A bicycle odometer (which measurei i : ms. .+ nq797tdupzne;kbx-,dgnrs distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happens if you use it on a bii 7s;7nnx-t9 .iu enz.gq,r+k :bmddpcycle with 24-inch wheels?

Suppose a disk rotates at constant ang: u7sbxw2tjztj ).dx.ular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases unift: zdu x.).27wxj tjsbormly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a sing6r*4hdnep733rwgb n(0uzw kv le value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque thancyq8wz4 o(d70b1 itfi 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 hands behind yourr/s, oq10eex47lvcq blr9o- d head than when your arms are stretched out in front of you? A diaglr 0o se97e4q1b- xdl,/ vrcoqram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear wheeh 5kv7cgocw );l and three at the pedal cranks. In which gear is it harder to pedal, a small rearv)wk;5goc 7h c sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have -i 1pmf 3r6wejslender lower legs with flesh and muscle concentrated high, close to the bodpj361-f ewi rmy (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers s4f usgx8jt,2 (Fig. 8–35) carry a long, narrow beam?

If the net force on a system is wt834kic:d i1 dor0hyzero, is the net torque also zero? If the net torque on aw 3d0ti4i dh:ky o1c8r system is zero, is the net force zero?

Two inclines have the same height but make d:2as 0cdhbozu 6abo:8zs,j5yifferent angles with the horizontal.2 as,do6 8hbz:usjbz yoc 5a0: The same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres sireo9,rg a 1fg4oqef++ multaneously 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 greater speed there? Which has the greater total kinetic energy at the bott fo+, +4qeo9fg1agerrom?

A sphere and a cylinder have the same radius and the same;q2p/ q9jolfgo yg :8b 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 total kinetic energy at the bottom? Whic8g oqjg;/ply f2o :b9qh has the greater rotational KE?

We claim that momentum and anfxf q8vuind 4.d;,n+p gular momentum are conserved. Yet most moving or rotating objects eventually sldxn uq,nd+f f 8v;ip.4ow down and stop. Explain.

If there were a great migration of people toward the Earth’tj*;n wqmwl.q(i m9d*s equator, how would this aff* tmlnjiwmd(.q9q * ;wect the length of the day?

Can the diver of Fig. 8–29 do a somersault without hav:ba/rsjq7,/2d( cfg a v5 pkh:wd h7oping any initial rotation when she leaves the boa(ov/db:hj rkpdg7a2p5w q,a 7:shf /crd?

The moment of inertia of a- 8zkq00 4 b-+vibiq-zuptq gpz m94qg rotating solid disk about an axis through its center of mass 84qgz-9-0 kq + bz0up-4bqziigvt qpm 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 holdingva9ek(b agi2 dd:8g4ovjvv49 i y3w3w a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain w2:og( ka9i4avdwv bve3 9j 43i8dygv.

Two spheres look identical and haeqsez 8h6c.4mk+8 g)xjn dbf4ve the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which i6k qe 4sn8fc x +j8dbm.)ehgz4s which.

The angular velocity of a wheel rotati *s* 5yn 5ml:tb4dzs e)y*/usv 9cqfnfng on a horizontal axle points west. In what direction is the linear velocity of a point on the top of the wheel? If the angular accelerat5*y /*fzs5)4usnlcbe n sqv:df 9 *mytion 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 edge of a large freely rotating turntable. Wwu.5 4gn 5xu;gpzxl; bhat happens;.u5u l4gx; xg5bnp zw if you walk toward the center?

A shortstop may leapy;5a.- bazizmzqdd0 6 into the air to catch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–3qa .- bm0z; iz6dz5yad6). Explain.

On the basis of the law of cohd+ j2v3tm.ucs( 7mda9vs0 minservation of angular momentum, discuss why a helicopter must have more than one rotor (or propeller). Discuss one or more ways the second propeller can v39jdu mts.h2iscamdm+(v 0 7operate to keep the helicopter stable.

  Express the following angles in r:/nbl j +g6ox8usq2n 5w;gbb 3hj9xi -dchey5adians: (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. Calculate, using thpssesjbyy+ x6 tzw(:fr k49dx7 z(e- +e informationw +y9xs y(6x-(jsdrek b: zf+ 4pst7ez inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directe lf4v ey8ar pn*68ks7 xh*qsy8d at the Moon, 380,000 km from Earth. The beam diverges at an angle7* fy 46sevh nplq*ax8 s8ykr8 $\theta$ (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 t- alwl*4stbav(6hi; te at a rate of 6500 rpm. When the motor is turned off during operaa;bl6-atv h tw( ils*4tion, 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 ogtx pqzwxl w34m0m+0ea5dd 11n a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what is its diamdxx0mw5t11+mzp a dq e4wgl03eter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many ct(f ;k(v 4.jm4 huijfrevolutions do the wheelsk4;tm.v( h fuc jjif(4 make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 0m i lzsi8t.b0cnqjeu au2l8rq7h21, 2500 rpm. Calculate its angular vesi8 h u8,2 zt701cali2.elj nqubr0mqlocity 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. 8–38o0czx:zn/kzi-1 m *po). (a) What ismp1zokn x0 z z:*o/-ci 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 velo;x2j crl*om w5city of the Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of af*6o1p q5z.f.ol6wr)om nyujm xc)3w 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 u*g5))s 3zx;lj pim f)sj,fi arotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration ,)j* ijia fmf)sp;5 u )sxzg3lof 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel acq3 +v)bv80np jn 3daip0ibc3 ycelerates uniformly about its center from 130 rpm to 280 rpm i +)p8y a3pvni3ijqbndv 3 cb00n 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 radiu md8iymt.n k3f;; *czws $R_1$ 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 thehy cuac)4al41mselves 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 as4 ) u14chaycla 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 resdhuil b8k) 1b zje*)o5vt9tdumd2(h 1 t to 15,000 rpm in 220 s. Through how many revolutions did it turn ij8u(evd dbo*5b 9uzh2t1kd l1))tm hin this time?    $rev$

  An automobile engine slows down fromxdim6 .az(k8e 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 highs)hkv,,u) g iv:l-cms2b,urll peed jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed. vlui:chu,l2vr- )sl,k,mb)g
(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 r+.0/pm7r izdqvt o+b to 360 rpm in 6.5 s. How far will a point onoti++q zm70pr.brvd / the edge of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turns 1500 reqrz+xmuqs. ;.l1;w-/ ovxxbme (vj2lvolutions before it comes to a r(l-1;/2 w+;xx.um. vmqsozjb vlexqstop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unirg aia/d 8sd,,formly from 95km/h ,da/d8a,i gs rto 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 revolutions as the w hgbrr/57 h9 gc/-glsd-zr; zcar reduces its speed uniformly from 95km/h to 45km/h Tgs9 d-hw5zrrzh/b ;gg/c-7r lhe tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight gc:k rqdj t/5,on each pedal when climbing a hill. The pedals rotateg:/ dq5r,kj tc 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 dod l6u1040,gc)ydjf)on gse ya s 6ctj+or 74 cm wide. What is the magnitude of the torque if the force is0gdyt 6l+c oy14uadjs)scj)n0 feg6, exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown j lhe-3m *a/ecin Fig. 8–39. Assume that a frictionc* e/j-3elmah 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 rti 5olgvvza) m j u2z.y/x 7+dn;g+x0ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released iv.zjny5oxlr+ g; ag )2tuv/z0 x+m7d. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder head of an engine require tightel)uqhrsh6 w(: ning to a torque of 38wl)h(:6hsur q $m \cdot N$ 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 9 eg2,wja d/3oz yaw3)y t.xmusphere of radius 0.648 m when the axis of rotation is through its ce.jaw)o32 t9yema x/ zdu3 ygw,nter.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7nx7k dc2yw: 9v cm in diameter. The rim and tire have a co729:nxdckw y vmbined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, lighqknlc 6 .la/o3t rod is rotated in a horizontal circle of radius 1.2/l.o cn3kl qa6 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 constaob2cu39udqn; 2vm;0 mtk uw9znt angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N ;2mbkn2mu 0uzqtd3;o c w9v9utotal.
(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 wa+in(mmp:mp j n+(9 zof inertia of the array of point objects shown in Fig. 8–439p +:jmz m(aimn (+wpn 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 consx/8f76*i80e. grddoj 3eo ofcy wk1tkists 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 cz 0z utht zhkif,o x3,6c3r7s*orrect 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 required steady force of each rocket if the satellite is to reach 32 rpm in zuifrz7 6 ,3z0x3sk * htto,hc5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 8.50 cm and a mass of v(v/p jvor-rzq rpn7k/( 5uz )0.580 kg. Calcul(v/r-jvo r(/n pkrpu5 v)zz 7qate
(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, accelerat9qcrzkw -apfv2n,7 ,ding 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 s1t+b:4dlxmi a mall hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two chilix4dm+a:1t b ldren (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 off and is event1+ ;a ttf)oh;4kltgfoyy .be, ually brought uniform g t ,.ltt oo;ye)bak+;4ffyh1ly 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. 8–45 accelerates a 3.6-kg ball at 23b .(x(i b+xfclhr9l dyqq(g7 $m/s^2$ 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 tanm3c mfpi4.1sdx;f.)) gfx ehrown solely by the action of the forearm, which rotates about the elbow joint under the action of the d;m)e 3pi x g4fafcx.1sn.f)m 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 con;h6x0bdauwnhg2yq1(jpw c da;9uv w7hp9;j.sidered a long thin rod, as shown in Fig. 8–46p;w2cdj9p uu6 b h7w0n ;hagw( qvjxa1.;ydh9.
(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 masses, mr-j15uz+, uvg igi0 g$m_1$ 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 four full qd.*p6 q .0 k8mu3 cnghmmm1xf/kys y8turns (revolutions) and releases it at a speedmq f..hd km6gpm u31 m8*qyncxy0k/s8 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 ofj 5m-8p+fclz0z yhqj.b ;z4f e $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a torqk,e g,k dkgc57x )mu,sue 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 wg05 r1azi-pzl ithout slipping down a lane at 1 air lp-5z0zg3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as thef ;0m v44il9nrfw0w3mj z fnm7 sum of two terms,f4m04;0fwv z97wnrmf i jmln3
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a rt+b33q7d ndi padius 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? Assume it is dt 7pqn3+id 3ba solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest asoc5kp*m, a s9nd rolls without slipping down a 30.0 ss*,cp5mok9 a$^{\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 stapjsdph; 7t1 bdm9ck1b,rj+d4 rts to fall and its lower end does not slip. What will be the speed of the upper end of the pole ju,k j+b drb4thmc 1;7s9d1pjpdst before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kwa)l8a r-ej7h7 h4hprg ball rotating on the end of a thin string in a circle of radius 1.10 mweh lh8r)4raj7h -7 pa at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular xzze j/8ytsuc,h x+)0momentum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm jz)hu y0s,/t+xz8excwhen 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 that is rotating at a rah q3f7ur3ig aiqxo :/0fj 4v)ete of 1.3rev/s If he raises his arms to a hoirqx4o3 f g )7/eiqh:uaj03vfrizontal 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.0(z6zxa)y0a, fc wddy 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing f,wyfaz (c 0ydd0x )6zarom 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 .(vlsxh- ohq7 from an initial rate of 1.0 . 7s xhlo-vqh(rev 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 ropsyom hy+6h hc2x; k-3tating around 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 radius 8.0 cm, ontox+ycys kh-2;h p3hm6 o 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 fig mhw:/k6-d4yy +qy cyanj*,tfure 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 pita- /w 1sgmpudu8 l107;z zethe 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 y.bemef:tb76l ;edg 3of moment of inertia I is dropped onto an identica:fml76 . ;eb eygdbet3l 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 fwhs4 nmyso o z8l(3q0j9q-g 5at 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 c neifhfl:qy45 wr-uj5 x 67b3nenter of a rotating merry-go-round platform of radius 3.0 m-i5 7 n3y4lhf 5u6qw :jebnfrx 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 rotatin 3n m,nsdj9q6jg freely with an angular velocity of 0.8qs936j,m jdnn $rad/s$ 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 col9guu7 qh .wfko2,)gzuzalx ym.yh, ;)lapses into a white dwarf, losing about half its mass in the process, and winding up with a radiusyu7l,.9 ahq2 mo yu);kx. zhuw)gz,fg 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 involvpa q.a ctp.n88kn6yv 0e winds in excess of 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass 2*qzh yzpy0-m$ 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, e :0x,-bthek zfd)ln.that can rotate freely without friction. The mom-f:nk .,htdl) ee0zxbent 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 d(0 -gou 5je,ekslnb*stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearoj0 5 ,ee*n-lgb dus(kings 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 ground with the end of the rope lying on th uu4 9lbo3 wco/iqxfg8.8amyug 7/:pqe-v5vwe top edge of the spool. A person grabs the end of the rope and walks a distance L,/oqe/quv8.wci b: u4 f8-5u lgog 9mypx3av7w 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 samexb8-yskx. el 6bsdx;( ,c ix5m side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular mssx6yexbl d,8 .ix k(- ;cbx5momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a )vsn*yenuepl xl85 33 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 cylinder of radius 0.20 m acft:skne:p k*z*+nm j7f8a 2oequires a rotational rate of from rest over a 6.0-s interval at c7 2k8mnt ofn:*ap*z+ :feske jonstant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, ejmws)h7t ,+cjqf-n l ly :hnr)d-2w+ kach of mass 0.050 kg and diameter 0.075 m, joined by a (concentric)-qsl)7jn)-:c yh j++fm, kh nrlww 2td 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 angular speed of the rear wheeu1q es9x phr4)l ($\omega_R$) 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 ixpw 9h7 ml8hy7 w7in)mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational coll7 hyl9m78ww7h nx)iip apse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pol 4zvo *tbpq0jaez,2-slution automobile is for it to use energy stored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kj0z, 4psb*zqt-aove 2 g, 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 ano ;3 + drbi3jbq4atp)b $H_2O$ 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 speedz7drsyj fe9 ufq8),sk + rk-.h 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 c8:n rhcky1/q +. d*uug3hc ywvan 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 thyw v +ndcu.:h1/q8* 3ykgu crhe moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor, 3kzpr : 7 0osv0lk*m4nb5jljrand we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step has height h jo00k :3 r lnjlp*rsvm4b5kz7, where h

  A bicyclist traveling wieio q6rvw)o(c y5va/m 3n8. e9rskf6pth speed v=4.2m/s on a flat road is making a turn with a radius The forces acting on the cyclefky/6(6a p8ovm)r 5o ieqr 93 s.wnvcist 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 nd w2+/mxhid(hpgmx4 zd6 *cw ff)87p1.5 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 5.0 s. What is the torque requiredp/fx 4x6w+8 z)dd*nmi cg dh(mf7whp2 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 as thinvv ninav3:l.l:) r g8e 3ehw1p rods, making reasonable estimates for the dimensions. Then calcl3na3vvi) p :gr8. : ee1nwlhvulate 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 cldp t)y ybarbz2-6g *9lqd):kuutch assembly which consists of two cylindrical plates, of mdz t 9l*qa b6:p2) kryguyd)-bass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 t9ks;91 u ga/e04i drbb o0l4bq3semtphe looped rough track of Fig. 8–58. What is the minimum a 9lb 4d 4qr butg1esk;msi o0p90eb/3value 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 not assume o1kev2b)b,ij kotl 1-$r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as thea u;h6a3 5gycwrm-( ry car reduces its speed uniformly from 90km/h to 60km/h The tires have a diameter of mcwy-r3a6g (hruya5;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