rkty3zt 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 , e60ru-xfi8jcwi zi5 of the rope lying on the top edge of the spool. A person grabs the end of the rope and 8i iur0cz6exwfij, -5walks 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?

  The Moon orbits the Earsqcc*tk3hjy (5( 7jtk, r z( ethpf61rth such that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbik1zc rf(r e,ht jyps3qkj(t*h( ct567tal angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a r611q3zfa: w xg3 yz 3kd2zpb)up y7z4csqrch4ate 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 cylind2kdf vuqf hpm/)5 /rg3er of radius 0.20 m acquires a rotational rate of p hq3r2 fk)vud//mgf5 from 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, eachpyc6;zbsqy (8lm fq67 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 tobl c f;q7p6m(z86s yyq 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 the reazjcr x 2/b wb0+c:h1pwr 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 wit4 b8ui bwcrl5*m/b6iph mass 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-quarters of its mass in the process, what would its rotatioi bm8p*luwr 4ib6b5c/ n 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 automobis0;0xx,jzc ty le 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 able to trcytz,x; 0xjs 0avel 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 utglz.: cp8ja 7dx+k7an $H_2O$ 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 speed v=uo, )sh: rk:gz3.3 $m/s$ 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 free4,ri q+,1vyj w3pp tq-fehi/ gly (i.e., we ignore friction) about a hinge attached to a wall, as-yh qgt1j/ q+ ipp,vfwi,4 e3r in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically tjo 1ew( d53lu0l+zjlon the floor, and we want to exert a horizontal force F at its axlt(l1zj jlu5o wl d+0e3e so that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a tu4swen e:5mw9rieo0 f6rn with a radius The forces acting on the cycf6nwsree4mi0:wo e5 9list and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins wh1z2xzckob 8z0irling 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 achieve this 1zxoz0c 8z2kb feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a s9ji7 llqcvj 01us b0u5olid 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 agl0jubq9j cv0is 51l7u ainst her body.   

  You are designing a clutch assembly which consistw dgd9cfrj5os kws 75)6 5khv7s of two cylindrical plates, of mk95)wd 7j7hofw r cvk5s5g d6sass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 r9qcbt 0 zj g4ih92s-qp );cquf+ftf(jough track of Fig. 8–58. )b;qj-c9q fj2hf9qs4g(+ufti ztp0 c 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 without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dormb m*4hg;rm 9gyin2e.s8:wn not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the ca1 a)p(yht9 bxiz1s g,vr reduces its speed uniformly from 90km/h to 60km/h The tires have a 1 g,sb)y9v x(tz1pahi 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