A bicycle odometer (which measures di;k)1z jdgca e 8+i3pyhstance traveled) is attached near the wheel hub and is designed for 27-in da+ icz)3;8 hj1peygkch wheels. What happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant av891gqzid+h8 h:ziv xngular 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 whziixh: d 8 zg8vq9+vh1ich cases would the magnitude of either component of linear acceleration change?

Could a nonrigid bodyrx avc 6 :oa29ydf5e3a be described by a single value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque than a larger force? Explain.s4 u0p8bwblo ,

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 qogj/ssv5ibk/ps ( 02-up with your hands behind your head than when your ar(2vq s/j5i g ss/0okpbms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has sene su90yf :sypb 7.h+mven sprockets at the rear wheel and three at the pedal cranksf9.7u bn m0+:ssypyh e. In which gear is it harder 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 abzo ,6sca-4)u lgutjc9le to run fast have slender lower legs with flesh a za4oc9 6u)uct-, gsjlnd muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carryjnkrzy26fr5j*w a z66 a long, narrow beam?

If the net force on a system is zero, is the net torque also zerodb n+k.y0w*su ? If the net torq.nwb0+ du kys*ue on a system is zero, is the net force zero?

Two inclines have the same height but make differ otu n8cc9gg;-p7p, u)lkcveg -yg -;lpp5h6 jent angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the spep y7geug-jhv8 cp6 -lgnc9 5uc ptk- ;g)po,l;ed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneously start rolling (from rest) do-oyna2emhv 5kcb1.b 7 wn an incline. One sphere has twice the reyb-ov2a7n.h m5 bkc 1adius 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 x+z3 v+t/1c09u:zhpkia qy gcradius and the same mass. They start from rest at the top of an incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the gre3c ch kpyvq g0:+/i9 zt1z+axuater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving or 1 bqo afj1q j*t*ysn v5poybf14628u:x ga 3fsrotating objects ev gj4y1:uqv*8b s2xn1 of*apyfs536a o fbq1jt entually slow down and stop. Explain.

If there were a great migration of pb4gt ,lony sv pq0*hsc44k8n cw015eheople toward the Earth’s equator, how would this affect thlh, 054yn1spg vwh4oct40c bq* ekns 8e length of the day?

Can the diver of Fig. 8–29 do a somersault without gi t 9;3:gdb8r:hyv7nihlp7v5 uyl l2having any initial rotation whedy g t p7rbvyl:7li iu3:h2h;9gv5nl8n she leaves the board?

The moment of inertia of a rotatt:te3ev7krtr itj* fyqb: ) /5ing solid disk about an axis through its center ofet3yrrj:5t :t)i */k b7f qvte 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 sspq r.r44v4oa8c4rwstool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, will your angular vesc48r qs4 .or4wpr4valocity increase, decrease, or stay the same? Explain.

Two spheres look identical anw f;)gh.0u y- k5/xtir x4s -,kkvrfscd have the same mass. However, one is hollow and the other is) hukr;tr-w0kfsyk gs.5cf,/-x x4 iv solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating on a horizontal axle poin(bnc)1 xnfsz*6 vy f*lts west. In what direction is the linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angularb)fx*y*zcl(s 6fn 1nv speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotating turntable. What0fc, y7brx ci18g+tnf happens if you walk toward th0t+nfg7yr,b1c f i8 xce center?

A shortstop may leap into the air to cabn;9t3t f8vn -e5i geltch 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 (F;lvni9 t g-3et5ebnf8ig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a helixa8e61 lm2 bu*( xrxzdcopter must have more than one rotor (or propeller). Discuss one or more ways the second propeze8(lu*r6 x2x1mbdxaller can operate to keep the helicopter stable.

  Express the following angles in rz*lp zfwd,0r (adians: (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 co4.sm4qosuvw* incidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Moon, as ssw qs4m*o4uv.een on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, hi *regsf nt56, ;)mgf380,000 km from Earth. The beam diverges at an angle 5r6hgi)ft nfg sem,;*$\theta$ (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 k9iemk5z5xv ,b ,+rb y. (zril kfj7z*at a rate of 6500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is the angular rx, y lze55kvbj z.k , kirb9(m+7fi*zacceleration 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 baq3 v:ka.e x tsyu-p0v:ll makes 15.0 revolutions, what is its diameaypev x stkq.0-u:: 3vter?    m

  A bicycle with tires 68 cm in diameter d(mgn0ai i l251azno- travels 8.0 km. How many revolutions do the wheels make?gdl5za (2in0oma ni- 1    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its ang--nk+ :;wpqmx+n fwhi ular velocipn:w+ nmi+kw -fxq h-;ty 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 makes1v3obf 8e 7k m3o2bo+fl(qqgq one complete revolution in 4.0 s (Fig. 8–38). (a) What is the linear speed of a child seated 1.2 m from t+lqo8e b3mv7q(gq23 fo1bko fhe 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) i/dhm3a + jxgq:n its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of a poin(scg:- kwkkb, t
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a centrifuge rotate if a particle 7.0 cm from b52fcjpbmy3 , the axis of rotation is to experience5 2bf,3 ycjpmb an acceleration of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheeq1 euwnu.9ybw7w; 0ty l accelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 suten w17yqw;b.9w0u y . 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:o;-rvne5 ndtrj wvh(hg04o9f*0 ohbs $R_1$ 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 pua/6os0plb2n dk1zi j3t themselves intskn1b6j/ al 0i3p z2doo 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. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformly from rest to 15gl u -5md w:4u:lp5m q,8fsosj,000 rpm in 220 s. Through how many revolutions l:fu psw 8sj:5u-l5 qg,4md modid it turn in this time?    $rev$

  An automobile engine sx(bk xw6*va s.lows down from 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 highspeedgj zx 98apr5d) jets in a whirling “human centrifuge,” which takes 1.0 min to turn through 20 cj5axz pg8 )r9domplete 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 fr 7trorjy, ox (toklf.oh(lq.,a c.n71om 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the w.l roth.a nxol7y f,o1kq(o.j( rt7 c,heel have traveled in this time?    m

  A cooling fan is turned off when it is running at 850rev/min It t:x )*f*jddq/qu ii4q iurns 1500 revolutions before it comes 4*/dq:j* iui ) fqdxiqto 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 6 0l0)tn zm9sky5 revolutions as the car reduces its speed uniformly from 95km/h to 45km/h The tis 9ztl0ym) 0knres 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:ym9 2y blj 406jazyuj as the car reduces its speed uniformly from 94bmy:9 j2juyzy6aj0l5km/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all ,v :wurtyl,qzw; 5 rrz1-e kz6her weight on each pedal when climbing a hill. The pedals rotate in a circle of ;-y: v zz1rweu65k tw,lrq,zrradius 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 ;r3dgvmzuivr6q -:gr9l zu)wj, zp +.a door 74 cm wide. What is the magnitude of the torque if tu +u)zmvrz i, rv gplrg.-6qd:3w9z;j he 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 h+mgg)h ch qkln8/v,m7 hru56)px/*qq xb7 toof the wheel shown in Fig. 8–39. Assume that a fricthqhht* kvm r )qpxxlng u6m7bq785 h,/+g /o)cion 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 ena5f+3zo 7pqn ;d xj(n.gzsil 4ds of a massless rod which pivoiz nf(qsj. gop nxz7; a+l4d53ts as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calculate the magnitude and direction of the net torque on this system.

  The bolts on the cylinder ;fzk/fojuuw uny7170 head of an engine require tightening to a torque of 38nuf/y; u w1u0oj7 f7kz $m \cdot N$ 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.u)y2 as4 r zw1kya5f9h8-kg sphere of radius 0.648 m when the a)29 ar1z5ws y4huayfk xis of rotation is through its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel 66.7 cm in diameter. T bq6am:3 s+kjiq:s+y nhe rim and tire have a combined mass of 1.25 kg. The mass of the hub can be ignored sq3 jks nm i:ay++qb6:(why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin( vovlj10e b,j, light rod is rotated in a horizontal circle of radiu,bovlj 1e(jv0s 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowlz m-vdwx i- cy(m/q)2n on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The fzvmn-2q)w y m/c id(-xriction force 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 inertiact /df7b: v 9pud3ycy5 of the array of point objects shown in Fig. 8–43bd7u ycv: tpf59c3yd/ 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 s r.pj(rtpzm3p 7e1 )cwhose 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 th m1u-6 t bfmxk(sdj3ej/ ,g8gaod9p7 ke correct rate, engineers fire fourf xk1jb(e-us3 mtg ad98d6/kog7, mp j 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 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder withh- 3dszzs 3s0r a radius of 8.50 cm and a mass of 0.580 kg. Calcds03sz -s rz3hulate
(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 it from resd/* ly mp(t :bgi, mimc/s)(fkt 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 tang6izs i )b g*wuym31kn-entially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpzi-n 1s*ui mwy6kb3)g m 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 shuec shf5t b7rm4b* :csf )ixk-/t off and is eventually brought uniformly to rest by a frictional to)s5 h*ctes7kmicx/f rb4 bf- :rque 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 3.6if*ux* se-bst1kkc( x3g8y j* -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 throfox6fv5h c.( z5 rwr6nwn solely 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 accelerated uniformly from rest tr6x vh fo. rwz6nf5(c5o 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 conspebw3v3oqx;b kq- ;4s idered a long thin rod, as shown in Fig. 8–46eb3;4 kwp3ovb ;-sq xq.
(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,2qp8j u twj 5no8u2bc, $m_1$ 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 fehr6lzlk8u2 6our full turns (revolutions) and releases itr ulehz26k 8l6 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 (hw;z*1wr4 ggl/ j5y 8y1p6e3b bacuxi2pp ghmoment of inertia of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine d5(l2v6 ;lemqafv)q s pevelops 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 rollstqz1l)y3 bffds b:u+io+n,/ e without slipping down a lane at 3b++ifdo zq:)e, bs 1yn ult3f/.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sufc4x g0su5 /ofm of two terms,x4s0 5cfufg /o
(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 7.7h vct. j pv)i4g4x8l5wiap (b50 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 a solidia8hjcv4(xp.)gil tp7 v wb4 5 cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg s3/a:25 bre0c1j(ktsnugl1eoa4s k w ctarts from rest and rolls without slipping downulo(ss1cg4 51cjaakk0:ene r2b tw 3/ 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 vertic ovv,5-2/ 9 f2icveusaq4zlh cally on its tip. It starts to fall and its lower end does not slip. What will be the speed of the upper end of the pole just before it hits the ground? [H92oqv ah v-4 cvezuli ,f2s/c5int: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rt 5u4 ah.0o /njwd*wbjotating on the end of a thin string in .54j hb/wwj nto0uad *a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-d+nt,fp-k io- kg uniform cylindrical grinding wheel dp- -fk,tn+ioof radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, han2a x /ny)m5v uiun-x7mds at his side, on a platform that is rotating at a rate of 1.3rev/s If he raises his arms to a horizontal pos/2m 5u7iu max )-nyvnxition, 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 kr (f(rn sm6siw5tt(8one shown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from the straight position to the tu(wsfm t(8rski6t (r5nck 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 incr1it e. g-jb64v5j2:wcb wc xujease her spin rotation rate from an initial rate of 1.0 rev every 2.0 s to a final ravbceww xtuj5j 1 bcj- i:.g624te of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rotating around a vertical axis through its center at z/ frq zd6t59 e8 arrm3rdw/-tttn)j-ha*e) ka 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 shapq/5r zt j)tr n/*mw t8hak3 tar-)z-df6e r9eded 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 momyb:y6terxe8s 2w- ye +entum 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 momentsd o/p1w xo gkj8r*va78 z1cy.um of the Earth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is dropped onti + vv/cawnwy:o)i/(uo an identicwvi w/ )(:iyaonc/uv+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*kdf*bjxkzq fr0m/ a*n,q1e: at 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 ;acp *wa. r6dxcenter of a rotating merry-go-round platform of radius 3.0 m and momenxd*r a ca;pw6.t 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 with an av12r wew fs)bc)i-;lz)b(mvt ngular velocity of 0.8 )b2z( s- t)1rlwm w ivc;evb)f$rad/s$ 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 dwar(w92g.t;b ;se 0x8fjl qlbfka f, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carf.f tk8 ;b9wl lb0q2g je(;asxries away no angular momentum, what would the Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 1r)gdyib mob* s6tgo+1h -hx6120 $km/h$ 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 v grn.7qu wj.35cxbo;$ 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, nuw)v zi xdw l4,eex z)+-5u:kinitially at rest, that can rotate freely without fricvne :ix, )zulud+4zx5 ww)ke- tion. 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 s3h3wm,kufnoz r)+o :zk 5cok usg*1m-z91uwof a 6.5-m diameter merry-go-round turntable that is mounted on frictionless k1s) w uzhums3wok+umrk5f :1o*z- ,3gnczo 9bearings 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 r ite*qj5:ihn 1olls on the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and wqnh1 ti* e:j5ialks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces the Earth. Determ0u8qvk dzy40 zine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, trkzy 0d v84uzq0eat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from restsif l1p hw1zfyq.5/e 3l(dz f) 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 in the shape of a uniform cylinder of radp+2 g*-ppzr j; h(nynmius 0.20 m acquires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the n *+ jhzpn(p ;gm2r-yptorque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.0f*s p j5d 9jw,k/nrg *ixn-mq(50 kg and diameter 0.075 m, joined by a9qn,*/spj ig*dm5w rkj-( n xf (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 1.0-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 sp 7t,ijbfg js. m:bks(1 5sp3lfeed 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, were r op,he6 fi2f2aotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravita6e,op fa2i2fhtional 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 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-hd.yo8- bwsf.pollution automobile is for it to use energy stored in a heavydsh - f..woby8 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 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 an tf3ysfdz( x+gvzbd (7.8: szv $H_2O$ 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 horizon+zme* b:pj cyz+31 oqk+zg 8yetal surface at speed v=3.3 $m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of massfn/o i(qi +z: o))a9vh8demdk M and length L can pivot freely (i.e., we ignore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of gravity actfdqo( z/:k8 )9me)vd honii+as 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 m36mtp md sixdlu,0wn 7o 3r 6v:(bwj2the 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). The step has hitp 6jr6dvb d3m7s(:x0m3 nwl,u2 owmeight h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat va7p3g3g xxm;road is making a turn with a radius The forces acting 33xg;gmv7pax 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 e4a0o4yo(ed gjh8s:2s kvj0b length 1.5 m and begins whirling the rock in a nearly horizontal circle abov od4ghyjevs:0j0bo2 s8a(e k4e his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque required to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder and herau3o.5n9b7gb0kfq id0kwpf1 (vr x*y g a5v0q arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched a0dak gv.qn gu(i 9xr73 5wya1 k0 bf*05qvpbforms, and with arms held tightly against her body.   

  You are designing a clutch asse gvmwmeo*/.7j s r c:wrfex,/+mbly which consists of two cylindrical plates, of m.w ,f+r mx:/er om /w*ecvgs7jass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 r2jwj hpmj--t.vp i+s6adius r rolls along the looped rough track of Fig. 8–58. 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.-2+jv ip hwj-jt p6sm the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but .o9,po* 2k s,v ,mjjvy -vjujiy3v t(cdo not assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduces m+jtht 12v8 iy f- fxnlt83c4nits speed uniformly from 90km/h to 60km/h Thh 8l2j+x-1n 4yvimtfcnt8 f3t e 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