A bicycle odometer (which measures distance traveled) ikqno c1)bj6 .hs attached near the wheel hub and is designed for 27-inch wheels. What hckq)noh 61b.j appens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocit r3np/:p 5 gndh.c7lywy. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular ve:.gnh n7 ypdl5pc3/r wlocity 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 single value of the mzrd2ew7 f ae-.6u 1g:ixnxc 3x6r)wwangular velocity $\omega$ Explain.

Can a small force ever exert a greater torq ,hjk,n*rxt: o wv6e9tue 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 x1:b8o 9jxu 740ltbzosu0 n hfwith your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to answeu8x190joxt uzofl 4h s:7nb0br this.

A 21-speed bicycle has seven sprockets at the rear wheel 4a4xgxs lr f9j /6r,vgand three at the pedal cranks. In which gear is it harder to4vxajl/x ,s46r9g fgr pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with f0 f,xuv6zf8i qb/u q(q4wfw 1zlesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational fub z48fwu/(,v0i wfqz q6xq1 dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, n: 6yi;(hszfz e)z7ryu 1ia hmqu(l/n0 arrow beam?

If the net force on a systwt ,4lfhd0f-c.y6dfn f at9n.em is zero, is the net torque also zero? If the net torque on a system is zero, is the net force zero 4,wfhd6t..tfy c-ann0lf d 9f?

Two inclines have the same he f(zcox n:xi48frpyjg2c 10)f ight but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed z xr:2p4 1gnffc0yxo f8)ji c(of the ball at the bottom be greater? Explain.

Two solid spheres simultaxyq0ryb41f na/q ;p/ dneously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinpbxq nf4 1d0y/a;rq y/etic energy at the bottom?

A sphere and a cylinder have the sam1mb 0xsgkof0.0zg 0xae radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has f1 000.gxako0sg bxz mthe 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. h,r3ij 1efsr+2xz/ zmYet most moving or rotating objects event r+sz/23,z rijmxhe1 fually slow down and stop. Explain.

If there were a great migration of people towuu or3a9vsv x, 3 sy3(pdsrl:*kp 8vb:ard the Earth’s equator, how would this aff33v 9por(yb3 ,xs *duupsslvrv: k8:aect the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotm8bpm;dicx ts6*7 lwb2;0yqmation when she leaves the boardt6is*x;m2mm 0cp87w; lqb ydb?

The moment of inertia of a rotating solid dis *p6h;:) rqrpf evquf4k about an axis through its center of mass*hvr)4pffrq :eupq; 6 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 stool holding a 2-kg m qztv bkq .fh4j/s)sv 3;u4b)prdc:btb8 b0s 0ass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay thbrtqcj0: 84z43.ubss0 v)hd) bbqkp/f v;tb s e same? Explain.

Two spheres look identical and have the same mass. However, one is hollo)o pf3j moz+k:w and the other is solid. Describe an experiment to determine :+3pz) jmfok owhich is which.

The angular velocity of a wheel rotating on a horizontal axle points west. In wi3zi lqnl u (rarq95 l 7qmrr-lb97pjr-we;8-hat direction is tr7m-lr qabuni jllrw(l ;58 -7- qreqr3zip99he 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 increasing or decreasing?

Suppose you are standing on the edgesaeq1q6)ob jt)u;8ku of a large freely rotating turntable. What happens if you walk toward thee8s;uuo k6))qb1a qtj center?

A shortstop may leap into the air to catch a ball d,z( w5i pvxfph:o;:eand throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the ;(zox:wp 5v: eifp h,dopposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular mome4m b7e)c j8n7aag9gdy ntum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second p)ayg dbe a4cmg97n j78ropeller can operate to keep the helicopter stable.

  Express the following angles iv kpj3cu (yd5x8eg,0 in radians: (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 a9-e(qmwz ion6 n amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seenzq 6( w9-moeni on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km fromy z9eza80gr1 i d2jq:m Earth. The beam diverges at an anggyd912 0mejqzz rai:8le $\theta$ (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-a e5hcqaw9 +*nbx5b i motor is turned off during operation, the blades*+-cwe5ib5q9xnba ha 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 l+3fzb+yy/ae-dknf41 s-g ps2)y a fzlevel floor 3.5 m to another child. If the ball makes 151-p 2 gs+ls-+fay4e)zfyd fy nk3zab/.0 revolutions, what is its diameter?    m

  A bicycle with tires 68 cmwe,l(a5 rs (h(bn4 jpsv2(gcm in diameter travels 8.0 km. How many revolutions do the wheel( h(jbrcmsn5 ps(lwv(4 2ega, s make?    $rev$

  (a) A grinding wheel 0.35 m in diameter fe3+c jov* 8ha+ (ex, d 7h/jjh3bksxxrotates at 2500 rpm. Calculate its angular h7jeos hd ( a *v+/e+3b,hjx8xk3fx jcvelocity 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 j wanzov*-+ivf6rl+ ug-0lsoglqg)b1+xh8.4.0 s (Fig. 8–38). (a) What is the linear speed of a child seate8+g z.wq ou*r1iovv-f)gsn0- lllbgj+h+ax 6d 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 vz;l8x *qqx :arelocity 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 sp84udt2)ifj hgfh 94h ni9ngl5 eed of a 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 0pilktj-ld my+2qe/.a centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleratio/lj2+0 yitpeqdk- ml. n of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly abonyw-h,p . ,dkkut its center from 130 rpm to 280d ,-n,yw.ph kk rpm in 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 radiu: 7i1slp jzv6kvq;br6 s $R_1$ 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 spac)a.3- eo /u0nlzabmfj ecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelnle/jz -ofm.a)0au3 b erated 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 from rest to 15,000 rpm w me- sigt79o-koaf,0pe.4,h ifa 6zhin 220 s. Through how many revolutions did it turn in this 4gt6emfik,.az 7f-0- hopw9s ieha ,otime?    $rev$

  An automobile engine slows down fr4 p geqe/5fia4om 4500 rpm 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 whi9 4ys*bl bof8crling “human centrifuge,” which takes 1.0 min to turn through 20 o 98bclfb*4sycomplete 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 240r: q co,z*cg 1w0u)tgz rpm to 360 rpm in 6.5 s. How far wrctq *w,0g:z c1zguo)ill a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850 h0 (quj7yws.p: vyk. nd,zvt+rev/min It turns 1500 revolutions b0:usdj( n z vvyh.y7+k,qptw.efore 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 reduces its speed uni-bglr wt-tv9)tcr:x u)4f9upv2 z1 sx formly from 95km/h to 45km/h The tires have a diameter4tguvxpsrb):vw2fu -txz-1tl) 9 9cr 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 redogh a1-li.q r:uces its speed uniformly from 95km/h to l1-i:. rgo haq45km/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

  A 55-kg person riding a bike pycu7 9g v0fqihfs2 .y)uts all her weight on each pedal when climbing a hill. The pedals 0fq)s7.gh92cy ivu y frotate in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. f).lg-x:g7gqf t1xz fWhat is the magnitude of t7f fgqx -.ltg:zxgf)1he torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel sy4zfm1hw x2 08q1gxn lhown in Fig. 8–39. Assume that f 2 11xm 0lqhz8x4gnwya 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 massle ndd/2 4 hm01 cygnsxvj,,zj6ass rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. C dz2s64 c ,jmjnx,vh/ dngy10aalculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine requvll gt0*btu ;b4fy03pire tightening to a torque of 384*pflbl b3uvy00t g;t $m \cdot N$ 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. xp7lailbjb wvs.+e,,2a 9no .8-kg sphere of radius 0.648 m when the axis of rotation is through its cent.biew,nab.j xlaolps 9 2v+,7er.    $kg \cdot m^2$

  Calculate the moment of inertia of sv4ld5 ono)i:*wb yk7h:y i; za bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass oo :oi:v y4 zsihdb;l5w7k*)nyf 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, luh8pmqf c16 )w)x/pln ight rod is rotated in a horizontal circlew/lqhx f1 upnc6m8) p) of radius 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 potf d7 ecn3au 1nkmx jo4:63cf/lter’s wheel rotating at constant angular speed (Fig. 8–42). The frict63jmu ecnx/ca7l1 d 4k3f: nfoion force 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 inerti 0xyva5ir rq- ji(-j:tl6med6a of the array of point objects shown in Fig. 8–43 ab6arldqr5mi(:0-viet jy-j 6xout
(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 consodvn:wvq) (8v i/5eyxists of 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 the correct rate, engihi dawc;l b/,.; 9dkrgneers 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 of each rocket if t/dd,.c agihbl w ;;9rkhe 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 radius ofyn:e 1w;2lx lm 8.50 cm and a mass of 0.580 nle;:2lm y1wxkg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating it from rest to ;re1 hc/zzf *j3 $rev/s$ 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-6y why 6jgf2t0round and is able to accelerate it from rest to a f6jwth062fyg yrequency 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 rotatilt)iu +gx)o bkq1zb,+ng at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque +q,k)ltioz 1x)u b bg+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 bwy 30vh8x3kx-z)/4ythwu bn3.6-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 byw+wu ;;m- yxmq the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accuxw m;-wm+q; yelerated 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 shownmd )j- t4auxs5 in Fig. 8–46t)s4m5au- d xj.
(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 o ka1z 4x2li)pff 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 within four fulymyt,ud+ ke cpho 3-ow-/u,ax i,q:f+ l turns (revolxhua:3,i-,-,tk+wef upco mo + ydq/yutions) 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 momecm ;w8vfnrn.)b /4pyyire k*) nt 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 torque ofta ug12peu v1,cm4w xz-nz,s/ 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 withh h-dir 7cnuib nyj-u62- 2b( 1hy5gmkout slipping down a lane at y jkhunm(-di2 --2ghy1bi5b7r 6ch nu3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earthjr)wldxl ;0skc; qj4pb d +nb:+ y+0ps with respect to the Sun as the sum of two ter0jlcb sd40+ ;p+ykj:sn pbrx)+q ;ld wms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.50 m. How mucfm) n ,28wmhg;2 dqcn:yx yd)h0ich9h h net work is d)n):2my;yqg h92hdwh cn8m,c xhf i0required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and roll33f+-cfb3) 5sf;s yg*ihh pfawfri )ts without slipping down a 30.0y tbsgfr3- ;iifcwsa) h3 ph+ )3fff5* $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It sm;5t0vq* r/xk8 zeky4)y wat starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the groukt )rm4yzt yx;kev0 8/qw5a*snd? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0vhwft f, .fq4(.210-kg ball rotating on the end of a thin stwvfqh(f 4.f t,ring in a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cyliw4ykm9*b 8:g id;njrh ndrical grinding wheel of ra;8wyi*g4d:m hb9jk nr dius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his sideq ,,0b8zyq:ka 4nkdqu, on a platform that is rotating at a rate of 1.3rev/s If he raises hi4ykk8bzqn,qd: ,auq 0 s 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 redu +ldw28plxzg3f2(q(edc;sgf ce her moment of inertia by a factor of about 3.5 when changing from the straight positio(+3wdcz pfdxg2le qgl82 sf;(n 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 inxsihetrzy)ql rvj0;+9btgr/59 cs: 0crease her spin rotation rate from an initial rate of 1.0 rev evet 99) 0:g+zs0 ecrl/;rh v5ibjtxrqsyry 2.0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating;qod m7q7ggr3k4 z f gr/yykr 7:if7m9 around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequen7k3g4:/g7r 7qkf dyqzfmio m ;7rgr9 ycy of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angulaktxwi ow*xv.bd1k 6 )6 yx8i/u(5lfdbr momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular ly o *e75ka8jtgdzv0y /h0u y+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 b*7(xjoxayvi1 26 l/vh ygb9t moment of inertia I is dropped onto an identical disk rotating at anguy7 16x9 ay lj*txbb(iv/ vh2oglar speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at k( 2z yy c*an*7 enfm4;jxm)el2.4 $rev/s$ 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 o1)myz oj vxr73w khf8-f a rotating merry-go-round platform of radius 3.0 m and mmx v z hor8-7)1jkwf3yoment 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 merryliss)94ll. zf -go-round is rotating freely with an angular velocity of 0.8 )sl4lf9isz l. $rad/s$ 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 ab4i3 ttg-hxxco9)go, xout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular moment9ct g,)x tgh-oi3x4 xoum, 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 f2 t9dxk8tozi98+fazx i.a usq a5i;0(ew) o qexcess 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 yv :zki)3-qu *2ro)8xg(in lkvx)x ev$ 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 fq(-ltrdhe4fn s z *xact16 (zxt+ w;c23h8rfrotate freely without friction. The moment of inertia 4 lxzq(2(tn-wz*t+dha fr ftc6fs1x8hrce; 3 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,n0herla:b9bczw x,d u v- t4)kpwa)) -go-round turntable that is mounted on f,:d)bct)b0xw-k) hwl a9arzp, e uvn4rictionless 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 thek4a;y0m nf8pe 0bw62e/ i. ax )jvnnqk end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a disyav.xnf)k qm;i/ 06n482eapjk e0nwb tance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side a/ gi*j ftbvi)/lways faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its or)bv /fi/i t*gjbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from5vt lc:o-xs5m3 w 0g6cd,mxim rest at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acq;q +ewwat8c9w-nx h 5j1n*jt)pwy1fkwc 4q /tuires a rotational rate of from restn w qy49)t* w; xtw5f 8-qwhjenw1 t+cac1/kpj 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 skzf ir767u;f molid cylindrical 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. ;7 f6fkm7z iruUse conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wpu (;ab//y, n y7hhesxheel ($\omega_R$) 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 mass0x88tflnip u;wwm- 2ilr4t) b 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 inl x0)8l- tfi8w2btr4 ; mpwuin 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 n0c)dydjy2 ,o ngnud t6 5wlbcg2n-6/ low-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and shogj2)nlcnwyncn-,gbd5 o /yu d d6t0 26uld 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 es2ot2y cclg: fzv.l34/v e3e52tcnvan $H_2O$ 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 (hoopov6yqjl7yt-bt8iu /5u )0h mv) is rolling on a horizontal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot fregkagl 1iqa v/r3n51 bzccc2 ,p ++n/crely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity a5,vrb1 p zklc+n/ai1g2cc3+ qca/r ngcts 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 v)1q 6u uft-lilo)w( 9jy oudo:ertically 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 (Figul-oj: )uo(w oid 6tf1uq y)9l. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road isxu g(s mg.d0wibp55 -p making a turn with a radius The forces acting on the cyclist and cyclexpw( sd.g50 gmbi -up5 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 inx 3/k gwr5ggqqai. :3mto a sling of length 1.5 m and begins 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 comemwx.3g k5q/i3g: qarg from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and her arms asm/yz i,y- w3ri thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and wii-yimrz3/w y,th arms held tightly against her body.   

  You are designing a clutch assembly which consists of tw3o, aua2rf o,do cylindrical plates, of mo ro2a, adfu3,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 r0v.swd:t1fsv8 *o 0/ttkzujw rolls along the looped rough track of Fig. 8–58. What is the minimum value of the veo8w. w*vd 0zvut js0kf/:st1t rtical 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, bav6j7iw0o eklw *q3a (ut do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducesxljg s:/r7j r ,ys00 4ml6bffi its speed uniformly from 90km/h to l /7j:smx6 y,fjr 40s0 ilfbgr60km/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