A bicycle odometer (which measures distance trar-8 .pijpne-/e,i ml qngsg95 veled) is attached near the wheel hub andme lp8iq- inng,e/9s rpgj- .5 is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a poip0labm ueqrdm8q878 k0r(b0r nt on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration ch87p0e08rq8ml qd barb 0 ukmr(ange?

Could a nonrigid body be described b .y mirn /*3hyyzqbd9nap4ly 4+ +z)gay a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expladin 68a 4l1o z*ik aea,jj-h;iin.

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 he5*v :br( tstjlts8pq/ad than when your (5 spjqtls*r/t b:8vtarms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rearv4 ;e4pkv 2qdq 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, a small fro k442;qed vvqpnt sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender8c2d0 msn vj,q lower legs with flesh and muscle concentrav80 c2n, msjqdted 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 wz)- *3fvc6 tdnb*1urbwseelzs )x ar.-e+ q 8long, narrow beam?

If the net force on a system fg9+*irztt*quv 5sx22dk9i gis zero, is the net torque also zero? If the net torque on a system is zero, i2r9qt5gf +sg*ti2k vx9 zuid* s the net force zero?

Two inclines have the same height but make uo6 u*qax1kv) different angles with the horizontal. The same steel ball is rolled down each incline. On which ik) u*6ux1ovq ancline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simf ,v-nklo1vr7 ms8odjnb) 074vha 7 mcultaneously start rolling (from rest) down an incline. One sphere has twice the radius k co4, -l)vnnfr8vo 1dhjvs a0mm77 b7and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start from 4(( 2xh6bz/ldb6yfavjm f-2bj fgo6 q rest at the top of an incazqd62f6 b(4hy g/ bv6 2m bj(ffxjlo-line. Which reaches the bottom 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 moment;f /;k( nn b i0jz6lal;uy7fc.i+n5 :bd kqydzum and angular momentum are conserved. Yet most moving or rotating objects eventually slow dok z/ l6.75i( y:uk0;dn ij l f;nnadqz;bf+bcywn and stop. Explain.

If there were a great migratiwvgvkv2tf-dj5+gko qt0t1+wc* 3 i:s on of people toward the Earth’s equator, how would this affect tktg*otvvc:-gwqj s130t 5 fi kvd+2+whe length of the day?

Can the diver of Fig. 8–29 do a somersault without having any infgwfn(l8 3h q0itial rotation when she leaves th f0 q3gh8wf(lne board?

The moment of inertif23m0n b jrhl/xl(s3ga of a rotating solid disk about an axis through its center of masnfjr3g /xsh l2 m3(b0ls 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 stoolm2yxip3.i fz 1 holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain. 3zi1m2py xi.f

Two spheres look identical and have the same mass. However, one is hollowva5nn9( vkl,ko d*4zr, uba0+ xks) zz and the other is solid. Describe nn9bzol*z4 ukd+5a) asz0,k(rxvvk,an experiment to determine which is which.

The angular velocity of a wheel rotating on a horiyvk:+jk1 6kxs zontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If6jkxy k vk:s1+ the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotatdp// dg4gxn)h ing turntable. What happens if you walk toward the cent d/dnx) ggh4/per?

A shortstop may leap into the air to catch a ball and throw it quickly. Ah0 l7j6i y4aiv;y 7rfbs he throws the ball, the upper part ia4;bvli7r y jfhy760 of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of cog6r */ ja(mmeasss .;mnservation of angular momentum, discuss why a helicopter must;s sj6m r(gamme/*a s. have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in rad0)pp*mm fjj55 dx5sd bians: (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 coincidencwry*tz,nx, s 5dbyp;4e. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, 5yd*w4tsxrn;y,bzp, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverge.,,gg3ouf2n .u mtejvs at an angl.. efmj2tg3 ,ugonv, ue $\theta$ (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 6500id.72etm,43om) h6 dcce3ohn prwwa 7 rpm. When the motor is turned o,3h 7r e7nmw2 6a w)4iotdchce3odpm .ff during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ba1xvzv1 j .s)q9.mz yufll makes 15.0 revolutions, what is its uxm)1zf1v ..9yz jsqv diameter?    m

  A bicycle with tires 68 cm in dia te.8dd*nl:nl 0iks: :4hfb pbmeter travels 8.0 km. How many revolutions do t08:it:e :hsbkfbdnl4 dl np* .he wheels make?    $rev$

  (a) A grinding wheelav j: z:zru pi;/ozu7kynx5::s- q cc6 0.35 m in diameter rotates at 2500 rpm. Calculate its angular veloci;cv : :uas5/uqk c px7::-nzzi yozr6jty 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 revg- yuaj jvi9e f89h3,xolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child s,ghya i9xu3fv 8j9-ejeated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit ar3,synfw:an;e33 tyw qound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of v2 u-,t6 zzmsea 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 centrifuzr4 pbc dm2;-w ot2ynsuj1z-6 ge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of 100,00ytow -4dz jr2smunp 1-6 c2bz;0 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniforml 2o n5, -nj8g6ot2 znrhmu3jqzy about its center from 130 rpm to 280 rpm in 4.0 s. Determi,n z5o28noz6 m-32 jhjuqrgntne
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiu:.y9;wkzl1dh op w 0bos $R_1$ 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 spacecraft put themselve z l/zf+a2vsh/o *5ajzs:dyn 2s into a slow rotation to distribute the Sun’s energy evenly. At tfz aaj:o/ y*5+hvz/2 sd 2nzlshe start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly 6)5z fcidr..n5rw qrjrd /sq. from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in thisjc..r6q/d5d nf)5.wrzri rs q time?    $rev$

  An automobile engine slows down from 4500 go. .,chqk m srgb :uau16w.-wrpm to 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 stresses of flying highspeed jets in a whirling “hut +hje.hnaqya8gc* 15 q0nb h6man centrifuge,” which takes 1.0 min to turn through 20 complete revolutionse61ay.cjnha0b th8q 5h*g qn+ 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 36 o51b7(cd.d +5t6k/*x ucdbuph oybox0 rpm in 6.5 s. How far will a point on the edge of the wheel have trk5p cyxc56 /d (+o u1*dotbhxoubb d7.aveled in this time?    m

  A cooling fan is turned off when it is runn62ec j nm)je4zing at 850rev/min It turns 1500 revolut6mnzc4j2 e ej)ions 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 6k*g7epxic c3b6s h 54a5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a6h34ige p*asx 5cck7b 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 revolutioo8 nm1dmbxmnt0 10km/ns as the car reduces its speed uniformly from 95km/h to 45km/h The tires have ado101n8b mm 0/mmtxnk 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 e9 +glpv egd9h4ach pedal when climbing a hill. The pedals rotate in a circlev9 gp4g9e hdl+ 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 folsb g6jbq) .-brce of 55 N on the end of a door 74 cm wide. What is the magnitude of the torque if the force is exert6g-j)b. sbq lbed
(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 shown in Fig. 8–390*/hp: vzsloy h0(wlh . Assume thatl0/hvw(ps h0h:*lyzo a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a maspmmqe wi 6w)/y+rv l0)+5blq jsless 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 directionjy5m0)ve+wq+ /)wlq ri6bp lm of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a07uqsj.q) am3 4v :p7 elqhkzt torque of 38 mk3 hu7spz0qlq:a7j e.v4) qt$m \cdot N$ 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 spu :+1oyjk 7 2hhfl60jatfo 9dahere of radius 0.648 m when the axis of rotation is through itskh 2lafhj7 0o 1j+9otd a6yuf: center.    $kg \cdot m^2$

  Calculate the moment of i3.bobkg *c1hjvw 0t2 +z8exvhnertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of8hvc x+t bwhg23bko*j v1e.z0 the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod isyenx+hf o jd15arg 36b 6)83ycfqswz 2 rotated in a horizontal circle of rad syzjb63dwff5c a)8 613n+yo 2g qrexhius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotatidf kb9f; ..gksng at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N tkf9fsd .; .bkgotal.
(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 ieb hbf vlfn2v4rf4n1n+k ; 7a1nertia of the array of point objects shown in Fig. 8–43 a1n fh 2nffr4vkl+bn1v4 ba7 e;bout
(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 oxygqb7qs:t+uol6wv/j p; en 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 cylindricr) a-d7c( nhyzal satellite spinning at the correct rate, engineers fire four 7)carh(z-yd n tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder9fiqno euau zsc8c)k(* :p:0 v with a radius of 8.50 cm and a mass of 0.ai 9:f*z epkcu:0c)8nvu(osq 580 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 rr*5/j nyr4 qrf*c5l.(xg5l2jx r vq gpest 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 hand-driven merry-go-r6 uoc)d i4:gjvb- lj6sound and is able to accelerate it from restso 4igbjcj- vd6: u)l6 to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,3005nvmi h k5*2 t*sej*ow rpm is shut off and is eventually brought uniformly to rest by a 5smkjvi o *2en5tw h**frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accelerates a 3.6-kg beo,+9dod1m v w m6p2y:4dh2m cyj4 hoyall 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 7pnkif92 dla3d r4y7mby the action of the forearm, which rotates about the elbow joint under the action ofyl7fd 93dkia7 nmp 2r4 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 considg 3dt wqo1vr/x)b z*(yered a long thin rod, as shown in Fig. 8–4 r*y)qg ov/ z3dwt(bx16.
(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 con*q0- yegr5xg rnxi;(c sists 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 acceleratekt2/ yaqx mz(zy 0;gd-s the hammer from rest within four full turns (revolut-(2y zaq k;xmy/dzgt0ions) 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 iner)l8wox r( iav;tia 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 tor-jw,kro 3her4que of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls wi7)p,s+bnw m chr5x5 (dw dgsc8thout slipping down a lane at 3.3chp5 8)(ds +mns5dr gbw w7,cx $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Eartwwk4(e1/ec zn h with respect to the Sun as the sum of two termse (/1e4wzwkcn,
(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 radirfyos3pk9f-/t. vst a8vwxw 5+hp 78 xus of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid 8 xss8ov/w p+ hr-p9ffkt5.wvty37ax cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls wnh0 sxae8+ma.8el yea8)zqr8 ithout slipping down ah maey88aqezr8 +s.nx)ae0l 8 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 iu3r bv7g3 nr.as balanced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the polgarnr 3uv .3b7e just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on ttpa-92bk hw qshzesx (1vbe2n*z173p dvr:7 lhe end of a thin string in a circle of radius 1.10 m at an angular speedsplve xz3p hk wq2b-(29*v: 7 r17aeshn ztdb1 of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical gri k.ft(gbg/3uk v 4eu*pnding wheel of radius 18 cm when rotating at 1500 rp(4*f kpe3 uv .t/kgugbm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate ol pdrqd w4rw02xn d:g)* )dk*lo,of4m f 1.3rev/s If he raises his arms tok old)r:d4fn0md w*)w,pq l*2rxdo4g 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. 8–29) can reduce her momentlhxb /x7ff.czx4n; z c2-c7 hg 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 tuckz;2hbxc4zhx 7c.7fc- gn x/fl position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rpv 4z1qb/pi j)+j ryma1 vw77xate from an initial rate of 1.0 rev every 2.0 s to a j1ri)jw4v1+y a xpp/7zqv7b mfinal 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 freqhucg e5+ +5fbsf v+z4iuency 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 t4 vi+5c5uh sff bz++eghe rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of azocx w5t;z(rrc g3h7 - 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 angulah1e/i n mfh0*4qg)wlx3pyz 2+ub sl:dr momentum 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 ide,gx ly 078hpisntical disk rotatin xyhg,si0pl7 8g at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns ate g ou: 3.vkmtbx-bf/wh/5*b.l(hp uu 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 r97n nb9ldb c)xi7qth /otating merry-go-round platform of nlc/t7q)7 ix99nhb bdradius 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 merryt3p7 izm26ojs;y3hjd z b)u6 t-go-round is rotating freely with an angular velocity of 0.8ib3s6j)j3 7 yt mpzh zd26uo;t $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about half its asn:x. ugwv5 ;mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(rounvsa:wn ; 5x.ugd 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 windsnss5tfy(l41u 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 mh6vnzxvds ns :rh:.7h 59z4v $ 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 rotate freelb mwmuhq)89zj0 8ee4f;/sooss)v qv:y without friction. Thu)m ;8/osm0evs)4qow8hjzq :be v9fse 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 thbb xi+ 0b*yr;ge edge of a 6.5-m diameter merry-go-round turntable that is mounted obxgb +0 ;y*ibrn frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lyingln) 8; :ci.lxontam q1 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 unwindlaci;to l .n)n :8mqx1s from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such th:ltu ol-58i llat the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to itsll5l :o-l8tiu orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate o9pn z +:uz :/spml,nkxegnu48n ,q.cq f 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 unif7ksa2mkvi*0m,ja/ck 0 q b,qkorm cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the toqks7b i0 mqmvc*k j0a,a,2kk /rque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid m - mcv d7+e5hy2gs52+rroq3rne8 cr jcylindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo jm+m5sryg+n7 ro8ehc r-2dc5eq3 2r v 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 suapey:n /k f76z bz.o-peed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as gc-0z g-7plkled ;67w chle;jgreat, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of rl6e c;d0 lzcwj;--7gl ke7hpg adius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollutid tw:q9 bf(h*yon automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a(tf qy*b:wd9h car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates an iqy-mz65t)2:mvhm new*tkn i+px8n* $H_2O$ 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 horizonta);,i0bqbqgxy hh;ts* l 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 igni3z)/i r3j ;v6mvyujpore friction) /i);6rm i yju33vzjpv 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 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 radiultju(5+g4don s R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests nu+go4t5 (d lj(Fig. 8–55). The step has height h, where h

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

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begin 0s-habwli r5n;hd)jjpim1 67s whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque cj1hjh ; l spd6r-w0)i7i ba5mnome from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder 2zkttkay +z(c:v (m ;pb-h* xwand 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 tightl2:tymtb(hkw z-x+zca v( *pk; y against her body.   

  You are designing a clutch assembly which consists of two cylindr/y tt9ps +i+qj4ymy/u ical plates, of m mpt i49qys+jyty//u+ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 thez14ug ng;m v okhnr7ym ,0/, holuk, kqw*xq48 looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop with *qqk , rolhvk,wu4yh 04,7;z/x n8m1uggonmkout leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, butjwmwh6sdjho ax66155uy u- l t 1zl0.w do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85r/xofo (s1**59jixgds q h qe9 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The t5s qfih9o/(oe9sxr1jd** g xq ires 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