A bicycle odometer (wh ibqm00lmjwz *)w+) uiich measures distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What)q ui*jz0 mmiwl0+)wb happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at c7l f;1cn ce3t5t dr,tjonstant 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 wh 3e5t;t,ctnrjl7 1cdf ich cases would the magnitude of either component of linear acceleration change?

Could a nonrigid bodc ahpk8vr p;.5f*f9djy be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger fo: vde g/t;.t0.li l77btxmw cvrce? 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 hands behind your i)u+61pt- :lfaash -k5i,5bvdxm d,qepj 2szhead than when your arms are stretcha - k zphue -s, dq2,i1tp655d)avbjfslim:x +ed out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wh bax/(bbcx z;8eel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? ;x bxz ba(8/bcIn which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on beinixfk :-hodm*c0;ay*dy 3 0gm fg 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 rotational dynamics, explain why this distribution of mass is advantageoux o-3gm0hdff*ycm y da0k*i: ;s.

Why do tightrope walkers (Fig. 8–35) cay e* yn4dnb9tbo3p8k1 rry a long, narrow beam?

If the net force on a system is zero, is the net torque aa)koco:k2z pse18,whl ia;b)jz3d 0zlso zero? If the net torque on a system is zero, is the net force zerc w:28;iao l3)jazpodekz kb1sh )z0,o?

Two inclines have the same height b+eee+vw 9i- ldut make different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greal9e+dw ei+v-eter? Explain.

Two solid spheres simultaneously ssmo /2xrhiu.v7xdzx*l.vv4 y7 o0n )j tart rolling (from rest) down an incline. One sphere h.dl yo/ nx042s)xo jxzv .irm*uh7v7 vas twice the radius and twice the mass 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 th 111eubt zfa:fe same mass. They start from rest atft1fbeaz1:u1 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 rotational KE?

We claim that momentum and angular momentum are conserved. Yep odtey l* l5+ (01yxms67rijdt most moving or rotating objects eventually slow down and stop. Explais1x0*d( pr76t ly+e omjidyl5 n.

If there were a great migration of people toward the Earth’s equator, 9if89hachx0rhow would this affect h ra80h9ci xf9the length of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial oo q3shl9je8(--cw/u vmpv ) rrtx)5l rotation when she leaves the board? s)- lhutovr qxv8-3( j prew5 9c)o/lm

The moment of inertia of a rotating solid disk about an axis through its cent0 :o,sgf:(jjpz ux8 + a(qmdoqer of massmg(:dq,: qj zp+afxo(jo8su0 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-kc+(e ,u uzy/yeo)kaq )g mass in each outstretched hand. If you suddenly drop the masses, will your angular vel oqy,)uy(u ekzce)/+ aocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same mass.zq:(zph1c t9n, ypmo l2m, *yn However, one is hollow and the othe q:ypy p2oz1c9nmh*lt mnz,, (r is solid. Describe an experiment to determine which is which.

The angular velocity of a wheld+j/ jbtvirr, tf38gf1 v9b2el rotating on a horizontal axle points west. In whj t/9b vv38 rjdr+fblf2i1tg,at direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the e,ld.o:lpxrjdm51g ) y dge of a large freely rotating turntable. What happrdjmyp5:l,g )olxd1 .ens if you walk toward the center?

A shortstop may leap into the air to catch a ball and thrv mndk2)74 oclow it quickly. As he throws the 2nc l m7)k4vodball, 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 of conservation of angular momentum, discuss why a heln;t hwh;.78mt or0d;e)twpzsi gl1 l.rjnu2(icopter must have more than one rotonred;t.lsgtw2(r l;u .wmpoh1i ; 0zn8tj7)hr (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians: (a)smtk e(3b;)b)y zaa8c 42yxpeq kh, r, 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Calculate, ye8 naq6xg *6 xwxen5,using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth5xx,66nax8eygq n*ew.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earmqwqlw c1agpve+/9 97 th. The beam diverges at an angleq+aw1 qv9 /gmcwe97pl $\theta$ (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 rate of 6500 rpm. When the motor is aw;1y)szha5 ak k -nv7turned off during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as thensh av 1zkka 5-;w7a)y blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor d hvavp iab*so7ovq5o 8u// 503.5 m to another child. If the ball makes 15.0 revolutions, what is its diameo vvi5*ua7// qaso vb8d5h0p oter?    m

  A bicycle with tires 68 cm in diam,p )l7 fcwpl)ki.k* kjr*oig(eter travels 8.0 km. How many revolutions do the wheels kck*pr,( . fl lp i*)jko7gw)imake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates )m ;k49nce-cd 5nz;zi 3sqtjuat 2500 rpm. Calculate its angular velocizq-ed5 nsct) czmk9un34; j;ity 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. 8–38). (alw+qqrz ht (j*c (4ds+) What is the linear speed of a child seated 1.2 m from jq+r(wcq4l+ (ts*dh z 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) d mu/51ttx9 8q 9iea .oghkpk8in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear slxq/2p+ , aoe6yt b)obpeed 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 centrifflb1a0twpko v 2 y*h9*uge rotate if a particle 7.0 cm from the axis of rotatio kpto1by*2vaw h90 *fln is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 130t wctbl5z3-cm,4o *n a rpm to 280wm3co l5 nctaz4*t -,b rpm in 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 radius8 kvixzk+ e-ar*vavps.v,7i3 $R_1$ 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, 2y)uga6etkr, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determinerektu,)ag y2 6
(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 15,0m5siq.hf 2 g:ub* m0ye00 rpm in 220 s. Through how many revolutions did itu.qhm:imy2s50 *f geb turn in this time?    $rev$

  An automobile engine slows down fww*elvf ;-jl(t saa69rom 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 of flying highspeed jets in a p7 +mi -cminq(xjr )7:zm oh;bwhirling “human centrifuge,” which takes 1.0 min to turn through 20 complet) hpj+xibi( m7orm; zn7-m:cqe 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 36ded n2d 7(mo a7; b6juhf+a4gj0 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this d h7 ( ba27j4j+m;fa 6ndugeodtime?    m

  A cooling fan is turned off when it is rundt0x c i6cg.rc:ig):j ning at 850rev/min It turns 1500 revolutions before it comes t i cgr60:t.:gdxcic j)o 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 cwkro2c ml:z )+b jjsdsk1l;89y 7qx)reduces its speed uniformly from 95km/h to 45km/h The tires have a diameter of 0.80lbocx2 yw)s1m+drjkj s7 :k ;ql8c9)z m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces it4kla0c0g)t 1m .h-sao;cv enn s speed uniformly from 95km/h to 45km/h The tires have g-t ; m)n 0hcc.k4 a0n1lvaosea diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal when climbing awea4xig/2bckw9s fydz x +ay) +pj-81 hill. The pedals rotates ex2 wfj1a9iyapxbg y-+z )+/ 8kw4cd 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 6sq-n /(ri miodoor 74 cm wide. What is the magnitude of the torque if the force is exerted(n6-rq m/s ioi
(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 2wrch-eu i4y5 of the wheel shown in Fig. 8–39. Assume that a 4w2 r ieyu-5chfriction 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 of a massless rod wh99/oom ze o:ugich pivots as sm 99:/ogu ezoohown 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 tightening toxw oo1) ksvapbkr6 6m6 n+ )yaa/0t(jr a torque of 38oo0yrnaws1xp6 t( +6r k)mav /bj)ka6 $m \cdot N$ 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 o b2zi9vf:hu3bf radius 0.648 m when the axis of rotation is thrb3b9fzuhv2:i ough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheelke n9fvj):wh4yl8w.w 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub can be k:fhe8wny) l9wv. w 4jignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is rotated in a horizontag.fu a+kg*squ+g) oz 2l circle of radius 1.2 m+g2.+k)zus ufg g*aq o. 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 constani8:etd,-+rhn zze k ;et angular speed (Fig. 8–42). The friction fterk: ;e zi8+n ehdz,-orce 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 of point objects shownnp5/cyy* .fs k in Fig. 8–43 aboutkn y5c/*p.sfy
(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 om q z16e+g04*afls qurxygen 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 spinemr*g efaam ,cal osv,s7fl71g: +9v4 ning at the correct rate, 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 req7f :esvaegl149 *oa mc7mva s+,rlg,fuired steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a ug htq)51f,mt9tz9 jkoo0h7w mass of 0.580 kg. Calculh079t q )ht9mku51zjotf gwo ,ate
(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 swwz/-: gaj jco2ings 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 hand-driv2/q43 y8rb jryjg;nluv 2nd *len merry-go-round and is able to accelerate it from re3; j4rr nvgq2*y/ 8n ulld2yjbst 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 k)cgyl sy18(gc3h h-1acbj1 cshut off and is eventually brought uniformly to rest by a frictioy-cjy sl8ak g3h(g )cccb h111nal 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 accelerates a 3.6-kg ball r:i n9/y,gdr2qhp*fu 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 of the forearm, wh5 uzkj4a5jkyxr1hwq75m f e49ich rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The 4kz9 uw4jj5a71ey km x5fhrq5ball 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 thin rod, as s-d:dvfs(etg3 y:el 9fhown in Fig. 8–4ld(sv3- e:fgdt :fe9y6.
(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 masszr + ;*mw3fcsbes, $m_1$ 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 tnmn14xe0 pe;1 vdy -fche hammer from rest within four full turns (revolutions) and reln 4 ;10-dxe1pefymcn veases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia ts,2)+ud pmkxof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine doevk7 .+2wj m;hvoe+froe, 0oevelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls 1m,su b bbgk;4without slipping down a lane at 3.m 4;, gbu1sbbk3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as )jbu(x8n 05gk zicpb;the sum of two termsg;8 )xc0ibzn5b (juk p,
(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 ofkfto 4*5 gsu:l *jds+f 1640 kg and a radius of 7.50 m. How much net work is required to ac45u*l: *gfo stf+kj sdcelerate it 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 resa0kr1(si a4 dfbv40oft and rolls without slippinbdv a04(4oaf f1s 0krig down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically t.h7:3c;ep gnaxpae5on its tip. It starts to fall and its lower end does not slet3 xc ph7gap;ane5.:ip. 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 moment-8ge5;7 x5oxj;dg s y-zjlbv ge,u )zium of a 0.210-kg ball rotating on the end of a thin string in a circle of radius 1.10 m at anujdeijozy ; xv-sb5 e)8g,z-g7 lx5g; angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angu (tlhrt5+-d5ww-wxe h xuc ;p7lar momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotating at 1500 rpm;+-7wwrp wxc-5dtl xu5t (heh?    $kg \cdot m^2$
(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 r y enlpb1oht7).mhqy6q-pk 09otating at a rate of 1.3rev/s If he raises his arms to a horizontal position, Fig. 8–48, thhn 6o )1e.9pb0lh-k7pyqty mq e 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. gqn. y9z;gvyvsm0 8s9 8–29) can reduce her moment of inertia by a factor o9;yvqs 09yszg8mg .nvf 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 speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate frb ,bauow,5fv c:v4eg;r7t sv;om an initial rate of 1.0 rev every 2.0 s to a final raeuwtg c;:5 4vvvs,forb,;b7a 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 axil5 xgqb*r)y u0nvzf3v3tru26s 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 obnx3 uz)vlrur f*gt0y 2v635qf 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 angulaf.7gpci7 6 a lqwc-z4vr 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 bv5 2vqzl1yd6the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$

(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I ism nqo7jsm8iav h49g : m*dyy8. dropped onto an identical disk rotating at angular spejq8 md4my. s* v79aohyng 8m:ied $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2dx7z vpj8-(r5 8k kthk.4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating merry-go-round platf7z r78glctk -zorm of8 7 ckz-7ltgrz radius 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 )gim0lo/;x(eb*1:yc 3*du xx j *lxw ek *tgcjwith an angular velocity of 0.8 *0xx:y)x wm*ou*l/tbx( 31kd;*c eciljggj e $rad/s$ 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 int i* .y3bqt82og3 ftffko a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming thgy28.i 3q*f3ffbtko te 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 outa3 w:n0o4ha f 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 9y 5.;za 6:*e ie cvetfrpdqf s6(gtn3s.y g/y$ 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, initiaw , f0hy3;0muzaa+pmolly at rest, that can rotate freely without frictio0 +mhoy z w3pm;f0aua,n. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter merry-go-rouo+ w)xw3fsm :kq *zalr)u ,ysgo39)tvnd turntable that is mounted on fygwxa 9) vr )so:mz)s*o klq3+3,wtufrictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the grc 8-:;ajpyf d3ha(qedound with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of j8ay: aeh; qp-fcd(d3rope 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 En v72ej a.i8ytarth. Determine the ratio of the Moon’s spin angular momentum (about its ownje8nv .atyi7 2 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 res;cby)p8 c o2fot at a rate of 1 m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone ino2co0d,u /2 jmq ( ;+tgkgvied the shape of a uniform cylinder of radius 0.20 m acquires a rotatiovdm2toejc( 0+/ig oud, g2;kqnal rate of from rest over 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 cylindricanrjrudqhfx:- ies lf /-x2;8v8.h-v rl disks, each of mass 0.050 kg and diameter 0.075 m, joined by a (c882-/v lhfh:. run x-fiedxr;- srq vjoncentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-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 7hd( te,l+gw 3a-imbb angular speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great,e i bdvhb32 (4yf:;yky were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume y d:bey3;i4k2f(v b yhthat 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 enerh:ug3zt9;5x io p8u cyqcoq/. gy stored in a heavy rotating flywheel. Suppose such a car has a t5qqiy z o3/cgt :u8 o.xup9c;hotal 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 a xm+e3pcjmk8d yy6/ch *bd;upp433kj n $H_2O$ 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 surface at speed v=3.3hxi(za vg+/ s3 $m/s$ 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.el/5 cnm6wy-ltdkl24 l., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular a-wll6cn 52ldk 4/ mlytcceleration 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 r. 1i -)h0pvjxh*vu -szerla*x adius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle *z 0hr) v. sv-ei-axp jxh1*ulso that it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s onz41wdouymnc+( x8b6;wy0 /o jaqvth06 zinp9 a flat road is making a turn with a radiy/ (vm1;nzop a6cbun6ti dqj y8h49+ 0zow0x wus The forces 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 a sling of length 1tlwrk2.-6cjgeq, u9t .5 m and begins whirling the rock in a nearly horizontal circle above his head, accelera2tjt rwegqu-lc 9k., 6ting 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 al5raunl8 8 pm0 solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the 8r0lu 58mlnap angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a cl25m6r xydp -9a 9vdgishqyvzbo;u: 6*utch assembly which consists of two cylindrical plates, of rpvm;dy *ub vzygad69-695:ix h oq2smass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 looped rough track of Fig. 8–5a55yqki8mfu( si/bx6 mkh -d-8. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving t/a-kiud m k85f qixb5h(ysm-6 he track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not asscodrra/498c f th7,jaji3d g0ume $r\ll R$ h =    (R-r)

  The tires of a car make 8mhtc6*rag2 8 w5 revolutions as the car reduces its speed uniformly frogh r 8*m2tc6awm 90km/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