A bicycle odometer (which measurei2.dg w p0 pra1gzz 3zhga.nb6j/)n(ugg5ex0 s distance traveled) is attached near the wheel anz6.z.nziu3rwjg )/g5ghd1g xg0pp 0 e2b( a hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constanu8 t0 cbni*hr+e9 syesq5*6-- zs gllpt 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 magnitude of either component of linear accelests zy9 -r6p+nug-e l0bil8 esq**5 hcration change?

Could a nonrigid body be desg9 b*f x(8d)u-qc r gli-pn1yscribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a2rot0 ext : *c5ken1-ftgl0 rc larger force? Explain.

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

Why is it more difficuh(( te6 qcn+nflt to do a sit-up with your hands behind your head than when your arms are stretqh (+tc(6ennfched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheel and thre ewl vw/hf762be at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large real7f26 w h/wbver 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-uj * lr8dalr/ able to run fast have slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotatiojal8l*r rd/ u-nal dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walis/g( w2qokg;w4a7jd b -3elgk* l3vfkers (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is zero, is a3vfdeh05c91jqj;7 as/ er uvthe net torque also zero? If the net torque on a system is zero, is therva10jseua ;f5c7 v9dq/ ejh3 net force zero?

Two inclines have the same height but make different angles with the horizontar2 ubh )a)6bmal. The same ste 2r)ab6ah b)umel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneou:j6vodiq8bak0l58 t vag hxf* :t a)d,sly start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass t g6vvk ,ddli5ao :0xhqb8a f:ajt)8*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 the bottom?

A sphere and a cylinder have the same radius and the same mass. They start from w s yhv :t kof9.qx7v3gi/gb8: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 rotatiow/xivf 8o7 q:ybth:.k v9 gg3snal KE?

We claim that momentum and angular momentum are conserved. Yet most moving *4w yv3g(4w5 x pfgrzjor rotating objects eventually slow down and stop. Explain4r4wyv*fjx zp3(g w5g.

If there were a great migration oft*ycjf/nb*jf 5)8 nwq udok15 wf0rw( people toward the Earth’s equator, how would this affect the length of to fr*wfcn )w5k / 1dju*5fyq(njb80wt he day?

Can the diver of Fig. 8–29 do a somersault without havit4d )uqr7o , ;ubl6ptmng any initial rotation when shm)ptot u6,lrbu7;q4 de leaves the board?

The moment of inertiapaaqtn035z6 d of a rotating solid disk about an axis through its center of mass n 56a3z a0qtpdis $\frac{1}{2}WR^2$ (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 o jl(u;x(2imo0u r3(+ywm hgywp m3 0 tfuc*5bhutstretched hand. If you suddenly drop the masses, will your a y+ pumw 0m3lu0ru3f h((cobt jwh(;*mg5xiy2ngular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, one is hollow anv0hdghao bu )73oe-)h d the other is solid. Describe an experiment to deah)7 b 3ou-hgehdo0v)termine which is which.

The angular velocity of a wheel rotating on a horizontal axle points wefjmbl.4kuk(s4 wcx .1 st. In what direction is the linear velocity of a point on the top of the wheel? If the angular j..(kfsl1x4mcb 4 kwuacceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on thhbdjy,p4 jh;*e5dcf4 e edge of a large freely rotating turntable. What happens if you walk toward ;jfy4 hecb,4 jddph *5the center?

A shortstop may leap into the air to catch a ball and thjm xiy-*4qy (padkg//row it quickly. As he throws t* yypi -gx/ jdk(am/q4he 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. 8–36). Explain.

On the basis of the law eq)69, aqib4qqeo m7a of conservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more wq6)qqo ,bmae7q49i aeays the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a) 3b0m 3gk uhzuq;g9 9 qxq6u3t9r0 $^{\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 ama0e(3f4.6ijwfgh q p+u,t xrar zing coincidence. Calculate, using the informati6a .rert3, f( 4wx+fgpuqjh0ion inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is direfdx1,q1rb 4pgiy/2i ;whcnj ;cted at the Moon, 380,000 km from Earth. The beam diverges at an angc/r ;dhjyib2g4 qn1 wxf 1p,i;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 blender rotate at a ra8r(,rbd ut(sh )7oefote of 6500 rpm. When the motor is turned off duringru7db,rt(8of )hs( eo 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 3.5 ei 1k fbvbbs1lixa fm(/af/0ot28 72y m to another child. If the ball makes 15.0 revolutions, what is its diamxff of i/lb178s(mi 10e2vk b/ aaty2beter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 k4 *fc ,cp m-/lslilot5z:kgq9m. How many revolutions do the wheels o sqz4tipf95 k*-llgl/cc :, mmake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate itg0 6aoist,qel4w)v :ns angular0 vinalwot4 e,g6 s)q: velocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolution in 4.iha0x8ow9; mp w-o qq(0 s (Fig. 8–38). (a)-a(9oi;0 omwxw 8hqq p What is the linear speed of a child seated 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 the Subl-dez 3s ynm 3ev .0ras3e+l5n    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed x1w/e gsg6cx+l9s0cf 7z )tymmmd deyv.345 xof 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 ame bn :.dg bkqjs6-l.* centrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acce es.6nglbqdj m*.b:k -leration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center f:w ;efxfbm1: from 130 rpm to 280 rpm i1:m; wxfeff b:n 4.0 s. Determine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radius nrg1*g+ rf 1vl$R_1$ 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 tc :f5 muy1+wkggs2 0vmhemselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinv2skf+:c5w gu mm0gy1 der 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 rp,)z)gq y 0tlkpm in 220 s. Through how many revlkyg) 0)z,tqp olutions did it turn in this time?    $rev$

  An automobile engine slows down fro h (f,ox*4mfnsm 4500 rpm to 1200 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses is12 7pmyd :il(rag,o76rgyy of flying highspeed jets in a whirling “human centrifug s 17dmgyl2igiar7y:rp6yo , (e,” which takes 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 to 36c7h vu 5;qibq60 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in t 6ibcqh5 ;uvq7his time?    m

  A cooling fan is turned off when it is running at 8t. r5 1 vpfy:r9unl+yq50rev/min It turns 1500 revolutions before it comes to t q:5yl1un+vryr9 .pf a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed uniformle, tv0dpw gnn+u9*u8ly from 95km/h to 45km/h The tiresg ud+0vple8 * 9,unwtn 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 cmku+652fbdz y pn7m :o4:0xz 1ecnsz 65 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.s cz kz6ep m:fc+1y70ux dn4m:bo 5n2z80 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 r6 64.5 dx mdez9repgzpj+-hmon each pedal when climbing a hill. The pedalj+65dr9p dp6 .ere-h mz4mgxzs rotate 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. What is the kf*)x2 ykypc ,i.q(armagni,*y ai cyrq() k2pk.xftude 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 shown93hakga/ qg0lk2 ) 8x fgym8qm in Fig. 8–39. Assume that a 9hy2ka) f /x838lm k0gqggqmafriction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attached to the ends x be p9d bgab.ba1g: zz266:qpof a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the g9pzbbdpg x2:b:.6 aezb6a1q 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 eg2vgm7q.tp ,nngine require tightening to a torque of 38 vn.7pg ,m2qgt $m \cdot N$ 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 t/b j/e.jpmxiw7s;:lg)s/ tkrx5jh . radius 0.648 m when the axis of rotxbrixj//hsel: 5j t;s.wgp7kt/m. )j ation is through its center.    $kg \cdot m^2$

  Calculate the moment of iner g9 1nc)ya- wt4e.6jwrsins-kgqo,8 rtia of a bicycle wheel 66.7 cm in diameter. The rim and tireiwo -q6,1 e9 nk.ngws-)sr4jgy t8rac have a combined 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 end of a thin, light rod is rotated in a horizo8 kxns1swx8i.uw s3ho+a1hh4ntal circle of radiusx 81h.ihsn3xh8o+w usaswk41 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 const-mum 2xk13flw ant angular speed (Fig. 8–42). u3w1xmk2- lfm 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 the array ofq.85v9 fjvqsezqv 1 2x4201ukgypi uo point objects shown in Fig. 8–43 about . svf1xzekg8j 2i qqpou5qv12904uvy
(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 whose totali,tl f sapj*6) 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 spinnin:ljezq dy)1k6 g at the correct rate, engineers fire four tangentia ledkzj)6y :1ql 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 0a(,6occ bxmcm :q. vkwith a radius of 8.50 cm and a mass of 0.580 c ccbo(.0a vmkx:mq6,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, accelerati+c7q ,f9pz, qhyyz,tzi0x uk3 ng 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 tanirgy mx- ; c0uxjj27u4gentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frrimu7 0-xc ;2g 4yjujxictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotati7+( xr:)jfb-s;elgse jv31 xn)h1)v nvthj gong at 10,300 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of)hl nv xs se7+gv trxfgj1n )-o1vje):h(j3;b 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-kg ball at 7i 9 1bpfam1oexr8 /hh+5s54eu ,syrzu $m/s^2$ 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* a+bs t-k+idw8cuc3l 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 10iaus b-lc k+8w c+*dt3 $m/s$ 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 consid6desi*q0rsp*we 6k x pi5s*;vered a long thin rod, as shown in Fig. 8–46 psdi r*;epxs0*w66i qe*kvs5.
(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 consiseavi/ (x a .jx7:w+jkrts of two masses, $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer 9ppsdh -.6ye aun f-d0 from rest within four full turns (revolutions) and releases ihfd--a u.n0 psp 9e6ydt 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 inergx 8v;b4*3 d fw2jmgtdtia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torque oqr:ri ktg, 0v j/ +cwtvas ;:-ozor,/gf 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 an9 bbntltm (j7 4t,)*cmyterc 6rt-x3y d radius 9.0 cm rolls without slipping down a lane at 3t6ttmt3 nby -rym (xr4l7be 9*j) ,tcc.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun vow8rgv q+s: 4v,pm t/2:n hdpas the sum of two t/+sn4v8rwv h qpv md op:gt2:,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 off7oj3i0f*bklptafbp5 r7;4wuc:w6 ql 2 t4r t 1640 kg and a radius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of t;:btf2q3wkpl*u67baf 4405lro7 wticrf pj 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kkh0izd q1obp rk ,v2m)ttw6 f5anj224 g starts from rest and rolls without slipping do1ziot f )r5,ph 0b22 amjtwd6nkqv2k4wn 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 fuzgod7( tv r99all and its lower end does not slip. What will be the speed of the upper end of the pole just befo duz7v 99(trgore it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a d-aq hxe(est; k*4ononz+cb* p,e8c 0 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 me e8-4nkchzaob,+esdpo xc**0; n(qt 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 grinding whv9*l6/ -wg5xy3iyhrc z1zqpk.0hdoz eel of radius 18 cm when rotating at 1500 rphq10 o plih-zyw*dr.k g9 zv3/c z6y5xm?    $kg \cdot m^2$
(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 ratecl rpbuy;o6v6 /st(g0 of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to lpst (0;6y/v bg6rou c0.8 $rev/s$ (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 of inet3s1vshm:q yub(n 7 7grtia 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 instq( 1s:m7uyv7n3 bg h 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 rate of 1.0 -mnhyha h 7v 1r+e;d/3ff3zc zrev everyzzh / 7 h;3fahe-v3fmnydc+r1 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 z-fqymr716c.u t/hro vertical axis through its center at a frequency of 1.c1ru/7.tz q6hry o-mf5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum as lyat0:)d .ongxx7)lua0t1of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentumr 5z-,a.rraomb 7gq q1 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 o0;rlwz+ ipn+dl, am- kf moment of inertia I is dropped onto an identical disk rotating atlwrik p n +m-;,lzd+0a angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 tvvp7c m3 wf1(r: v/il$rev/s$ 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 merry5hobpo b73cyshb:+(z bu w k,;-go-round platform of radiuo, bsh+bc(h 7;yk:5zb3o wupbs 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 angular ve9x,lzcu xe io;c34q 1xlocity of 0.8 u il xxcz3;oe9qx1,4c$rad/s$ 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 8ik 1 (mjs/jy2u ;lclgc+gf o8a white dwarf, losing about half its mass in the process ;j1( smo cicl 8fgu2/+8kyglj, 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 wiii: e 5 r2n:4e)ytewldnds in excess 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 ky5hckt *6kox/nzbf9f7 o 1e2$ 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, i8y,ygihbu z;fz: (bi /glvs)5nitially at rest, that can rotate freely without friction. The moment of inertia of the person plus thg/ilbby5 hzyv(szu8i:fg; , ) e 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 diameteffy/sghwyq-6gw10 u1 r merry-go-round turntable that is mounted on frictionless bearings and has a momew-g0qfg 1su1 6fywhy/nt 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 rol,yevcr,tn* kuawqd4e n9e28(ls on the ground with the end of the rope lying on the top ev w u*e48,tyn9k(rnqee c2a,ddge 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 far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth.79zf:a0 uqx+-2yh z u akstz0o Determine the ratio zxfy0t7u -z qkho2+0 au9 az:sof 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 o 3c ev;to.:xzsf 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 shapez-1yc p(f qzut)7 .nlo of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over np7qz yo-1lf)cutz.( a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cy 0kqg1bwhxwql ;kr 7)6;7h,ro h jyep0lindrical 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 calculat h 7wh ,xjlphq67er)y0kk;1qgrb;0owe 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 osr(x9h1b w3et7o/w yspeed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but wy;70l 9pn cfzjith mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitationalclz97y0 jf np; 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 lo nev*h+nje( 5btiu(ct z0vv( oux z6;npv61y2 w-pollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m anv*6vjnuxn0( eh+;t 5n 2v6(zb1 (u zp oyiectvd mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates anq44rpsw/ww6jr: cyu 3 $H_2O$ 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 surflblja6(w ab5:(;dfilj;4 se e ace 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 p55n 2ddx;k5tgz s jx(l)agw9pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment 9 );zk pdxw5stj( g5nxalgd 52of 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 rarb74k r;,mfnddius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55) ;,fnk7 mrd4rb. The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn with /4;c0bnpxoti i 2obe:a radius The forces/i:otx eb c40nb;o2pi 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 rock into r3t4w+b u+qauh.9ljra sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle l+hr +tu9.3qua4 jrbw 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 ak( .ff,- b2;yzgme)o4oiqi b y solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions;.f-yeo,biqmy oki (bg 4)2zf. 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 assen, r5ipa9f83wosmv .q mbly which consists of two cylindrical plates, of m9swofa m5qp,8n3i rv .ass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the lhf9tvu,y ,nyp6/;w;mkws/r z ooped rough track of Fig. 8–58. What is the minimum valyt un;,,/psry 9;6wvmf/ hzwkue of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, butu6wj: cbw;.lb2 r; fntc4p 30pz8:/adpzofvy do not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed uqff*c ya.ko4j 20g h,nb+xd.f niformly from 90km/fkgbc .fy*x+0hd,2j4 nqafo .h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s