A bicycle odometer (wh8jkw j:0r)njgfy6 i/q ich measures distance traveled) is attached near the wheel hub and is ikq60jygf:wr)n/ j 8jdesigned for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. er 2:doye-x9 ahj,iy wn m7;1cDoes a point on the rim have radial r97j: ywy;1ae dc x2hm,ei on-and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential acceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single valu1nykj0f()36x5m e(fe/dne o ilujgx 7e of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a j07pw i9vp +5gcbzm:r 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 difficulr/q gzkh: v;3 +ug*l4f sw2puut to do a sit-up with your hands behind your head than when your arms are strev sk:uug f/4q2u*+l;g 3w przhtched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle hw2 ourdk+mk9)9xa(kp z6;xr tas seven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harwk2ora; 6dmpzrt+ux x( k9k)9 der to pedal, a small rear 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 run9xk 0ug( ibk-q fast have slender lower legs with flesh and muscle concentrated high, close g(bxq ki09-ku 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)mo vg8+h cwyq gz5 ms8splx-k0 qa 4ad/3zb:0, narrow beam?

If the net force on a systj) s :* puf.9.4h5varyvfz lemem is zero, is the net torque also zero? If the net torque on a sz : f5vu r4.jpy.9vfal*h sem)ystem is zero, is the net force zero?

Two inclines have the same height but cph*ql (nq5ez(d p :m;make different angles with the horizontal. The same qn5dp ch(zp* ; :qmle(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 simultaneously start rolling (from rest) down an h+:f(iy kuf wi1vc83l 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 gre l3ufy1i iw:(h8+fkcv ater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start from gk 53(jo1fc:lwr ;/) wgccgvzmrn2q+rest at the top of :nz (l 3rgo/w 5 wcq1rmk;g+2vjgf)ccan 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. Yet most movin45j vcrdaw1 u;j0ap:yg or rotating objects eventually slow down and stoayj cwvr4 ad50p;ju :1p. Explain.

If there were a great migration of people toward the Earth’s equatorg in*;k cxqb4e.6)pn b, how would this affect the length of e4 b*qnipg6xk c;). nbthe day?

Can the diver of Fig. 8–29 do a somersault without having any initialp/9jlsg1tnmaw-7 0cg rotation when 9p-j/wml17a 0s ggc tnshe leaves the board?

The moment of inertia of a rotating solid disk about an axis through its c2 92zukgx u*zrenter of92ru gxu2*zzk mass 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-kg mass in each out 2vsjtql.3a ,icj5cp 1stretched hand. If you suddenly drop the masses,j cp.2,q3 c5is talvj1 will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical and have -egxm b u5x) zmmxgj.-vg.r8+the same mass. However, one is hollow and the other is solid. Describe an experiment to det-r mg8x5g x)xmvg+m-eb .. jzuermine which is which.

The angular velocity of a wheel rotating on a horizontal gz)2vgkpct 5i* ngu 5b vc*h39axle points west. In what dirt)3nchvc5pz9vg*b5g*u kg i2 ection 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 eda l *wz(b)14)xqjta ziiw/po 5ge of a large freely rotating turntable. What happens if you walk toward the cj) iz )(z4xo/a 1lbtiww5*q apenter?

A shortstop may leap into the air to catch a balc:zwmh g7c o4p ;.mrj/l and throw it quickly. As he throws the pc7.m grm o;:4cz jhw/ball, the upper part of his body rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss ttp3i: v +m.v3up8w rcwhy a helicopter must have more than one rotor (or propeller). Discuss one or more ways the vrcmu33: .tp8t+pivw second propeller can operate to keep the helicopter stable.

  Express the following anpow/n)4v/kd(p.q,pc( vyt efgles in radians: (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 becausee ww74z 1p2 cm;y;qexd of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radiansc4 dz2;py1qme w wxe7;) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges9k3bq*m036ay 6o qxpfw bv(t l atb 6(*b 3 vloq9tkxfw3pm6qy 0a an angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender1 5 qc7lr+8 vgrl/:)erbfovxq rotate at a rate of 6500 rpm. When the motor is turned off during ope8qc 5 l7frrlvx/evq +go :rb)1ration, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to another child. If the ballrau2+ft x55ota+bc zv4ky6 .j makes 15.0 revolutions, what is its diameter? tajz ++. x5vatro2bc65 4yukf    m

  A bicycle with tires 68 cm ie3ww.htyx-n2 0g,yl w n diameter travels 8.0 km. How many revolutions do the wheels makeh ,.nxy0y3etw2-lgww ?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calcv9f.gydjcr(q.4 d xq 1ulate its angular velocity q4j vyc1.(d9 qx grdf.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. e5 *ieu-n(nzo4 hg6cb8–38). (a) What is the linear speuo -i4ehncgze5b6( n*ed 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 afe eg2aaby63 :round the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a point b b0jc5,4sx pm8z4j t. ivf7nt
(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 gep:2oo33r2;v c mhlr7.0 cm from the axis of rrm2g ;ovc :eoh3 prl32otation is to experience an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheelvz uc,3); ljt dyuj:q; accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Determi qu;,cu:3tjlj) yvzd;ne
(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 fxfs 1xno2bm k 5wj2-)$R_1$ 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 thejqyf i4.2 mfxg-wrb.6 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 tim.m xb.wj6- 2 fqy4gfrie interval. The spacecraft 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 ud(iaj2 z m. 1-ddexpc;qod j5 xf)o*f(niformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn i.zd 1emq ija -(*djxo(dpo;c f) 2x5dfn this time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 ryk-4 :payate 7pm 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 whirlin7j x2:fvkr3on0.qwz lg “human centrifuge,” which takes 1.3v0orqkw z:jl72 f.xn0 min to turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6 zo. ek+ -*szkiv*mv3b.5 s. How far will a point on the edge*bzsim 3 z kv+kv-o*.e of the wheel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It turn+ k8mnc*j6b n v/wvca0s 1500 revolutions bec/na vkj nwvb0m c*+68fore it comes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unit)(o h3imak.dbecg;g ,s2q: xformly from .qc:; axsmi dbk 3h(got 2g,e)95km/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 revolutions as the car reduces its speed uniformlyl,o /1m/c g0nwbm puy; from 95km/h to 45km/h The ti/cnm1 pg/uml ; wybo,0res 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 mu1og0n ;c yn/n,cebn5g, 3gfputs all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius u3neg,mfg/ny1nocbnc g5 0;, 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 8 7pef(jm*qpz/ *s6a,gw(p f)er bu gwa door 74 cm wide. What is the mag ws/7 p)upfrg ((paqbzefmgj8e* w 6,*nitude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheel shown in Fig. ix,/ f5lz6n7)gp - kmqrpj;uv8–39. Assume that k7pg )p/,r6x-zfj;5vui m nlqa friction 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 endst:b7gr+oyj y0 6xu-ld of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direcd0:u7g+6-rtoxyyj b ltion of the net torque on this system.

  The bolts on the cylinder head ty0jw5ni+bte*lng: a z ; 2fh7of an engine require tightening to a torque of 38 n: tz ag lnywh+;b* t5ie2jf07$m \cdot N$ 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 krd((1j//i6na8 o-xirsprd wf radius 0.648 m when the axis of rdrri-n(/a6( d/ ixj psorwk81otation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm .sq- ( c:(fwezssk4ly4ra4qd in diameter. The rim and e.(d4a: ryzfkl-sqcsq 44ws(tire have a combined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram bal9jea4w, m6cx64ascn ml on the end of a thin, light rod is rotated in a horizontal circle of radius 1.2 m.cwmcesj 4a,6 69m4 anx 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 i4+h , (xj;ha 67bgo oxuyon:6qveh,cat constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N total. exyoo(;:n 7hoc4+hu h6j, ,6v abixqg
(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 inerti3em qw2;0 dbdtmk3 jl*a of the array of point objects shown in Fig. 8–43 32jbl30; d mdmqetkw*about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen atoms whose total mass ipsw 1ds3yi7u3z )d; eis $5.3 \times10^{ -26}$ 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 r ;e- cl:-xivvtate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite ha-x-vcei :;l vts a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius o7 ,21c kqy-q*+tri0lai olac mf 8.50 cm and a mass of 0.580yltk qa1 -rc*2c l oq+a7i,mi0 kg. Calculate
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swings a bat, accelerating i(bfk6v1wwsd; t from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merry-go-rg - 7z07r2 n7k2qqe os+xabgxu;1tdhpound and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each o2ah2rs q1k7gqbe-+pz;x 7ngt dou7x0ther 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 roy w gr:+3hds6 1lce ,lq6hn;lztating at 10,300 rpm is shut off and is eventually brought uni:,lhg erl +h1ly6 sq d3z6c;nwformly 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 accez78c cpd::khfdj 0 3adlerates 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 solelxu mj, ndw1cb )(3m.dxy by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is accele d)xmxndwu1 (bjc3,.mrated 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 m stnq g(7 b5(d)w.inerod, as shown in Fig. 8–46. 7isbq5nw d(() t.mnge
(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 mas 2bvy8i( vawq2ses, $m_1$ 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 turns .jlxw /uph-j 7kr))sb(revolutions) and releases it at .)bsx w r-uj7)kh/pj la 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 c1diy3), q c 5ne*b6.iyipdicof $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develops a kh +du kfv6)k ,g,dx(ytorque 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 anqdl-j68 f/ dvgd radius 9.0 cm rolls without slipping down a lane at /q6dj gvf-8dl3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun yxfgj6 qbsmg c2d6nc;3nmn 6 nx28u84as the sum of two c cmdgsxnqgnnyfn26648 3mxb u2j 68 ;terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.5vdr:eza 4u( p10 m. How much net work iz:d u41(rpav es required to accelerate 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 k9z x/ hb*v:wruq0g) mcm and mass 1.80 kg starts from rest and rolls without slipping down a 30.0 g w9brh:)v*x kqm/zu0 $^{\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 bala1 guj fu;q7,zonced vertically on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upp,gqozj uf ;u71er end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end ofi4seq6t3f jx n9+tpz09w bg h2 a thin string in a circle of radius 1.10 m atqx69wp ef2nb4 itt9zj3h g s+0 an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momtgv7*k /ywzu9iijj42s ;,pjm entum of a 2.8-kg uniform cylindrical grinding wheel of radius 18 cm when rotat ;j,w4 spvijkuyz/g7 9*2mti jing 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, tc 1. clo:,argwt r.7eon a platform that is rotating at a rate of 1.3rev/s If he raises hotce,. rt 1clra.w g:7is 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 ruw4paxq9kj 4n / +1uw: fiuo04 romm5keduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tuck posiko9mw/ija1w 5 +upxu ku:o440n q m4frtion. 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 spi po a2y 6 k.nu.23agp,dnu,tfyn rotation rate from an initial rate of 1.0 tp aag2 n.p,k yuo und62y.3f,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 rotating around a vertica c-9+jvidcc( nl 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. Th9cidj-n (c+ vce potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angular momentum of a figure skater spiyahp ./md de7a /2pa+onning 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 Earth 3u vq m:x+aci:
(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 in(ee4gl 3tbw fdn-lt 9 :t10zts dropped onto an identict get4bfe0nt lntd1w:3z9l (-al 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 at ig zk 8cid3w-, *,cc9sfduy.g2.4 $rev/s$ 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 rotavfyq9 1za3 j+hting merry-go-round platform of radius 3.0 m and moment of inea 9+1zyf3vhjq rtia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular veloci9vveme28 j ldlw86vnn 2u*kq*ty of 0.l*e2n6 q2vl8 jvndukewv8 m9 *8 $rad/s$ 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 aboutiy uw-00e -6k:dr1et0bd d nei half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the los:i kdy i0ebd1 d-nrw ueet0-60t 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 pw yneh3;d*f5+e4dm/nd a 8ltwinds 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 msvm o4 9ywaoi/2pa;-$ 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 withonh t2h1uj);vd:s,zc o ut fo;v1 n,sjthuz:c h2 d)riction. 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 diameterx*x6em zptz1bu f ofh)5k-k 9; merry-go-round turntable that is mounted on1h bzfx 6*k5-mktp fxuoz;)9 e frictionless 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 ground with t-8qqv-mz0txk9ewsp sd5d2i ;i-0plz he 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 rope unwinds from the spool? How far does the spoow-d8p mk0et-zssdl9 20iqi;qp vxz-5l’s center of mass move?

  The Moon orbits the Earth such that the same mjdb 6qyh:1ses 9qhwa (k ;ir3-w68gaside 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 Mod swqhky:98ra- mea 13 ;qj6swi gb(h6on as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at ajpg y:(k7n2 6he 8rj+b-eivq7cpm;ei 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 cylin mf:sc,ma2ut32f(d y vder of radius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleraa(,v23 umm tdfc:y2 sftion. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0l unj0g4h acdq ,81o,v.050 kg and diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mass 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0gah4vd u0,n, oc1l8qj-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 tq 6 *z6eb+b ;niwnswf*y;t8,pfigyv:he 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 mao/rkl xk*g2 -:/ ws n3kvocvx3ss 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neuxrvk/*gol3 cs 3v okwx- k2n/:tron 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-pollut9kuv ufb;4 eu:+ldr /sion automobile is for it to use energy stored in a heavy rotating flywhrud v:uflb4/s +;eu 9keel. Suppose such a car has a total mass of 1400 kg, uses a uniform cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustratesl3x an6 1qe:dy 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 surface at speed v=3.3xvn90djr3* ll;(bd a a;i1boc $m/s$ 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 lengto x2 )fdh8ufe.h 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 angular acceleration of theof)8e.h2f xdu 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 vertico,v0vw io20 foally on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55,wf oi 0v2ovo0). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is makingwu3qt) /oc0b - kpfvk* a turn with a radius The forces acting on the cyclist and cycle aftqk)p*-kv03 bouc/ wre 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 it)ezf0f.u .n rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest fi .ntu )ez0.fto 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 solid cylin4a+y9a6naxnzc t 7 ay*der and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater wi6aa 74a nx+n9cy azy*tth outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two cylinxl*ywmm9w8 l6s;o um 7drical plates, of mamm;w6um7swolx ly8*9 ss $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 an5(j:-pe-x7rzoqqhjg n ;fd*od radius r rolls along the looped rough track of Fig. 8–58. What is the mj* :ezxj;opg hqf5(odq- n-r7inimum value 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 ib)t+ ftwm*y(0r. t;0;vkoel*a umxe not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces its speed unif/fmm ejj m-9-aormly from 90km/h to 60km/h The tires have a diameter of 0.90 m. (a) What was the angular a- j aef/mm9j-mcceleration 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