A bicycle odometer (which measures distance traveledrxo rbkpr1-mp0*1xjnph )+ 7e) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with-xr7*x+npr jeppbo)1hk r 1 m0 24-inch wheels?

Suppose a disk rotates at constant angular (j) fgha-3 rdwvelocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radia3f(- warjdg) hl and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be descrhgp8w0d 0 phllya82+cibed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Expla1 2y4nso)f d7(qswos r7z1+pb kidyvz-y -uq9in.

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 difficul ldb(fx.38b mlt to do a sit-up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answer thxmbl bl.d(3f8is.

A 21-speed bicycle has sev 8 6c;n-qxggc5visk3 ken sprockets at the rear 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 sm; nv-8igkc3q6kc s5 gxall front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slendxrbvuei /152cn hd51 ver lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). nvid55 1 e2/hbvu1 rxcOn the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bec*i x17 0oa8ksw;)x ppef -bgham?

If the net force on a system is zero, is the net torque also zero? If the net upyve- b,8n 3/fal) ae*p /nwetorque on a system is zero,a, 3eap/*)uyp/ e8lewvf nb- n is the net force zero?

Two inclines have the same height 4 snfw)zfu 6klahx ;yfnox22(q;5nh 6but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be gnqh6 us; 2foxwz56)x ka yf h2ln(;4fnreater? Explain.

Two solid spheres simultaneously start rolling (from restliv vz fgte 6:m(fedmk m71k:g)z.0l4) 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 t4fd: 6gi )zme gz.0tll:fv 7(kvk1e mmhe 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-y-6 jg(yvuqh6 mio+k. They start from resthq+k-m yov( 66yu-igj at the top of an incline. 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 momentum and angular momentum are conserved. bvefbhss7n,a 3s5es 1/3k0b zYet most moving or rotating objesv3,3 a/f0se7 1 sh kbebsn5bzcts eventually slow down and stop. Explain.

If there were a great migration of people z4r inur faa( yf0l+4ir( qsp827*xlutoward the Earth’s equator, how would 0l4zla ru *2n+ yr(uri f4x7sfpq(8aithis affect the length of the day?

Can the diver of Fig. 8–29 do a somersault without ha -:m1 t6nhel9k9ziqquving any initial rotation when she leaves the boardn :uql6q1ehm ki-9z t9?

The moment of inertia of a rotating solid disk about an axis through its center ) qg u26b3 .bvammxr0dof maam0)bdg2.vmxuq rb63 ss 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 0 tf kg/wyvjygy95f9(stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stf(9 gtyv y9g0f/wyk5jay the same? Explain.

Two spheres look ide l;wf j+ m 2ki/ryo7sa3:fjk-vntical and have the same mass. However, one is hollow and the other is solid. Describe an experiment tj3k s7il+jm2f:a-yro v ;fk /wo determine which is which.

The angular velocity of a wheelw;i :n +s(erot6wyi8g cj2a;)daj8xm rotating on a horizontal axle points west. In what direction is the linear velocity of a point on the top oo t xw+i(ra;cj8gwydj:n 86i2e)asm;f 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 increasing or decreasing?

Suppose you are standing on the edge of a large freely roj36i.siwb3dtb7 8c uutating turntable. What happens if you walk towarducw6j7d bs ut3ibi8 3. the center?

A shortstop may leap into the air to catch a ball and thr*wu0,l ddwy *98tv5qt5wazp h ow it quickly. As he throws the ball, the upper part of his body rotates. If you ltywvu8 *0*pda5zq,ldh 59w wt ook 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 conservation of angulacndiz+:85fnq .pnkev :jb * y0d/zm9sr momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the hk.9nei zfn j5 sz/vyn +bd:pd08m:q*celicopter stable.

  Express the following angles in radians: (a) 30 4b54yb36fyu ntjsx0q $^{\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. Calseo).ez3,v9h db)pbrfjpc 7- -f r+g /i5ezu hculate, using the information inside the Front Cover, the angular diameters (in radians) of th.sh 7pvee,-hd bjgf zop-+9ucr3fi)5rbe) /z e Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed ag bu8c l/j7alt(4q-hft the Moon, 380,000 km from Earth. The beam diverges at an lf/c8g( 7jb aut 4q-lhangle $\theta$ (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 rayn.6)3vfgfm7)hs s ok te of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular accelev6k7fh fyg o)3m.s n)sration 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 ball makerm wn84 9j7 rncmkb0w+s 15.0 revolutiocmmw8rnw0jrn49 b+k7 ns, what is its diameter?    m

  A bicycle with tires 68 cm in dia 4lg78kzi1j ftmeter travels 8.0 km. How many revolutions do the whee481 gikfjt 7zlls make?    $rev$

  (a) A grinding wheel 0.35 m itjx;(t qmj)9ci a( t+un diameter rotates at 2500 rpm. Calculate its angular velocity in mq+(jctx(j)ttau9;i $rad/s$ $\omega$ =    $rad/sec$
(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 i-q -ox9:2n8z mqzzeg 0fo y)g(Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from t2:0-nzziq8exo9)fqo zymg g- he 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 ho pp auo.a z8d.39n4mits orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a vtgfo20 -xn/apoint
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from the axi/p wtq d2()ojls of rotation is to experience an accelera2/lptd j qw()otion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly95qk6dyrhy l8 8 nlnn,g zn)2p about its center from 130 rpm to 280 rpm in ydln9 y8nnk)52h8ng,p lz 6qr 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 7e ey(yz*zz8a 5x wph8$R_1$ 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, astron w43*tu haabdq4rs8mdy s28,lajlx;9 auts 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 interval. The spacecraft can be thought of as a cylinder with a diameteruw28b49a;8jm atsd4lda s ,3xl*r hqy 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 6l/lt )6mv.g6 lmjs1zlcsj. wrest to 15,000 rpm in 220 s. Through how many revolu1lwgs6 )mls6lj.z.jt6/lmv c tions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 120 .soacpl fp584d+-hk8iqjle- jvx9-g0 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 je7d*;mptns(fwf3 8a57 i )c6 rnwm tmspts in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutiompnw*w t)s3t pafi dr;7c7n6(5mf 8 msns 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 jvxj /lc1lo ,2.li*w z240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled,*jxl2wo.jv1l c /zil in this time?    m

  A cooling fan is turned off wb/4wkar,28g8a xs ynshen it is running at 850rev/min It turns 1500 revoluts, r28ywxa a/sgn b4k8ions 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 revolutions as the car reduc /,h 4oq5;uhdg,duevpes its speed uniformly from 95km/h to 45km/h The tires have a diam,4 /hp ;vdudheogq5u, eter 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 reduces its speed *1q-cydzkrav 1m m 9e4uniformly from 95km/h to 45km/h The tires have a diamqz1 eck*9dmy 4-arv1 meter 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 pu+o0tn xa 9,gap k1brn:ts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 b1k,t: an rox0p 9g+ancm.
(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 ode- docb4b ttih;,70 nf a door 74 cm wide. What is the magnitude of the torque if the force is exe b4 bcd;nt t-,dhie0o7rted
(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 +y0wh2stby5 ur)i x7(ekiofk28j r o-shown in Fig. 8–39. Assume that a fricks jyi o r f5)7urkx2ywhi8+o(te-0b2 tion 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 ospcfmwdw h-u0/ u:.cfb57) ba massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then pmc7) wbf0-bfowc/s:u d5h.u released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of 0dhaj.e 5h8 kjan engine require tightening to a torque of 38aejj0kh 5dh. 8 $m \cdot N$ 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 n n b1f82. 0kc6kyerd uti*un6radius 0.648 m when the axis of rotation is nrdt8.kbcn if 6*nuyeu0k12 6through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel hl ctas;98hag.r 8 vw266.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg.2a88lst9ar .c ; hgvwh 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 horizonqjnp6 y57yx (ktal circle of radius 1n576k qy pyjx(.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 poth,fu d1t0 s1m/o hw3amter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N to3mad1t/0mo, sw1uhhf tal.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown izt8f mpj,13e kks 8nc/8eux0v n Fig. 8–43 a1 xj8vpe3esk /cn0ut8zfk ,8 mbout
(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 ofh53nbvq4m e 9a two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at x)5fy6n ojkoz*. (cm ethe 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 steady force ofxo j)6z f.o*n5yckme( 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 withi -s05mvlb5ry xi)-5q x4jj u,gbrd2q a radius of 8.50 cm and a mass of 0.580 k,ji5l-4)2i0mysqb5uqjr 5gx -xr dbvg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest tok.cu*wh 1cu9y 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-7 ,g9; ilovhde6x,uzgdriven 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 the torque required to produce the acceleration, neglecting frictional tz6d9gl 7, e;,ouvigxhorque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually brkz(6p37i iwe1py.zi hp xnk 0*ought uniformly to rest by a frictional to n3p(1iz hw*6.pkipy 0k ize7xrque 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 ay7f8,io5tiu v,dj2 wbz:t lg* 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 byt6 l+6qvp j/c/s6oxsx the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acceler+o/ v6tcqs/xx6s pj6lated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as shown ih+f5 w stf)2fhn Fig. 8–4)s 5+hf2h ffwt6.
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two mayt.u 5w )4derxs -pcf2sses, $m_1$ 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 acceler3 )fm g xt3l/ayat7b(aates the hammer from rest within four full turns (revolutions) and releases it at a speed t 7t/ l3fyam3g)xb a(aof 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 moyz; djl4qr. d9lm:3rd; on po:ment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqurw t)uvyyd97q3 zgg3.e 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 wit59k0nk-ya *6iy00 :a noo skga.lbq vthout slipping down a lane at 3. ikavo a9ny*osk05.g a-k6n0 tb:ly0 q3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to / vb/ yp2j+xyhthe Sun as the sum of two tephv/jy/+ 2x ybrms,
(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*;easu9b mlk,aw +c: l of 7.50 m. How much net work is required to accelerate it from rest to a r,w +lbu sal*k9e:mca;otation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts j:, /dnlu+b.k8v puigfrom rest and rolls without slipp nv:p+8ljb.ukg/, du iing down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanch0asz9p q dy/0ed vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of thh say9pz/d 0q0e upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotat83yz. 7dirr ae; wno.king on the end of a thin string in a circle of radius 1.10 m at an angularni.o. 7eza;kwrdy 83 r speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grinding wheel nos/0 l:/w q8q2ir wxfof radius 18 cm when rotating qfsoq /ixlw0r:w2 /8n 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 that is rotating at a ratlg jqo.) n6,jpv:g g1 qy1kzq0e of 1.3rev/s Iqv 0j)j6o:nz ylkpq1 ,g.qgg1 f he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her mom a3fbyzj+-ld; r; ;goeent of inertia by a factor of 3egf bj zl;ra+;y-o;dabout 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 is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from duk2f bs1x;g-an initial rate of 1.0 rev every 2.0 s to a final rate of xdu1fg2s;bk- 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 thiewr+/ i4wbq *th6 ayu -09rnim01nparough 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 nru r wtny4ma-/hiai*0bi0 w96p1+ eqof 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*d nu*olh (d 1xukqwu(s). 9q1,w dqop 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 momentum o:q i1q ocj(5s)bcde(s3s0 cypf 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 cylindv91f6xugf /o urical disk of moment of inertia I is dropped onto an identical disk ro9fxu/uo 1fg6v tating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns y s z)l-ehw50u8p*m,mglt*av at 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 n ici,d:lt,bi0/op; 5xlaqs3 at the center of a rotating merry-go-round platform of radiusla,i3dc ox iqbs0t :/il;np5, 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-round4o/)i r oezvu2 is rotating freely with an angular velocity of 0.8 i u oozv/e2r4)$rad/s$ 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, losinpsfgh4 (p 10 d5sn2ymig about half its mass in the process, and winding upg(2y014ipm5d sfs nhp 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 excessypa 32mb z eubu/u.*:k 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 3imn8ueynviw c,l9 4 -$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a platform, initially at rest, that can rotate freel p-m39poi irwa m+guh6:43g jmy without friction. The moment of inwmphoi 3gg -p:4mm6u 9jri3a+ertia 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- a1wvfd+*r+n:d :-on:vrrg rigo-round turntable that is mounted on frictionless bearings a v*ri+r: ow ndrf::1a+ndrvg-nd 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 of0 i:pzx:,x mwbvk bf wala7/ uidh1,a6j., x0x the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipp xb6wx0a bpj0mka1 , ,.i7 hxdw/uia:zv:flx,ing. 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 same side always f ;c74 abr wps(-jy:tulaces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earjrbauw -p(:7stcl4;yth.)    $\times10^{ -6}$

  A cyclist accelerates from rest n*aysvoyq 1*0at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of am89lqr+)t szradius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at const9lrt zm )a+8sqant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg je hy;)hnp;u9 wm:trnrf)-/oand 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 e/nrfjo);u h e ;:ptwn- mhry9)nergy 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 hhp ,36cr uuh2is the angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with j/vnusk rxix/76 .alq,8 mjob z38i3kmass 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 inkuj6xzq mvor ,7l 3k.x8ij/as/b8 3 star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution auto iz3bxk2)v:iwmobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has )3:kxzwi2 vib 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 mbmulv9r( 7/*-yj-nmg b+ hmh$H_2O$ 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 bb)q25nr k; uysurface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore frictfs8w1so 8c8/cau*2o e: vefr kion) 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 accelerati*r8euf8woa o v 1c:cfe/sks 82on 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 radiq5 /4y na7ekl8onmh2lus 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 (Fig. 8–55). The step has height h, whe8l kenonlq m7yah 452/re h

  A bicyclist traveling with speed v=4.2m/s onl lds xuvdyfsv6dp o);7bb,161ne.,f fr u42 f a flat road is making a turn with a radius The forces acting on the cyclist and cycle af rlf6df), es7d1f.y ul;1nb2v4ou sp6b,d v xre 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 rocxr5xy k5fk4qf:f y*q4weby4-juk*j 7k into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle abov4 fq-ux:55e7x qwbyk kr*f 44fk yyjj*e 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 as a solid cylinder and her arm 1afcsvsr1 y/1s+6g wbs as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched11ssv b+gs1fc6wa/y r arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical pl:v3(n fcwmzl2 zeeg),ates, of malwf:nz2vm(), 3ez gecss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 h3an(bpo6d/3z *wn(js ;6p q)anlgkqrolls along the looped rough track of Fig. 8–58. What is the minimum valua6n6* kb/os(d )qp3n j ;nwlpga h(z3qe 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, butgje )fv 2q.b:j do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 r:et p*94 :lbv1o dzkwhevolutions as the car reduces its speed uniformly from*1 pevlkwz : dot:hb94 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