A bicycle odometer (which measuresj,ocoq - +rveuahgb4w0 j )i+:h4)yhn distance traveled) is attached near the wheel hub : voujaq,b)grn ic-wjh )hh4 0 e+y+o4and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rim ha9ccy+l+ djzi lr,k6 cp8vwf )1ve radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component olc)+ +6fyc91vrkp wci ld,jz8 f linear acceleration change?

Could a nonrigid body be described by a single -:bjevr m.etc.vnphf790;d l value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Ej8,6 j8ua qwuhxplain.

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 hands2zwhzo65g ) nmxc b5 x(ml67kh behind your head than when your arms are stretched out in front of you? A diagram may help you to answ5 o)(zmw 2h65xgkn 67 hlbxcmzer this.

A 21-speed bicycle has seven sprockets at the rear wheel and three a abr/ vwdqam*9pm-87nt the pedal cranks. In which gear is it harder to pe9*87a-bm pdavnq/ wmrdal, 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 wit1nkq z5b82fexh flesh and muscle concentrated high, c8e21b5zfkx q nlose to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a long, narrwb m8z aza:xj t6ljog,/l0sx36k5p3qow beam?

If the net force on a system is zero, is the net to9q.b2m 6n4*;dqu 3yqtpvx ijo rque also zero? If the net torque on a system is zero, is the net force xi9n 4bqq*3o.q62pyvu tjm;d zero?

Two inclines have the same height but make dil a;i96e ovpau1y--/2ualhy 7 hw g(nufferent angles with the horizontal. The same steel ball is rolled down each incline. On which incline wileu lyi9glw6 12u-y/ u(ap7oahh va-;nl the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) d5 gey, vp7x1adown an incline. One sphere has twice the radius and twice the mass oy xavep, 175dgf the other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They sta 3o:+l zxaxd9grt from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotationallg3x+ xdzo:a9 KE?

We claim that momentum and angular momentum are conser+ .;ijfgatkg .n/*ed n1) xoycved. Yet most moving or rotating objects eventually sio.ac.d); +j*yfen gt gnkx1/low down and stop. Explain.

If there were a great migration of people toward the Earth 6;x sih7a6l;ia+drav pbp--k’s equator, how would this affe i-i; h+ pbadp7a;vkalrsx-66 ct the length of the day?

Can the diver of Fig. 8–29 do a somersault without having anz m -30ai6emjjq):xs9wnnh-jy initial rotation when she leaves the63 je)- mx-jwmzjn9 qani hs0: board?

The moment of inertia of aig1b * +pecq.e rotating solid disk about an axis through its center ofgeqec b* i1p+. mass 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 holding7yibw3x +bq:j a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, orjyx7q+wib3 b: stay the same? Explain.

Two spheres look identical and have the same mass. Howev syci dw2*g2hjw(-a1xf8ot c* er, one is hollow and the other is sol2 i(*ftc xw*ydo 1g2wch8- sjaid. Describe an experiment to determine which is which.

The angular velocity of a wgr- g9 kpy1 c0;vtp05j*r vmfoheel rotating on a horizontal axle points west. In what direction is the 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 v-jg9kg00o;m5fppv *1trc yr decreasing?

Suppose you are standing on the edge ofrh*c5g 8 9uqkk a large freely rotating turntable. What happens if you walk toward the centrgh5kuq8* k9c er?

A shortstop may leap into the air to catch a ball and thuy/l;:vw h:/;jyek g lrow it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that hisl;:vjy/ wu yl;ekgh:/ hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the lawvue 0vpdz.+dbr0, ;2tx7 dx uy of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the s;b200vuez,v+u7 .dtdxx rdpyecond propeller can operate to keep the helicopter stable.

  Express the following angles icbgjs5f vws7bd 53f0 1n 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 bey() do)r;(x) ryqnw ekcause of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of );)r xyyne ((r k)dwqothe Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direg-t76v),b20me lw :uw h :e zyzo)m 3oljl;alucted at the Moon, 380,000 km from Earth. The beam diverges at an a w:-tull)m;7au zlzl gwe623j,:)ymh0 eo vbongle $\theta$ (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 raqs7l6vm-*4brp+pi zospw- m; te of 6500 rpm. When the motor is turned ofrb p6pzi7vp+*;ml -o qms s-w4f during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3hkqxal58zx 1(.5 m to another child. If the ball makes 15.0 revolutions, what is its ak1x(8 zx hlq5diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many rhnzbmo7w t 1/,4e11tbl1zm7k oh -voo evolutions do the wheels-m1 bm1 e/ wt7htb ol 41onhozz7ok1,v make?    $rev$

  (a) A grinding wheel 0.35 l* vzsr4bfxjik gt1dzn2fps17z / 55/m in diameter rotates at 2500 rpm. Calculate its angular ve/41dgf*7fn kjzp z5 i2l5vs st z1r/xblocity 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 mant*,l y)p (+s/jvrpij kes one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child s (n+/vjr)yptisj , *lpeated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around th, rp jqzoa f,z-:s-u(be Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedvi w20;z2 k;tswpxp b+ 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 a centrifug pqn,y 4 fgvta d7e/dc2;jc;-zqh5,wve rotate if a particle 7.0 cm from the axis of rotation is to experience an accele, ed,7;2f5cqn/gy;chv-p dwtqz jva4ration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 2murz7z1 u:(9xp j af4rg4k :d+m dpxdrpm to 280 rpm in 4.0 s. Dekd(7rmz :u prg pjx2 af+ z1d9x4:mdu4termine
(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 radiusyea3idft+r, /r;ogy1 $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo spacecraft put them6j*(qcgyaexrzy 1v (6selves into a slow rotation to distribute the Sun’s energy evenlyrgyz(*y1 e x6qajcv(6. 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 rest to ua8xt :t/ oho*15,000 rpm in 220 s. Through how many revolutions did it turn in thiso tt*x8 o/h:ua time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.n3qo,5ex bcn 75 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 highsp(f7k a gb5:ydiqn b3ga c.da :1h*h)kfeed jets in a whirling “human centrifuge,” which * ) 5ka3chb( ahnfkfb7:gd1.gq d:aiytakes 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 240 rpm :h rwsz9nc3b g/t; on)to 360 rpm in 6.5 s. How far will a point on the edge of the wheel hab;cs z two9n/)hg :rn3ve traveled in this time?    m

  A cooling fan is turned off when it is running at 8* q2+b/jff fur50rev/min It turns 1500 revolutions before it cfub+ff/* 2qr jomes 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 revolu0zyi*lo l;mc -tions as the car reduces its speed uniformly from 95km/h to 45km/h The ;c- *o0z lyimltires 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 asje10k en4-j 6d: uyy+j7nc wgo the car reduces its speed uniformly from 95wnkey7 - j14+j u6cdyoe :ng0jkm/h to 45km/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 puts all her weight bpad t x-uv7r.d9 qh*,on each pedal when climbing a hill. The pedals rotate in a civ9tr d aux.dq, -*bh7prcle 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 e/rb,7iyhw .m 3bj7yn ond of a door 74 cm wide. What is the magnitude of the torque wjn .7y,7h 3moy b/irbif 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 theb aasy)wzb 6+r0.)nsk axle of the wheel shown in Fig. 8–39. Assume that a friction 0n)b6s)w.+ karsyz a btorque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass/q2c)ftqe rom ;hi 5m) m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and5fhmitqomce) /2)qr ; direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening to a torque of ;a l eu/uj 08udufu(2do+ -pgjkun .f738 uukun. gdp /uj f2;fde+ol ja-uu7(80$m \cdot N$ 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 1eb:0c cxd 3b9f9qm4i6pfy f ,b0.8-kg sphere of radius 0.648 m when the axis of rotatiy93bpqcfcibbd ,m ef9 :fx6 04on is through its center.    $kg \cdot m^2$

  Calculate the momentlof; t:u7rl4yu:,n,jy- g uja 3rk )el of inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass ,3a kr:,gujyy 7o-r:je;ul ll)unft4of 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, tvm k/h +wf8x30c :gwxlight rod is rotated in a horizontal circle of radius 1.2 m. Calculate /w3t xc vxh8f+gmwk0:
(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 constant angulxwh 0q6rm9ml(n k2sy* ar speed (Fig. 8–42)9hmn2lx6*k(yrqs 0w m. The friction 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 inertia of th8gjt2 -i5 3xqekjtss2e array of point objects shown in Fig. 8–43 8kstsqgei 22 3-5xjjt 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 consists of two o nq fnf0n*.7q/w1annq xygen 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, eng7iihh zl*0w1x st/*zy 7nrrdx a219eeineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a rexwsh/t*xnd *7 a01rh ylz2z1ri7 i9 eadius 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:e,rla s a4h-)b plm6mu: tjo( a radius of 8.50 cm and a mass of 0.ab ) 4eru(:aml p:,hos mt6jl-580 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerajgg tz8gr(eauza du2+ qp++t:+4 lp,y ting 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-go-round and is( mobmxv5iyy46) l f:c 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 radiusovy4yi)( mm b56l: xfc 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 rotatinb g*vmst.3 (zjnx4r6+i.ogymg at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional tj x6bmv*r 3t.y.gn(s zi m+go4orque 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 b-axml e.n9 qvt1./sze.2nkoa 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thr :6j,ii qm8+epdzeow -own solely by the action of 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 +-peiz6m :d, 8 oijewq10 $m/s$ 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 co9rqz 3mk8no8+ma k5h ry)q q9pnsidered a long thin rod, as shown in Fig. 8–4 m5qoh )zpqrmkn3k 9ry 8+q9a86.
(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 massesq n-bme8-lk(sr::w ixt4 b 1o .t2pbgw, $m_1$ 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 i *+x u oqpjtdjp-2s97from rest within four full turns (revolutions) and jjx 9+sq-dop*upti2 7releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inerte2kg1*c8gt nmia 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 3 po en87iy)sth iw1hjw0-ym-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 radius 9.0 cm rolls without slippingnly f1aw140 np5u *h3d+rq gpk down a lane a54p +gn r13uhnd *wa 10lqkpyft 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth wit7 k kf ha*3 hzadp.qv/w4uo/z3;gli,uh respect to the Sun as the sum of two t g3 zpzl3 i4 u/ah7ku./;hd*oqa kfvw,erms,
(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. Ho zq:1 *eqb- tn+l6vfvew much net work is required to accelerate it from rest to a rotation rate of 1.00 revotzv*l+ qqef-n16e : vblution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg stk )d1kvifbna6 opxnw1,)97vf arts from rest and rolls without slippi 6bv1,iwk)fp7nv1x f n)9 okadng 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 its tip. It starts to fall a iro0p7nos 4 1qz;)sdpnd 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 conservation of energy.]zo7oqri ;n s0 p4)psd1    $m/s$

  What is the angular momentum of a 0.210-kg ball rotati3uin)drwiln6k +s 7;mng on the end of a thin string in a circle of radius 1.10 m at an ann3)inri+7 6wu; dmskl gular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform zaze3uvv-c5yp/ :8l qhm7v q8 cylindrical grinding wheel of radius 18 cm when rotating at 150-v5 / zlu ae3hq p8yz8m7qvc:v0 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at ty d4nvei0-i8*tna /oa rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.88od0na v/i-nt i4t*ey $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown1a2lkqc :k/hr 8 nagbpg u06)j in 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.ukq 6 ng80ac1jpb/k:lra h2) g If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from gbg 3uj7j- )camxlw;j pny-)/d byl45 an initial rate of 1.0 rev every 2.0 s to a final rate 3m ;)-gb)j uj gwaxj5ldcn7p -y/l by4of 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 a9ad9d9 cb iodot q7-*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. T7iqa-a9o9 d ocdt b9d*he 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 fp7 j4lkr qr3m4igure 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 momentumm*1g+3 .zov plng ul0b of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onto an identi iu9 xr(r6nyq30 clyc-cal disk rotating at angular spcr 69l3yi- q( xnycur0eed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2r jwxww0kevr90gzf 4x)c*8k zx3 +b;6l l8mhs.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 ur0k07q x8 sqkof a rotating merry-go-round platform of radiq0ksr k70xu q8us 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 freely with an angularufd/ :u) ;ljykvr5 /cr velocity of 0.8 ruvrdcuj;l /5/:fk )y$rad/s$ 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 haap)de, axgh4( lf its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lo eg4axh ,p)(dast 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 c;nk4yn(phm :as ix .(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 7anh:l2zo- q(lgwr3qjgxwa4 08 t4l q$ 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 zqx -67i9ninuplatform, initially at rest, that can rotate freely without friction. The moment of inertia of the p7x uii9zq6 -nnerson 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-go-round yaq)tty3l axj519fuun5(ee* cdwfh 9d+ .oi2turntable that is mounted on frictionless bearings and has a moment of inertqy9a ao1 352euh.)ydinf+ (f9jt*utd ec5lwx ia 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 lyij1q /re. ta/w *,kvbeeng on the top edge of the spool. A person grabs the end of the rope a,j/1qwe*a./bet evr k nd 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 far does the spool’s center of mass move?

  The Moon orbits the Earth such that the g0)z2mwkh pf f,j;9a2skodj. same side always faces the Earth. Determakw moj0)gdp,f2h 2j.z fk 9;sine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate b gq pwrk(h+n.5622h ydt+xunof 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 cyn7 a+ (.:n i8ph1pqgkx*zg62myjh hlblinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor. h2x.6n+b p pnj1:zy*akighl (78qghm   $m \cdot N$

  (a) A yo-yo is made of two solid cypxywy;7e+jzo.x +jl0 4nr:ds0*qghe lindrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solidjxsxyol7:hpz+ 4;j d wrenq+. 0 ge*y0 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 1.0-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 wm rr9d(nrht3mvs1 ;;jheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rota y,vijqo)wsj i7*,( wyting 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 s ,yjow)q* i7,wi(jyv uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-po fnnyg1.)aio f-mw4w+llution 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 should be able tgm naoiw+ff 4-.n)y1wo 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 illustras rw g4olpj-q*-av12-ndv pf2tes 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 horizont4vcl4m z8t garcy3c2/ al surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we ignore frictio- nj)(lqft5 x5qcx;von) about a hinge attached to a wall, as in Fig. 8–54. )f;lvqcxqx-oj55t n ( The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing verticall 2*q0ewoez.kv2+d uuiy on the floor, and we want to exerzue e d+0k2wvo2*iq u.t 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.in4iqgx0 ol2q1x(i+laf g; nv n)c91k8pdo;q2m/s on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the norqd4;9o0okqpc;n( li qv18)2+axxig 1li nf ngmal 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 (6eg80lfyxeh*9mo br into a sling of length 1.5 m and begins whirling the rock in a ne *hlgy6rxf8 be09me(oarly 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 come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylin z.z luy3ra2j/ k;o-lsder and her arms as thin rods, making reasonable ea;l.j2 y z/os-kzlr3ustimates 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 *,f fr w1r(tahof two cylindrical plates, of w(1rht*f,af r mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 alx)q a9h6fh9ek ong the 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 )e69xqfhk a9hreach 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 ass0zkni8x) rj+1czs r/cj-yf :qume $r\ll R$ h =    (R-r)

  The tires of a car mak*awo3 ezml +9me 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What3olz9m aw+ me* 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