A bicycle odometer (whic8(r.*bb.uudt2i1 crrzlqp 9qz h;q - ch measures distance traveled) is attached near the wheel hub and is designed(*zih bz-rqqp..u2qd8rtcu1 b 9rc;l 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 point on the rim v9sw82xgk 4 udhave 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 mak4 svwu9 8x2dggnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single be 4b/kg-rh25kys7:tjo a o/yvalue of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger forcew5 hv s*i0g4br? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your han/lvjh7 oh t4 / xu917j3cxelcm4jk rb,ds behind your head than when your arms are stretched out in front of you? A diagram may help you to answer thkxxc/ 391 ,m j7jrlb4 u4/t7jlchvoehis.

A 21-speed bicycle has seven- dxx zlw3;2 8ztte/ue 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 small fronz -ew2t8ltde; xuzx/ 3t sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slen-2aq:lonjnr b *7xc r3der lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribcxnn-r* jlra o 23qb7:ution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrow bew+g bs.o(z,lu am?

If the net force on a system is zero, is theefrho/oaa3 rh uj)+yh a;)74o net torque also zero? If the net torque on a a+7h)oou jryah ;/o4r 3 )efahsystem is zero, is the net force zero?

Two inclines have the same height but make differz20 t+edy ca04fl0zqf ent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at thedc0qlyfta 2f0 z40 z+e bottom be greater? Explain.

Two solid spheres simula a,v)e i1;bqktaneously 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 kinetic energy at ),i1 ;beqaavk the bottom?

A sphere and a cylind wxe ek/fcs:0)k gg;i4er have the same radius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speg f ke:wi)gkx/e 4s0;ced 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 conservedkmqv)9v h-8prvt l cvxwn wj7(+6 4eb2. Yet most moving or rotating objects eventually sl p2n4cvvj9v8qk7e+6tbw xwml(-vrh )ow down and stop. Explain.

If there were a great migration of people towari2cw mh8sp4 3awj ;pp5d the Earth’s equator, how would this affect the length jc4ampwh3 8 pisp;52wof the day?

Can the diver of Fig. 8–29 do a somersault without having any initial ,g/v8m0,xroh ql vv(wwy:zw2gk 2r r2rotation when she leaves the boardvhvomg82w(,zyqxgl r v0kw2 w2r :,/r?

The moment of inertia of a rotating solid dicz3f j.ajldh+;( o4k9 maexc+ sk about an axis through its center of masscj3o;a ec k9fajzml+.( x4 h+d 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 rotatinggt2)+.tbe38a hfx oo o stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, of32+ tooha.txg)8e b will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollowf(0 .i 65o6kzyhmtjsg and theiksgfy(5 tj6 6m0o.hz other is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. Inqp- 3on4icjz-ol m-f7 mro6 *n what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration pop3 icm7zn -n4l-joo-f * mqor6ints 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 rotating turntable(x k6+p/ohihc. What happens if you walk toward the(o6k ixph h/+c center?

A shortstop may leap into the air to catch aifd o;/ saoh6 gis1h.0 ball and 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 opposite direction (Fig. 8–o;0gdsi1h./6 hsa ifo36). Explain.

On the basis of the law of conservation of angular mouou1wt1vrg zo 52hk5. mentum, discuss why a helicopter must have more than one rotor (or propeller). guo5 z11o .tkw2hvr 5uDiscuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in/bdbac , izb7u-f em rh7q9,9,qh2 :yt d/czaq 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 becaudh v,i3vb 1ey p(gog:ddx+ 1+ase of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon,vx +bad(o,h1dp1 dy+gi:e 3gv as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directedvpbumahs( px 2z 7ks+5lo+f- , at the Moon, 380,000 km from Earth. The beam diverges at an anp,ms5f7z h+o-(+ avb 2ulpsxkgle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. When the motor is tux/ rkwakzx;.;t1 b a-mxwpt/3 s r4hq,rned off during operation, the blades slow to rest in 3.0 s. What is the angu wttx,k;pr ;3axxak-sb. mwq z r41//hlar 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 ball make0 c2w8xxdi n,x r(f:7 u5urgwqs 15.0 revolutions, what is its :xw25x0uqfr7 8g cw rxdu(in,diameter?    m

  A bicycle with tires 68 cm in diamey,+j2e)9 q: r8mxkwreqnwld , ter travels 8.0 km. How many revolutions do the whew)m:q2e ,nkdwrexyqr+ 9j ,l8els make?    $rev$

  (a) A grinding wheel 0.35 m in d19xods(s cm.t0fem +q iameter rotates at 2500 rpm. Calculate its angular velocity isef. m +otsx1c9(q 0dmn $rad/s$ $\omega$ =    $rad/sec$
(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 revoq nmyd:,,la4n lution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m:ynq4, ,a nlmd 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 itwq 3; ca ymmhg5+dd,k7s orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a po:4d*m;bn r/aoa) 3vk7yud-x t (kbqtmint
(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 centrif9xhps5+b6ob l uge rotate if a particle 7.0 cm from the axis of rotation is to expehb+65 9sb oxplrience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm to 28l aa(f gjoq2530 rpm in 4.0 s. Detj5(2g la3oq afermine
(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 radiusk y3;a:7ejc; g7pdb ll $R_1$ 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, astronautsv6b;5 ktuq 3n1gm ifc0 ,t.kqx aboard the Apollo spacecraft put themselves into a slow rotation toi60mf q 5kqgt 1.,;cnb3uxtkv 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 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 resf a5jf:2w2xdnt to 15,000 rpm in 220 s. Through how many revolutions did it turn in this txnw 2fd5a2fj :ime?    $rev$

  An automobile engine slows down from 4500 rpm to 12o8m7qgk 3 krn.00 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jets in a whx3* mcvlvdd 5e f(7wkbfq3l8)irling “human centrifuge,” which x57m(3v3bdw vl)*ql effdc k8takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 2445*l-pt l varf0 rpm to 360 rpm in 6.5 s. How far will 4vftl-r 5lp*aa point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it i zgx*e0/q u5xxs running at 850rev/min It turns 1500 revolutions before it comes to a xeug x5/0x*qzstop.
(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 tp jlqd -xgsq2-4m42moy:d7ued 6-gnq he car reduces its speed uniformly from 95km/h to 45km/h The2pq4jyelq :umnmdg 2xd 7d-g-q-4s6o tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unifsa:zqlg0 5v ip89mo 1mormly from 95km/h to 45km/h The tires have am m1vlq0 9i5z:sopa 8g 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 t47* hplw*yt+ wibk m;all her weight on each pedal when climbing a hill. The pedals r w* pkttym7w;*4h +libotate 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. Whatn b.a.ccx4:nn 9+g7afctwa uh70zw)h is the magnitxbaaa w 7z.hu7+ g 4w :n9nc)0ccthf.nude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. .gj.vvdfv 6t (pv,9 0*bkfhu t8–39. Assume that a friction torque of 0p(vhuf.9. dj *,gf kv0tbv vt6.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass mjvro5 to.j 6)4)h*odrmt,k cx , are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initial,*moohrtd j.4ro5k )j)6txv c ly the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engi/)mou9m l ;g+i d9irkvne require tightening to a torque of 38 mg +kiu m9)div/9rl;o $m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 mbut)/z gq+-v3me) ke j3 g gpcdac6cr)86bv.h when the axiseb cmg.-b r6d /g6c)3ak+3q)c8t gj)peuv vhz of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a b l.t .,rbser 0)bs3enwicycle wheel 66.7 cm in diameter. The rim and tire have a combine tn e3e 0sr.b.,)swlbrd mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the zc6ubxjs zd*iv/( cc5:-rwpw jbq pci0)- 38qend of a thin, light rod is rotated in a horizontal circle of radius 1.2 mc pjbi: /0rwv zq5c pw-u-)bc3 6jsxz8*(cdiq. 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 pottj5yx ;vwnioec yd33 1o:x 9lr2dc7i h4er’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.jdcd yyli53w1 xe; vchr7ni23o: x9 o45 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. 8–p y 7hw6)oph6b43)ophby hwp 667 about
(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 consivvv9j (uoy+2kk dq js2m 3o(s;sts 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 cylindr,pqcjon .1k 5zical satellite spinning at the correct rate, engineers fir kqcz1jn 5po.,e 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 the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uni8ke,u*jha y1 eform cylinder with a radius of 8.50 cm and a mass of 0.580 kg. Ca*u ,h1yea8ejk lculate
(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 swij 8,z.byi9qixonl,8+f jp(/u kn1zf qh j* ae8ngs a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-ghjz* v )b5t n1+rj1cp )oc2yaao-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+a ah )ybn)jz2*5rjo 1c cv1tp 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 10,300 rpm is shut off and is evevdjl8y9 7k-llntually brought uniformly to rest bk 79l -yld8ljvy a 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-f:ydas 4njz rva4/zw1x ya- ,.kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action of the forpsjx5y9q u 8n9earm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated u5jpsyq9 8nu9 xniformly 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 in Fi mi.xuz;sxop u+2lza(i* z3q :g. 8–4z(+ul;z.s3oi*uma:p i2 xxqz6.
(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 masses,f ,x0/ulgj6k; kfyy1o $m_1$ 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 +2, zxc -e/udb15s par tb+pb5g ai/ap from rest within four full turns (revoluti5 z-ag e1a uxd cb/paipb/5++r2s ptb,ons) 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 momeuizzut/ pr2ijc 9)4axqzh-v wc0g*+8nt 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 c6q pk:,)8 euoo1xioetorque 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 cy4o,7 pa a; a7r zu9d r/r1brxnj6ehx0m rolls without slipping down a la674/h,rr0px9objra7 x nre za uyd 1;ane at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum kd 8tz (n1k4dzc4u5qlof two terms,q( tudl5k4z8kdc n41z
(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 much r/,3ypz z 9 gnty+cig)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 cylizy,i3gz t rcyn)/+9pgnder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and ro8 y/0ui) 48aieexxyybh zns;,f5x j+nlls without slipping dows ybh8 ny8n f,x;j0)exaxiezi4+ /yu5n 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 balanced vertically on its tip. It starts to fall an5kxd6vj q-g xp -y5m-gs+4ncfd its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use cyfsm- p 5 +g knv-g6-4x5xjqcdonservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotatingbi -7 1 frt,he4kmjrfnc69ax. on the end of a thin string in a circle of radimhfjkcirn -x 4b.7ar,t9e16 f us 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 cylindrical grinh3.b:a5zth20map u1 xn qodb4 r26slpoj5y3gding wheel of radius 18 0dq lp6 ao3:4m5rs122x j.ybbznh op3a ght5ucm 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, handumnjf4l2j-2o r t5 .xis at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a h4m tfol2j2n ri.-uj5xorizontal 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 ua v+jpn, n1)2ldco d(7ukx(pin Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotnundvpcp xkj o2d,( (1al)7u+ations 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 an initial ratyg4 b4l+qd ;aar do13pe of 1.0 rev every 2.0 s to a fidd3a;bqrap1 +y4 4 olgnal 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 aroundh lyjdt4(loqf8 +4dvs5x:wh - 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 cl-loh:( s5l qdt4j+y 8x4wdvfhay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning fp8(mn za zv 5uv 6qwi(k0-e(xat 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 m5a skhuq 8xc4gf:j7o;omentum 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 droppemai sd0t)9zi 4d onto an identical d)i49aizd 0smtisk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns a(.k hjvyrc+0ct 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating mem.t5 /rbl4of776 xv xkxdvr 1hrry-go-round platform of radius 3.0 m and moment rm 5bofx kt/vxh7 .vd17xr6l4of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotalkspgxoxl48u. t 6 +p:0jaw*sting freely with an angular velocity of 0.8x j:8 a+xls kl4p6 swo0put*g. $rad/s$ 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 dwaqh./ryx4h15 y4b*ptz efj1 urrf, losing about half its mass in the process, and winding up with a radius 1.0% of.frp*y5j b4 qer xuzh11y/ 4ht 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 ex 8kyvowfoh2k-; kd s uk7m4*x:cess 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 .xd -l ;qem iqq+c5f5ra5.i;cmydon9$ 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 cp* dye e4vam3(t,lo4nan rotate freely without friction. The mn*4mylp3ede4ao , tv(oment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.iwru7:s8j o d2 oa9x i7to)p.t5-m diameter merry-go-round turntable that is mounted on frictraw7d tj:pst2o i8)o9i.7 xouionless 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 lying o0dka )(me,mlen 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 unwinds from the spool? How farm)emak(de l 0, does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the ni zpw6ld: +o3ap/p y5Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In th5npw y3p +:/lpza6dio e latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist acceleratesu,*hd vzs z*v; from 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 my px(q3lhpk1 49utq 1t acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calc 9p(p3ht1tl1uqx q4 kyulate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cyqko* bhahz4nur i(cm*+cer1 qef,88 );s 8rjvlindrical 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-q* u8rhr ecrk+)s8;4n1f zh8qij c, b*(vme aoyo 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 thdl*i905y6co yb h67di7 nyynae 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,,/) -tyo pgypa but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every ga yo-ppy,) /t12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollbgx b5a -f:) zw5 ,uvygc:4mugution 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 gw,bvm 5 xgub:4fgcu5)a: -zyuniform 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 illustra1ej 8.-wur gc+c0ea bites an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed vozng9sf 0o j29=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.e9oz/,u owbgo0k d) (c(p hoe/n., 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, deze9dh 0bp/kgo o/on wo ((cu),termine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. I5fj ux4b3(v 7-e7vai t;i f+bby lkioe mz++5wt is standing vertically on the floor, and we want to exert a horizontal force F at its axle s iz3 5le++(5a+;t7yivo j bub4weikffbxm- 7vo that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4 d2f,5v4gnny.jrjp;6 n mkog:.2m/s on a flat road is making a turn with a radius The forces rn4 gjodpn :mk5g6;,vnyj.2f acting 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 roj)ltb5(jtl.: aj 0z amck into 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 .ta jmjtjl):a z 0(l5bto 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 arms as thin rods, mr (dhs4l0 nf etwwl.6/aking reasonable estimates for the dd6lws./ehr 0(ftw ln 4imensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consiszpe,huhol6et; 1 ea. +ts of two cylindrical plates, of mass a.z1eht; ,eole uh+ p6$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 *7z8vo3uj 4 1n la-ahw-r owuorolls along the looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must 84n-7uooz v -3*aw jouwha1rldrop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu134dlq ggu c;ome $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed ug-r n8i9+svt fm*.ntgzl;+b qniformly from 90km/h to 6v*+ ;rz.gs+fi98m- qnbgn lt t0km/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