A bicycle odometer (which measures di6+yl 9t;z 6z4zy xqsflstance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheez6zfy qly9t;xl6+s z4 ls?

Suppose a disk rotates at constant angular v ffq7rv2:-vfz qeu.h3elocity. 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 v3f.- fe vr2:qqz7hufthe magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value of the angular q1o)a1s ih5a zvelocity $\omega$ Explain.

Can a small force ever exert a greater torque tharn7 8se ,mul omg 5:o:wsbasu5m:v;8 gn 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 sicy 3e(dy3h u1gt-up with your hands behind your head than when your arms are st ueh1y3gc 3(ydretched 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 tf .xkwj*mq,r bl0*qk2nwj l-7hree at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a ,q 27*qfjbk w0llm-n j.wx*rklarge 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 hav :oj9lleq rje.t17 1pre slender lower legs with flesh and muscle jjt1rl:l 7o9.pr1e qeconcentrated high, close 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, (ro xv ),pua j6lp2gq)narrow beam?

If the net force on a system is zero, is the net torque also zero? If the neps1igwc;bi.g -w-ig8k y5 d* qt torque on a system g5*qw;ibiidp- w c k.-8syg1gis zero, is the net force zero?

Two inclines have the srtgvsh91*(s8ja .hqo (31y jgv-shg came height but make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline wi1yv ss*vsh(q gjh-t13 9 (gorcah j.8gll the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolle(jdvka n4(f-bl;n +g* f9weqing (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the in ;+b*ew(n( fe vg-nak4l9djf qcline 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 sacma78 5lprx7 xme mass. They start 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 p7 a5mcxl7r8 xtotal kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and akfw026otv 9tvy0(50 e dem diungular momentum are conserved. Yet most moving or rotating objects eventually slow0uoytw e 0 0ivd f6ktdv(5m29e down and stop. Explain.

If there were a great migration of people 5.dm rt cjfya-c5f;c6toward the Earth’s equator, how would this affect the ; 5cf6ytca5fjrdc m.-length of the day?

Can the diver of Fig. 8–29 do a somersault without tntdu c:i+ +c, +ome0ix .r0fp: yaws3having any initial rotation whed0e+ip cn ,w iyfu.+m tx0+oa:rst3:c n she leaves the board?

The moment of inertia of a rotating so y/zv;7 l; 0jpi)yql.z5xnec xlid disk about an axis through its center of mass isqnj e /vxc;p)7xzl.5yli z0y; $\frac{1}{2}WR^2$ (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 eiqs/lnj 9h)+bach outstretched hand. If you suddenly drop the masses, will your angular velocity increase,jlh+/ib)s 9qn decrease, or stay the same? Explain.

Two spheres look identical and have the same mass. However, o3tcarhp8 y 1:ztb.he,ne is hollow and the other is solid. Describe an experime3yac :bhez8p hr,.1ttnt to determine which is which.

The angular velocity of a wheel rotating on a horizonta 0hxw2i ioo*0,ffnf c5l 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, desch0 wc25iio0f*f x,nforibe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotatingbr5)po:fk nn * turntable. What happens if you wbn)5 rk:*onfpalk toward the center?

A shortstop may leap into the air to catc-7h o)8pg+zg6 wqz5p/lbqzcfh a ball and throw it quickly. As he throws the ball, the upper part of his body rotates.z cbzgz8/6qpo)7f - pgh5q+wl 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 of conservat(fy(*g/vt cae7xeb* u)gt 7kwion of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller cane7vf/7agy ktge(t)c(**b wu x operate to keep the helicopter stable.

  Express the following angles in radiansbru:s5 ;q vm 9t)cjr)f: (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 amm(:t00i 8qq;nf ppj onkpi*;dazing coincidence. Calculate, using the information insid(o iji0np k;8nmd;ftpq p*q0:e 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 directed at the Moyv*k +)31ynp vx bd0)ewc/ dzvon, 380,000 km from Earth. The beam diverges at an anglxkyydv/z+ w0 vepd3bc )* v1n)e $\theta$ (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 jk x(wwgad l 92g:fp5 jw8s+)wa rate of 6500 rpm. When the motor is turned off during operation, the b+9gk pw)w(lfd :j2jw8 xas wg5lades 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 ano.o)wlgc: 29 shg1ky g8 cmfk:cther child. If the ball makes 15.0 revolutions, what is its diamec cw:g1sk9fhk) g .g2mo :yc8lter?    m

  A bicycle with tires 4g;)sbx6d7hm4 qihu h - mx6kg68 cm in diameter travels 8.0 km. How many revolutions do the wheels xm b 7-k;g6iuqh 4xms)hg6d4 hmake?    $rev$

  (a) A grinding wheel 0.39kzki. ec6e gw0 /kkr:5 m in diameter rotates at 2500 rpm. Calculate its angular velocity in k0 kigw6kr/z c9ek:e .$rad/s$ $\omega$ =    $rad/sec$
(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. 8–38). pvxbn4i69 hl b*azgq2bv(j,of8;3 co(a) What,*zbi 42l6o pqg( a v9nv3x;jbcoh8bf 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 arouu6jh+6 j o4xyand the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a y:d 7*doxmr1 hz,g-pk 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 cm from the .y7(r8aem uyc axis of rotation is to experience an accelerat(yc8a .mr7y euion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acceler:gvw.o 7 qrs7eates uniformly about its center from 130 rpm to 280 rpm in 4.0 og7 wr:v.7eqs 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 i l+vezym f +0i-ivcqk(/q,5z$R_1$ 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 them7.f11aq , wnavlaq. doselves 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 spacw1o a.q7aaqvl,n.1 dfecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15,000 rpm icf48u nmug cu mfx7 9mk/w)02rn 220 s. Through how many revo cmu/7 8rcngu2xf 4kw90m)fmulutions did it turn in this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpma1s3u1sl zvtw (vi-s / 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 fd da sz /rnxb++g+:tl+or the stresses of flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 /lxzndt+++ dr+ g:abscomplete 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 360 rpyn0yc32n 5(pmt*2 rl b7qeygem in 6.5 s. Howb 2en*qcly7yer 5y30 g2t nmp( far will a point on the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is ru c:- wnt,2nb2asqdkgi6q n( t;nning at 850rev/min It turns 1500 revolutions before it comes 2nw(:b nn2ak-6di,c;qtt qgsto 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 nj g66:cp/haf65 revolutions as the car reduces its speed uniformly from f6h:gn /ja6 pc95km/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

  The tires of a car make 65 rem qd v2e(d/q2m76asorvolutions as the car reduces its speed uniformly from 9d (q2e/qmors6 d va72m5km/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 09/tr r d-h9o( jz0mstbqen k,bt 6e7jputs all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 17 m 0jt/ s6 9h9e-e(d0n,orqt btb z7rkjcm.
(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 do 80e-sf9b a-*vgiz xbuor 74 cm wide. What is the magnitude of the torque if the force is exerted-8zs9u*afbbe 0gi -vx
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. 8–39. Assq8ixzqxr isfzct .1 ;7r/65qoume that a friction torque of 0.4zxqf qti/r. 6z8 1q5ixr;o7cs $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, ay7z0c 2hvax i:uk3e*.wqt; vire attached to the ends of a massless rod which pivots ak0ytwu ;.ixv 3ca *izqv h7:e2s shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require)puuhboa j78 )u/8wnr tightening to a torque of 38aj /huronu)b 788)uwp $m \cdot N$ 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 ofr*rg/gf 8i4j1 branylioo rm j :550o9 inertia of a 10.8-kg sphere of radius 0.648 m when the axiofgom 9:5 *rr8/o4b1y a jj0grnr5liis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter.l,hc*tjafaso:76+ qj qxny58 The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be,f+ tycqhn867 *j5loa a:sx jq ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball oni8b6.rdn bev;ws6 c 3u e:iy0l the end of a thin, light rod is rotated in a horizontal circle of radius 1;3inbs6e:y0ui. 6c 8vlbdrwe .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 constant angular speeb6)kxpcg+7a fd (Fig. 8–42). The friction force between her hands and t xc6 k7+bp)afghe clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of point objects shown in Fig. v/g6z .c0k gjs8–43 about zv/sg0 6jg.ck
(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 con; ea4efw9roi c8d ,6vssists of two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satellite spinning at the correct rx1o)5huzcbhdzr*fi *r-v*cp*0/ usjate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reacr uxuo*zc*p5 * rv1 hi- jhz0f*c)b/dsh 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.4x3: qp o)njmg50 cm and a mass of 0.580 kg. :o3 4 xpq)nmjgCalculate
(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 swing -h4n.osbbyg4f4 i(3,ir +lp hirenv5s a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small pa9epvjc cu hv/i;grqx00fbgg2::, 3hand-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)v /;fq jc2 ,ibv03ucg x gr09gaph:e:p 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 shuh-cc8 )vp :zponzq97ut off and is eventually brought uniforv9c7-) unp8c phq:zz omly to rest by a frictional torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–4xr wgcl1qn/f1u 5a):m5 accelerates 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 the action 5*dr ( cay7i3ojz1dvbof the forearm, which rotates about the elbow joint under the action of the triceps muscle, Figd3orjc 1(ya*bdi 7zv5 . 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 th p5 e2rjzn fiolm9;y -v63zf3wno(pu8 in rod, as shown in Fig. 8–46rojio3fnz5e yw83-v2mz; pp (ufl6n9.
(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 o kbi:qgd25l8 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 within l(ghnfyb mi:h7,.5d d four full turns (revolutions) and r h(dg 5:,lmhb.fin7y deleases 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 7dfm.2)+vgcx*tm hot moment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops ast:72 rjxk6ja 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,9ghbljgu+guda0 wj/ mjl6 uz vb6/72 slipping down a lah+j jugj2 gu7g6lbu,b 6z/ v9/wlm0dane at 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic eneses7z y2mdp)e*,axr r0m6f 2 krgy of the Earth with respect to the Sun as the sum of two terms,fz27m6*,s) s0xedprkm2 rea y
(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 k xot.( bpaf /e*r8p;: mqwkv-ssdx1k.g and a radius of 7.50 m. How much net work is required to accelerate km x(-: pq .a;/wtkb* odsevrfp.1xs 8it from rest to a rotation rate of 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 kg starts from rest and rolls xfvj0c x.(*h8w9fq d qew8s-+a:p hljwithout slipping down a qw vp0jf8h:9*je dc.+ l(xhxw8- a fsq30.0 $^{\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 ts8iil 345 art:s4c .ofm6 sdevxc6/mdo fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hinc5m8rasx3msflse44iv :cd6ti 6/ od.t: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the enl +n ;fj-epdul , y;pb4w(+cind of a thin string in a circdelwnc-( l;p 4pn j+ uiy;fb,+le of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angul * rescdxifzn;t oz.b3 y.3 ;7gt,ca)tar momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm? oc;3.r)fb.ceaz*tyn;ts x 7zig3 t ,d   $kg \cdot m^2$
(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 platformg3 7t sep1 y8q.ds2*s+tuso rf/ukjj; that is rotating at a rate of 1.3rev/s If he raises hisgoquep y usr+jt/ 31s2s87df.j*;ks t arms to a horizontal position, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29) can reduce her mhiluo v mpx)b (3u w;wyn698d)n;fam3 oment of inertia by a factor of about 3.5 when changing from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speedfn(8xmwh dublm ;ai ; 93)6yw3v unpo) ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial rate of +lz6 ( (e cy24gkxpuv(jns5gg 1.0 rev every 2.0 s to a final ra(jcpnku(4y g zg+25lx(6gs ve te of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis thro5xmb-vkw6 ye ,06gy vyugh its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of6vwgky6 0xb m y5y-ev, 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 angula6m 5 ixxhq192-t yftntaw);pwr momentum of 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 momentum of the E2v-ssvl*nm h1*ic ) lyarth
(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 awqqsdysi aik8 kg-y30;dqs-w * 8:- q a-du;ynn identical disk rotating at an y i;qk:sws daquqn8k ywsga*8ydi0q--3 d;- -gular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 23q6jiuy*y.a ejes -9 ; h6shgz.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 kgqgu*kb9nz/55 ug q b.y stands at the center of a rotating merry-go-round platform of radius 3.05ugkqn5 bg/ *b9y qzu. 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 rom5n5/tf2r vs rvst*+stating freely with an angular velocity of 0.8 tsns/ v5 mfrtv2r*+5s $rad/s$ 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 abs/ou f*-hz8 3 /cdrrlok *r5waout half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost massk* wof3 osr/u /lcr*r5 zda8-h 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 of yj2o;duvb4c5 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 dx/uefcm 3 i36$ 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 freely lxp)w,z(cp) x without friction. The moment of ipp wxl(x,z)c) nertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person standya vjurw+yig7/ 6 ro7i+7t8 pus at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of ine ar/g u67uiw87riov yy+p+tj7 rtia 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 thqnu5rn6- izixj:oc+3e rope lying on the top edge of the spool. A peuq nnrz+o5ii6xjc-3:rson 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 th izel-4 436cu;u 1ig3bbnrbpf e same side always faces the Earth. Determine 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 part-br343bn1fzlpueii c; b6u4 gicle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate th ctd5 (nip*: b,/x-5iwz*anrmhd (h 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 iw1ke0 yku/ vy+n the shape of a uniform cylinder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s intervale0 w/k+v yy1uk at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylin6 q,lpj.g)wc hdrical disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindric pgh)l6. q,jwcal 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 wheell6th:kkbb0p5ok). 5-f q0 shga bq;z s ($\omega_R$) 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, wer:zo43f nolg j2jsjn*w)m6+mq e rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its ro+6of lm 4wonjg:qn3 jjm*z2s)tation 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-pollution automobile is for it to use energwjsz4or 5hmwa5bbu2d *3bk9evj ;i- t8:ujg ;y stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 k i;u vkrjmshz35b ;*8j:g 5abuw2t-o9 wbjed 4g, 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 illustrao cmna:lt )x*1tes an $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surfacyz *j e;bc;ylt)x*i1o*g t7i18mlkmye 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 andgsa+0 (:/qsm t glm0pso*5n(vo2uzfc length L can pivot 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 of release, determine (a) the ang(q*s +o:5s0a vlmgcp( nzu2ofstm/ 0gular 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 mgvty7g46. ywfuto f.7 ueu9, vertically on the floor, and we want to exert a horizontal force F at its axle so that 79tft u .6yvugou 7eyw, gf.4mit will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/sjd0bsg3 en )/e on a flat road is making a turn with a radius The forces acting on the cyclist and cycle are the normal forc)/3ngsjee 0d be $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ 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 a sling of length 30flr kpv h/3g0 ufv,f1.5 m and begins whirling the rock in a nearly horizontal circle a,vupfk /f30f3 lg0rvh bove 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 solidaswa( 8i z6j8d/+4cffxsj4 cv cylinder and her arms as thin rods, making reasonable estimates for the dimensions. The/fd(vjwx48c+8j4za ai c6fs sn calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two 3ob /jjzull.2 cylindrical plates, of ljbuol/3.z2j 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 along thwre( g c.21+hwey6vytfl 4)ble looped rough track of Fig. 8–58. What is the minimum value y th+2 elcg4)e6fb.wv1( ywlr 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, but do nx4;3rcx+ibb5 lv8 0zpaglfu /9mnf;c ot assume $r\ll R$ h =    (R-r)

  The tires of a car ma jmeisxvsx729 0:t h5bz39c6b- vtwqtke 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 anc itw 23zbbvt97-s qxje965mv : 0xtshgular 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