A bicycle odometer (which measures distance trlue - +n.uzyy4aveled) is attached near the wheel hub and is designed for 27-inch whl 4y.nzuye +-ueels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Doesj5qb ; hu :3d.1ud2ma o5jbtls 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 o1t5hb :u j2udm3b ; dosqal5j.f linear acceleration change?

Could a nonrigid body be deslvf ckrc- ,q: p-q*)lpcribed by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a grq :hc 8fyx+y.n: )dumreater torque than a larger force? Explain.

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

Why is it more difficult to do a sit-up with your ha5o hydna j59glct. tn4sl(z/+nds behind your head than when your arms are stretched out in front of yodn t(+z at/l4ch5 s5y gnol9j.u? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at2.llk 2n ne2je the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprolj enk.ln2e22cket 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 m1m*x:zbqc nn-j; ko- lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basisczxomnj:-*q1 -b;mn k of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers ( o /4txmzr4ho6Fig. 8–35) carry a long, narrow beam?

If the net force on a system i3x-sn b :d c5iennm-f :+hwqk3s zero, is the net torque also zero? If the net torque on a system is zero, is the net for:c3e i5-qbnx3 d+nn k-fw:smhce zero?

Two inclines have the same height but make different angp*i ;l (uaz*otles with the horizontal. The same steel b l*u ;oi(*zpatall is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultal32xqd by*8dgcht(c f5*yo+ a neously start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the greatebfy y2cg8xd ldha*q5o(c*+t3r speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and*f3yrz5 hp+b z mk;:l;tt1zsy the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bo hys;fm l :;z5tb*r1kt +y3zzpttom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum anq:9,ngr . /+hyocrydid angular momentum are conserved. Yet most moving or rota:yo n,crd yr+. h9/giqting objects eventually slow down and stop. Explain.

If there were a great;nzfwi -w 330x-hludt migration of people toward the Earth’s equator, how would this affect the leng-3;h tz3nwluwi fxd0-th of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial ro+5g m.g by;3 endzt6nttation when she leav +zegt b3md.;n nt6g5yes the board?

The moment of inertia of a rotating solid disk abuw 1wxj)8w4(yc3utf5j+ffi sv zw,0k -qi8kb out an axis through its center of mas5qvku4kw8w(w jf3f + f xwc8bsyti)j1,u - z0is 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- cw*9zel r7jh059;rzxh);uxdlp wcv 6kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increas wzc5h;jh lp7;r9 w9zux0vl)cx ed*r6e, decrease, or stay the same? Explain.

Two spheres look identical and have the same massf; y6qwt p,2tby0eux0. However, one is hollow and the other is solid. Describe 0x 0;w yqeby,f6 t2utpan experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle points west. 13jwl,tke2e jb/ pi:frv)go (v:3qrz 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 w r1j),v:wk2e zrgbjv 3/e l3qp t:(fioheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating tuqlpm 67v-u; lgva.e/ jrntable. What happens7ugj pa./vll6 - ;mvqe if you walk toward the center?

A shortstop may leap into the air to catch a ball and throw it quicklyqu dzy (,ajzaj(y9k- 0. As he throws the ball, the upper part of his body rotates. If you lookk(a09zjy- a,yzj qd (u quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, g2bvqf 4/n hgr87man z09v*;as rklm8discuss why a helicopter must have more than one rotor (or propeller). va m g4hq zngv8knr/ l7*bfa;2m9s0r8Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radiansv-umj)doo4r s m/ x5;5aop.vy: (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. C9 -39wc 3zqilq1qdckfalculate, using the information inside the Front Cover, the angular diameters (in radiaiq-913 wl3 9zfqdkcq cns) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380ev+)e2pq7p )xmtiudw, n 3 go:,000 km from Earth. The beam diverges at an angleoegidv2)ex m upq 3w) ,t:7+pn $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rota -wabaj* +8xgwte at a rate of 6500 rpm. When the motor is turned off during operwwab8a-xjg *+ ation, 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 m to another child. If the+6/ s;fir84w pncyb dt ball makes 15.0 revolutions, what is6 rbc/w+dp8s f4y; nit its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolg)p9 i rq1s.snl.dt1 outions do the wheel1s s.p 9.qn1 )ltriodgs make?    $rev$

  (a) A grinding wheel 0.35 m in diameter 9 bmhqf,ag7ocv wti th9, 43r+rotates at 2500 rpm. Calculate its angular velt cvqhb9o,gtw7aihfr 4,3m+9ocity 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 4.0 s (Fig. 8–3 *jb).xie)ug q (d54mtzq qv,eo -e3bl8). (a) What is the linear s4 e.xudqeq(b) zgl5*b)qj- emit, v3opeed 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 arouna0vsi yskxq7;u xb/hp9z2:r ik2l/x* d the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed3 ui gja2bjj,-x 2vt3x 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 centrifuge rotate if a particle 7.0 ctk;lg mya;h; tv+n oh729jre2m from the axis of rotati tl;oyer; 9hmkant7j22h+ g;von is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130 d1tv9d4p2iqz ),mf0nz t ng,srpm to 280 rpm in 4.0 s. Deterp)2ztds9d,0zimf,vq4 n1g t nmine
(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 radiusbhbvbzf 7jt (; cey-42rm2 cr. $R_1$ 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 a6kk. uu4a zg vg z(1qy+q-b,qdboard the Apollo spacecraft put themselves 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 cylinder with a v6 ,qu (bd gzk14 z.y+qa-kqugdiameter 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. Through howj;;u/dhpvgad 0t.+ qj :r06yvpr 3fr e many revolutions did it turn in thi; apgpy3jhve 6r; :f00tru.jrd+/dv q s time?    $rev$

  An automobile engine slows down from 4500 rpm to 12007s9 ntob trspg(,a3z*e-bta8 rpm in 2.5 s. Calculate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying highspeed jb1ipt y,)s-qv f:1sci s((lg iets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete fisg)v qs-y(i t:(i11p,sc bl 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 2405: 4m+ic 7)mkiyh yshe rpm to 360 rpm in 6.5 s. How fark c hmy7misih+:) 5ey4 will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850re-.r. lcz mg;hlv/min It turns 1500 revolutions before itl.gmzc .hlr-; comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions pauoq 6t32k5aas the car reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80 m.32 oqku6p5aa t
(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 revg m6sr2gl,g;sv6jibxbp ,z6/m 42 kuduces its speed uniformly from 95km/h to 45km/h The tires have a diamlg6i2s ,gp,v2gru;v4b/6 bs k6m x zjmeter 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 on eacd xvif- j(w3e3h pedal when climbing a hill. The pedals rotate in a circle ( xfv-ijw33de 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. nu14e.hj2r 4sfim+igf1op8psp:1 uiWhat is the magnitude of the 4pe12i girufp+f un psm.so4i1hj8 :1torque 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 abopn; 54ri-3n rtp8f tefut the axle of the wheel shown in Fig. 8–39. Assume that4pr8tnt-fnr e fi5;p3 a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, :n fdz/(wi:wx9qq+u w,yvxa*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 t(ww9 wxf*z: /:na iy, vquqx+dhen released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightening toon 3on ei) t+e/x*-y.n )lqmkn a torque of 38 t o+*q -)eioe3 nnnn/ky )mx.l$m \cdot N$ 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 o* igk aqt d3dvtzh-2.,f inertia of a 10.8-kg sphere of radius 0.648 m when the axis of rotation -iq,adt3vg2*dh zk.t is through its center.    $kg \cdot m^2$

  Calculate the moment of i0 8ihz;ip7k -; joplumnertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass hz7pim0lo k;up;8j-i of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the ne6c;fx- 0fy l:ef:lp end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m. Calculx-: ;f0clf efp:y 6lenate
(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 wheen5j20*ml7klaxp; x l ll rotating at constant angular speed (Fig. 8–42). The friction force between her handkmx*5 ;la7lp0lx2n jl s 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 momentu*hpb /pp1sas w -e ,lq +v:of3dz7ov: of inertia of the array of point objects shown in Fig. 8–43owo:vudz a3:lpp+,-v/ q1fes*p7s b h 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 oxygen atoms mqq2i ;glm5 *twhose 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 cmaqfo81hq of/b,6 9dporrect rate, engineers fire four tangential r6qf9am 1dbpof/ ,o hq8ockets 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 unifor9z hn975z8zabz; jlo6 qqmya:m cylinder with a radius of 8.50 cm and a mass of 0.580 kg.q zlzbm6y: za no;za9hj5897 q 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, acceleaouensxyd o- *0; e,4brating 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 ablo(jkb 24vnwq1+ p n2yge to accelerate it( v+gybq1np jow4 n22k 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 frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut offz, o00h/kdr dmb; (laa and is eventually brought uniformly to rest by a fricm0,/;k hba0oldrz(adtional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 acce frzi/44an ;ek fzj74elerates a 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 thrown solely by thelt1bk4 4 qo /b)nrt.ri action of the forearm, which r/l)tkq. n4b1bt ro r4iotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accelerated uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thrv hri 7kc(e,rmt4fm)dh i9. z *9a8irin rod, as shown in Fig. 8–46 9cr87 diafvm4 kri,(mit.9rrz) h*he.
(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 consf(co1e6(jsl +og 2(e*sfx rdpists 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 from rest withinx:ok b(k*4 m +wrc3qdgf;9razxs 52ex four full turns (revolutions) and releases it at a speed w*429x rgfx5q rbxm 3+(k:dso;zce akof 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 inerenl.k 74jtjf*cmr5m1u 6ldo9tia 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 dev+;r6 aednov8 vcd ojabwey+r6f-/h:6elops 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 rollsf t;ggkvlv+u -g *(t((l ccg(r without slipping down a lane at (frgctl ugl(tg (v-gk;+vc*(3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum j(wxmgv;m,rn oobf 9 56+t.fm of twotfm ogn+ ;xm6v(59mj obf.,wr terms,
(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 oxc f.3cuh* 1yuf 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 1.00 revolution per 8.00 s? Assume1x.cufc *yh3u it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls witurzqbek *j p9g, 6;4ujhout slipping ej9 ; buu 4q6*p,rkgjzdown 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 balancedoqp3lt/;yb/dnaz(q4m6g y o; 7yey*t vertically on its tip. It starts to fall and its lower eta ;zlp;nmq/b yqody 3oyt(4/e g67* ynd 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.]    $m/s$

  What is the angular momentum of a yw t-ce tth3/ffl8;/f0.210-kg ball rotating on the end of a thin string in a circle c- ; e//h8lty3ftwftf 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 grinding whl.. iar t4bx .tqfn30neel of radiuqa rl.4nb3t0fi..xt ns 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform thaq.abxvfy72y (.rx v9*ut scym +9xn5y t is rotating at a rate of 1.3rex x sfnbyv7v59.cm uyq9y*r t2(xya+ .v/s If he raises his 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. 3 oygx*93demb1hf9;qyd 4 k hgrwt.pbz9. i- n8–29) can reduce her moment of inertia by a factor of about 3.5 when 4moy.99;gd gpwhkbn .by3r f3qd1 9ehi*xz-t 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 angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation ratn,:0hixgw /y8) p kx qm-)fi;x,wcw wde from an initial rate of 1.0 renk)x w0,dim qipwg,hxwxy c: /)f-w;8v 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 a0a )g/flhqp q0round a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radi0lg)/p0 qhfq aus 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spinning at 3.s sw0)r *xby5 (ici6)bom lyal7 fdj7.5 $rev/s$ 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 momet mp+il ggr)sd 2b0:g*ntum 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 momen4 h(:xxkxm iv;t of inertia I is dropped onto an identica i:;x x4vxk(hml disk rotating at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns bjlyk.6yn d7;.pca+(a +xe rlat 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 okali-e*is r7cwtf /oou 7 n713f a rotating merry-go-round platform of radius 3.ase7c3t /-w rl17fi*7iounok0 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 e2qcdmw2q1n 0qbeku 2-;zyo) is rotating freely with an angular velocity of 0. eq2)ymq;cw z1 neou0-bk2qd28 $rad/s$ 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 co; 0uhiu7f z,dgllapses into a white dwarf, losing about half its mass in the process, and winding up with g;hu7fd z0u i,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 olp6 7s qd3ioh 49,lw4pnocs) af 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 gl* 9z+p /fn *olvw0pvrx9m-r$ 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 rotate freelr*tj0mx g6c: h+ v91ge dte5jny without friction. The moment of inertia of the person plus tgj 6hj x1d*:0 vt+getcme5r9nhe 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 r w*kfmjngu8a :o(()eat the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has ar ojuk fm( ():e8an*gw 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 w 6 cxr u*x-/amu8z:acbith the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a disr/abx zm: uu*8x- 6cactance 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. Detaqqw .m;xd zxp 82na84ermine 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 naqm. ;xx4a8 d8wq2pz as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at r2(voonb, c /16wihs ni*9ky qa 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 cylinde-y)f/yuv )br,z)mmv fr 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 deli/,fbvzu)mr)y v)yfm -vered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, ekuo:/ lq x+x ;6vojy*4:)ycxjss0seu ach of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches ; jy*:exlv:/ukscsxou )jso6q+40xythe 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 angul n5pdm;js:8v.e(e2 9 ahcgrzqar 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 of our Sun, but with mass 8.0 .ykwx)b6m jr5 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 woub6xkm5.w j)ryld its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-p0a. 7u6cxmg /4rf8 tr;ev6jg oo 9jddkollution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car h6dk0g;ec 46 tvfxdr9 mjojarg7. o8/uas a total mass 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 illustrates aq zmx dm g xh;y:q)mqd9ro)acp2wol.v,a-6 87n $H_2O$ 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 horizoht/ 7lvx ua1u *d3w3j x30sutfntal 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 friction)oa(u) , es n*i0zio0pjj y,2vs 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. e * ,spj,sv(aiun o)yo0zi20 jAssume 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 stancz2pqi/q4o ),j i0nejrirw2 h+se+w5 ding vertically on the floor, and we want to exert a horizontal force F atn0wo/24+rzpc iq rjj5s eq) eiih+2,w 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 spe zzr0iu9n ig zo6;9o7ued v=4.2m/s on a flat road is making a turn with a radius The forcesi09;u7o nzr9zg6 iu oz 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-kgqj 600grv*.pc+wns j9xe,uw t 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. 0t9 p0c.jw+6evg*wqnux,js r0 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 cylinder and her arms iz1zaug,wejd ceq3-6zj /8:t as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning s d3wu8,c -/:1e qzz ezjaig6jtkater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which con/nsny 5mymx,2sists of two cylindrical plates, of m,mny 5ny2msx/ 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 alonxhxr98ol8 rt:9:ewdye 24gsug the looped rough track of Fig. 8–58. What is the minimum value of the vertical heigh4:9dxo x8h eru8tsegrl29w :yt 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, but do not 202dlhpco ob,fu;dfjf t, 0.iassume $r\ll R$ h =    (R-r)

  The tires of a car mak1im w malb(50be 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) What was the angular acceleratb(l50a 1wmim bion 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