A bicycle odometer (which measures distance travel59x7 remtlrk k (3hpp791wlqced) is attached near the wheel hub pk19c37 97lrhqplwtr k xm5(eand is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotatejat0 z)xb/yt3dkl- tq6ify8io4 4o/ cs at constant angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the mck0xy/b4/z-l 4t63 f id8itt)oyqojaagnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of jgr m1fx ijg72lpu 0fx(.*q(kthe angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a largerj67 2jsp7s)tz cyzwe+zll)d fd+5nefqx u:1 9 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 witucuqk 6ff -f7cf04 w0mh your hands behind your head than when your arms are stretched out in front of you? A diagram may help you tfqf7fwm0f0u -cuk c 64o answer this.

A 21-speed bicycle has seven sprockets at theqna zypsr0*r2- 9g zk1 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 itk 2rn-z1s ypz*qar g09 harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fa3uv a 4lw-hux8st have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distrib 3uxlavu-4w8hution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) 5:;+( 5tuklnuigau flcarry a long, narrow beam?

If the net force on a system is zero, is the net torque also zero? If the net r*z. kwp.))w7aw;khge qlid7 torque on a system is zero, is the net forced7* ;z)g.p ekh7r w.wa wlqki) zero?

Two inclines have the same height but make diff1- nyatz ls)pq503mh pi;.el ferent angles with the horizontal. The same steel ball is rolled down each incline. On whqm3np;a pe th-l01)iz yl5.sf ich incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simu;ywc2zlvjl g(omxz554/l r*yltaneously 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 (/z*;4oxcm5 wzjr ll2 lyyvg5? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start f 6rwqs:2b px(urom rest at the top of an incline. Which reaches the bottom first? Which has the greater spsx pw6ub2rq:( eed 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. Yet most moving or 83eaba )-hprt -j9flzrotating objects eventually slowl-fp-)a 8a 9 ezjrtb3h down and stop. Explain.

If there were a great migqiu7 (sz:v ruyo6 m01, ifp:mny )8rguration of people toward the Earth’s equator, how would this affect the length of the dayuy qy07m6z :u8is,g)vo1 p u(ni :frmr?

Can the diver of Fig. 8–29 do a somersault without having any initial roedl ) 7*jf4 c;g1yoxwhtation when she leaves the boa hodxw)ygelj4 ;f7c1*rd?

The moment of inertia of a rotating solid disk about an axis through its centap odun9z0( l)er of ma a0o)9up z(lndss 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 mass in each outstr;5x4s1vzmn kc 2k ha7rx:;qx8vd 8exi1d.o dc etched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Expla7vdx a4dr1cx5 1:8;ix;hkoqdze 2c 8.m nsx kvin.

Two spheres look identisii qc/ze72v4cal and have the same mass. However, one is hollow and the other is solid. Describz24/i7svqie ce an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wu5.jdt ir7czg s9(q :po9c 5clxlg+q5est. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points gg59z x :7jo+iqlul9sq5rcp5c. c d(t 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 turnta5e j))) ahci6mes p6sible. What happens if you walk toward the esepsj)i mi) 6ca56h) center?

A shortstop may leap into thew hgyy *fo/dw:v:. ;sj air to catch a 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 direch .g*vdfs :j: w/yw;yotion (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why ed)0.x8 ctex.j*dzy :o p tyo-a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propellerj.c )d t0d *tp .y-e:8xoezoxy can operate to keep the helicopter stable.

  Express the following axz+ fl n75-btwfq 17kangles 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 an amazing coincidence. Calculate, uoffrm zp /h0.egy;,7qsing the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, a 0o/7 f, z;reyfhmp.qgs seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beacm)7dz-+osl+h.)t zyex r/vpu ex- m ;m diverges at an ang- /dlzc )7e)t ep.zo+x+-mvy xuh;rsm le $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blendeo er,yg23cv 7q1h 9vcle9qm k0r rotate at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the bvc30 coqg279l eq9vk1ehy r,mlades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If thevio/3u 2fw:3 ne/ z0 nop(jsre ball makes 15.0 revolutions, what is its v(fj32o r/0w nne:p z3sui/oediameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How manlz. d+2bqi8cf y revolutions do the wheels l+2qi bdf8.cz make?    $rev$

  (a) A grinding wheel 0.35 m in diamete9 s dwtnyfm71op 69k6hr rotates at 2500 rpm. Calculate its angular velocity in 1mokh 9 ft67ypdn6s9w$rad/s$ $\omega$ =    $rad/sec$
(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 makckf:i 0 j: 6+ueblvb4ses one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from the +4jfbve:s60c: likub center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around thm9o5 0ti 7bntke Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of ,lhic303fk; t g2velbwg (z +ta point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate ium1sp r;(cx0dvic2 fa v8z *b7f a particle 7.0 cm from the axis of rotatio0v mv1(2 a8 c*cxu; dzfis7rbpn is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 rpm ton-lz4oets *)gylgf/ + 280 rpm in 4.0 s.* n)e l/gg+ flzsoyt4- 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 e rql72.xvr *u$R_1$ 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, astronaw )gcvze (z3t -zxuds;0zq++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 fro uwvx;z)+t( egs0+zcdz -aq3zm 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 in 220 s. Throb3qbg9 yvfcl50qz/ i0ugh how many0iz b5/b9y0qvfq glc 3 revolutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Cal3 tbd *idiuyj;okf2 2-culate
(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 thhq.z fc81ji ;nw;)kuje stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutio .f1 ;ij8n;hzu qck)wjns 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 b o(+0evu-duyhis/ elpp)jb bc//69a uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on tl0/9pd ic)u b a/+yuh ev(b-6e/pjosbhe edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when ;sczcv(5 h *dftg0)o1x bhjj2 it is running at 850rev/min It turns 1500 revolutions before it comes t bzxhj;tc*v12)f ojgs5d 0(h co 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 speed6ak(gks fj-v1- xf :hv uniformly from 95km/h to 45km/h The tires havx6f afkj:(-v vksg1h- e 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 reducesrsf t(j.. zqt5 its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.jt.5rz(. tfsq80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weig(vaanftz5 3 k;ht on each pedal when climbing a hill. The pedals rotate in an3f;z(t av 5ka 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. Whatpp3-p6ixv51 zdaxfy+ dj i3 a4smp06j is the magnitude of the+04d jz 1-yix3svj appd3pp5i xf6a6m 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. 8–39. Assumc2y8/ qcj 1m2l*tm;gct oq v2e 6lv3e 2egkb9de that a friction torque of kmcqol*ltmg c2vtdg 2j3b22 /9y1ve c86qe;e0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends of a massle:rm5j 02a1ptls( xh mncfj:c :.rvez -ss rod which pivots as shown in Fig. 8–40. Initially the rod is r1:t0 cm r5 x.nzc-elj phm:f(s2ja v: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 engine require tightening to a to4qws qhw0f :px/.y2mxrque of 38xf: s /mxyp2ww4h.q0q $m \cdot N$ 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 , e48 l98nmqwv8wgpa kgdd/( oof radius 0.648 m when the axis of rotation84 ve9go/adql8,pwdmgk 8n w( is through its center.    $kg \cdot m^2$

  Calculate the moment of ; c/)/w8gzu mj s1h)runhe (wuinertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined massu);ug 1njsr wh ez/h/()8mcwu of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball i(deg-h;+:ay6s mjsjvj a 1h* on the end of a thin, light rod is rotated in a horizontal circle of radiu(j esjy-aai :+ d g*;vhhs6j1ms 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at c.)jwhru7llvo1 u0i8n jw 6/ixonstant angular speed (Fig. 8–42). The friction force between hjw/jhv i0xlw.o8ui 67ul r1)ner hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of (8op w oer 01lratc+p *22ge.lzb1 dumpoint objects shown in Fig. 8–43 abu p*go de+1(8crlwoz1.2 a plmtrbe20 out
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whrckc0,h4x p vt9 *ket+ose 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, engi,h6ou be(ip)* xfv5z gneerf)eb 5(6i *o,pvxuhzgs 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 the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radiu:) sdu0z nqco;y4lngo1lis7 9s of 8.50 cm and a mass of 0.580 kg. Ca9 g sscud7nloy0l4oq:iz)n1; 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 swings a bat, accelerating ixy6- fn95fdj2beu +qet 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 smaf13( ldya)vvuncgt ,k kk;+ qj e2qw76ll hand-driven merry-go-round and is able to accelerate it from rest to ak2 afvctq 1yek,3lj (v)uwkg 7d +n6q; frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventuar(,bza1 ck,bo,: sstflly brought uniformly to rest by a frictional torqst (ozk ,b,a:,sf1r bcue 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 cnxn 9cm)r-lq2 8 :dee3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely by the action off *)pyf y w33at3eit:y)yv2l m the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 1plefwmf)yy33 t: y v23yti*)a0 $m/s$ 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 lon3; *:wppzc -pga ewdh4g thin rod, as shown in Fig. 8–4c d;3*aeh-wpzpg: pw 46.
(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 masserrps8j+( w x p30 yjp0;nyzkj1s, $m_1$ 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 wehp0fhs w+4 n7 0p pg hhop-6 ,ia.hkhbr/bb.6ithin four full turns (revolutions) and releases it at a speed of ,ib ph0 n.0prp6hba-wg6 hbf /h.+hoe7k4h ps 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment* m1wxc2i5ybe 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 develop 3o1;2bhzbe fns a torque 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 radht2 j-7yo8om eius 9.0 cm rolls without slipping down a lane at mhj y8t 27oeo-3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with rel9e 0cty 75/wp/3rpbbl m(fqqspect to the Sun as the sum of two terms/(lqt/9rpwl5 c ybeq0pf73b m,
(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.g.eh e16h3oxx How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.0.o1exe3hx 6g h0 s? Assume it is a solid cylinder.    J

  A sphere of radius 20y,j6om.ibcup )jz84 r.0 cm and mass 1.80 kg starts from rest and rolls without slippingci.pzbu,) jjr86moy 4 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 balanced vertically on dob5oc.k + wk m98e(bhits tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just bwbdh(c+8 5oekm.ok9before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ba7 obp7z8p7 cdill rotating on the end of a thin strinbd77o8i z7cpp g 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 cylindrical grindin 9gj(jdn uw8kx7lh7-b vod z*7g wheel of radius 18 cm when rotating at 1500 rpm? hbo-ldkjwj97*877n(v uxg zd   $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at a rate o wncw6 33a:ehu -eqp*jf 1.3rev/s If he raises he- w3nw q*cp6ej:a u3his 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 moment oi+djzq a ;bq,h+ j4hl;ai,0fqf inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angula hha4q;+; +,i b 0qjql,azfdjir speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate hcy5j3ma68 xvof 1.0 rvj6m c5xy3h8aev every 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 around a vertical axis through its center at u16uy 9tb) y gycpwu+m 0n+t-ua frequency of 1.5rev/s The wheel ca 0t)y69c+y n uyu-pw+1g umubtn 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 frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure34 :u 3bbjr)y5gzq; t 7n-c iof5;yrobx,btmt 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 t qe/zbk7ll h52./b nkh po48hof 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 cylindriq 45lqgy kx)y9mnagi;u ;o8d2cal disk of moment of inertia I is dropped onto an identical disk rotating at ang4anl5x2gy)im9 qykdq8u ; g;oular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at hj a7 wn0- k/cd8jyncik7(q6u 2.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-ro4 ,5hmq4e1 afh 6iyhprund platform of ra,r1mh5pf y6h aqh4i e4dius 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-round is rotating freefwv(.aq,8 ypqly with an angular velocity of 0.8 (yv,pw .af8qq$rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapses into a white dwarf, losing about ha e ;p )x02uk,fhxxs8mbu. r;jslf its mass in tx seusm2 ;xfp,0hrub x kj8.;)he process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess 9 exb 4jx0qk nq*xn.3c2znu (yof 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 pr9 hj 1. d/itxp8cl6v$ 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 rokcj8be,zka k3ts/,,m tate freely without friction. The moment ofkksbt/ e,c,k8,jz3a m 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 +od t3epyu6ep emvex fes/h8q1j.l :u;r:7q0 the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless beauu m0qee:p lx3q./+ t eofes71d6 v jy:h8;rperings 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 n:7d+7ntf*t c3ht b oyof 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 slipping. What l7:nttd3* +tco7fn ybhength 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 alwa4o 0oay+ o2iekau n4sb8+-5c .e hekcbe, i)qxys faces the Earth. Determine the ratiobckye eai4i-+ 5n ue24cx.booe h+qk 8,0aso) 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 Earth.)    $\times10^{ -6}$

  A cyclist accelerates fromsp 14epvm dyb+tv x8+u8 *on *(qswg6q 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 a;2wjiwug(gmk7gyo2kr k r0. 1 cquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torqumy1 0ggk j.kwr 2w(i7;or ku2ge delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of ma1xr6m-ut t,y vss 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.vutx1r-y6, mt0-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 thenij8,z 7u2hrg 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 ls.8cq9 q vb*tof our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lostqstb.lv8c*q9 mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energ78 u/og f0: fukkgj,zxy stored in a heavy rotating flywheel. Suppose such a car has a total ma8 g,f o0:kfgj7 u/uzkxss 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 illustrate :l ,qm54m8:x7eeebawrf: vjl s 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 v6t uobm,gh2rohjtpp7- ;4/wsurface 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.( hee .x(bp2h-0l vgdj0 11b4ysswoj f, 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 acts at .bds h4ey02((gx-e bv wo 1ljf0p 1hsjthe center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has rw rzsd.27qpq ,ajvwm31u jn5 5adius R. It is standing vertically on the floor, and we want to 5jwm qzp 3,1u.nw radq v25sj7exert 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, where h

  A bicyclist traveling with speed v=4.2m/s oo xsunx58 s55vn a flat road is making a turn with a radius The forces acting5u855s xnovs x 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.y:xaiea *g+*h 50-kg rock 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. Wh egy+a*ih*a: xat 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 bgc8gds y8.m9cylinder and her arms as thin rods, making s89m. y8bgcgd reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylindrical plates, of x7rv3ar ywfxza q)q w+70r./ pzu52rb mas.xax3r/q7qf pr v)wz r07 u2zr5b+yaws $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along ;opf7 4zun +rqj4s: ytthe looped rough track of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point ofn+4ftjz4s y:;7pu q ro the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but dob: )r 7lfzlf;3vtb 9mi not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car rh*kb r azl,sr-j io*5*l5an ,qeduces its speed uniformly from 90km/h to a*lokh-si z b*5lj5r,n,ar* q60km/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