A bicycle odometer (which measure a; v s8mnzah;m*hg0 cf:-rps7s distance traveled) is attached near the wheel hub and is designed for 27-inch wheels. What happenvnr7pz am: ag 8; ;h-fc*ssm0hs if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constant angular velocity. Does a point on the rimies8p5hu-x 1v have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential ach- vuips58 e1xceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value v )nxytqdr w 31-r(za,pi 4r hj/-l(qvof the angular velocity $\omega$ Explain.

Can a small force ever exertzaz125.siuk b: 5zmm)chv su2 a greater torque than 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 youjp mns4 3:-nsa9;mf jbr hands behind your head than when youns9ms3 p ab:4 j-jfm;nr arms are stretched out in front of you? A diagram may help you to answer this.

A 21-speed bicycle has seven sprockets at the rear whyzcc)t 9yhto: .u /lz2eel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In whiczy9)z lc:t yo/2.cuth h 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 haynzyok ru90 +ug0.c4a ve slender lower legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis o+kz9 4ac yon0g. uyu0rf rotational dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carry a longoff2 )kvla*o i w*,x1m, narrow beam?

If the net force on a system is zero, is the net torque also zerosvl8j,7 vgo dqa3at8 j/sy-+ w+p6a-j c0vcp a? If the net torque on a system c8 pj/6-acv+ d-7vs +jplgjo,a0swa3qay vt8is zero, is the net force zero?

Two inclines have the same height 7th8zli 0q6x mn/h8r0bujv f1 but make different angles with the horizontal. The h88x6fmh j 0l 1/rzvn0iqt ub7same 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 (4zol)t co:kk s64a09yb0xc m hfrom 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 sakbk s4096:c0x )tzlyh cmo4o peed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same ra+-y;tv;zk2 qvdhy;a4-ns xyfdius 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 greater rotational Kvsd2;nxtvh z + 4yay-fky;-q; E?

We claim that momentum and angular momentum are conserved. Yet7r1x +lvq)tky most moving or rotating objects eventually slow yxr+7) vkq1lt down and stop. Explain.

If there were a great migration of poo2xr0; y+hm4 2yilxv eople toward the Earth’s equator, how would this affect the ler2oomv yy ; 24x+h0lxingth of the day?

Can the diver of Fig. 8–29 do a somersault without having any initial rotatib1neze 2 xj13zon when she e321nx zebzj1leaves the board?

The moment of inertia x1 ,hy nlq.u9tof a rotating solid disk about an axis through its center of y ,t91xlq.nhumass 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 e ri;3*7jmpp v(x-ihr.xvi+ ry ach outstretched hand. If you suddenly drop the massesv -r3 pm ii+i.vxp(x*yrhr ;7j, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical an.+ vzo 5f ;ixscw4s hr-*d(npp)8iexld have the same mass. However, one is hollow and the other is solid. Describe an .)opsvp ix (ir ;sl e5n84+*h -cdxfwzexperiment to determine which is which.

The angular velocity of f) 0d e;opsc9dg1lh kn)e; 8dya wheel rotating 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 acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is thp) nly)0he do 81;sk dcfeg;9de angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rota8dq ecfy 510urting turntable. What happens if you walk fc0 r1qe dy85utoward the center?

A shortstop may leap into the air to ca3*ccoah .p bz7gd87 +v xqr, smen5*fwtch 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. 8–36). Explbc8*.3, mh fzxnd5 a +*qgrwsp7ovce7 ain.

On the basis of the 1b uypzauk: r.pl6/s;law of conservation of angular momentum, discuss why a helicopter r szp ;/ 6puka1byl.:umust have more than one rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radians:i 9;hz7jsqb u 729+bmftanz)zy6r- d m (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 becau tcw qj:qgm7o+a2 ,+klse of an amazing coincidence. Calculate, using the information inside the Front Cover, th+,q7oa m2:qtjg cl wk+e angular diameters (in radians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directe9,7ojo fsf7 gd mp*;tvd at the Moon, 380,000 km from Earth. The beam diverges attos jpm;of9vf * 7d7,g 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 blender rotate at a rate of w*0b u 0bersc46500 rpm. When the motor is turned off during operation, the blades slow to rest in 3.0 s. What is t0bw4c 0u rb*eshe 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 thm( bm/ izy;en(e ball makes 15.0 revolutions, what /(i; nemymz( bis its diameter?    m

  A bicycle with tires 68 c2o/y vpa (nuk4m in diameter travels 8.0 km. How many revolutions do the wheels m p(kovn2/4ayuake?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates 5/be.gtkuh*8,xac 3 wcvxj4 c ecy7d) at 2500 rpm. Calculate its angula5.bc/w8yg, ahk*xv)x4e7 u jctc 3dcer velocity 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;q zyn/p g-r3h makes one complete revolution in 4.0 s (Fig. 8–38). (a) W;hzqyr-g3/pn hat is the linear speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit around thrb4o;rvcd8 r)a0gg a9e Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed of anaq j,4m(t8nofdc5+a-2e z ta 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 roujk8 ;:6dy;u :zp4kd kw 1yah*ydge -htate if a particle 7.0 cm from the axis of rotation is to experience an acceleraw :ddyj;h46hude:kzypa1*kk- 8u gy ;tion of 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates uniformly about its center from 1 wpk/huhsd,wm7 q20/xgul, ;i 30 rpm to 280 rpm in 4hux2kmpq w/is 0uhwdg7,;/,l .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/zz rl,t ,t 7wxtc-5n)gwikh /s $R_1$ 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 37uhfw rvfh;0Moon, astronauts aboard the Apollo spacecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they af h0hwf7v 3u;rccelerated 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 rw(v+-ga-ium atm9get* 1yc51l o elg *est to 15,000 rpm in 220 s. Through how many revolutions di+g1 u9oy-tel a ig5tamwc**ml( e-g1vd it turn in this time?    $rev$

  An automobile engine .h s6v,qcqti8zvp3 1bslows 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 highspeed jets in a whfbi vtg)(mvg9h x/m;e 3;pe)hirling “human centrifuge,” which takes 1.0 ;/ b)ximpg)efevv t9h3hg ;(mmin 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 un 8b)yusv(wls-;y6b g uiformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the b86 wubv ( -ss;)ulygywheel have traveled in this time?    m

  A cooling fan is turned off webh*i n,auv++ hz3xi.hen it is running at 850rev/min It turns 1500 revolutions before it cova3n+eiziux. bh+h* ,mes 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 redz- 5bji.gsqe 9uces its speed uniformly from 95km/h to 45km/h g5qbe.j-z9 s iThe 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 revolut :h deqncr )6l9ci(e*v lz9gn/ions as the car reduces its speed uniformly from 95km/h to 45km/h The tires have a ddg/hr9cli(nev) q9 :6el *nzc iameter 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 hggp5wq ;b;s) uer weight on each pedal when climbing a hill. The ped 5g)g spuwb;q;als rotate 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 4g* w, m0ycapx7cf0ie55 N on the end of a door 74 cm wide. What is the magnitude of w c0 xic4gp7m,eay f*0the 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.caabfvc05fhd yk )ix3k +28y, 8–39. Assume thatxf)8avhca3ky05,i +2y fcdbk a friction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass mh4b/msxh6k. .oxzxdq/.5s h m, are attached to the ends 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 direction of the net torque on h xod/x q6hz/sm.x4.h s5mk.bthis system.

  The bolts on the cylinder head of an engine reqdf 4fqg lz;yj.*k(d*kuire tightening to a torque of 38.q4zldkfyd k*;g(j f* $m \cdot N$ 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 of radius 0.648 m wuca5o,k+taz xng56h0 hen the axis of rotation is through its centec,au5xh6 0tzkg+5 noa r.    $kg \cdot m^2$

  Calculate the moment ofdnehs7yklzrcu)w4v - ,2+g 7lwfu7w+ inertia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The may- n7+l7v w)ueghdu74 f,wsrlzw ck2 +ss of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, light rod is g i3o.fk -4crona kq,1rotated in a horizontal circle of radius 1.24 1r3k ,fk.qoa-icgo n m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on a potter’s wheel rotating at constant angular spes7m2 4)n (myuz1gqxcqed (Fig. 8–42). The friction force between hex(72quq mcmn)zs 1 yg4r 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 inerq/ 3zfx *z xzxh3acjk2 )q+-dptia of the array of point objects shown in Fig. 8–43 af xa3zd)*qc/qjkh xx+pz2 -3zbout
(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 to nz r016foxfr3tal 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 cylindricalh*2dyi /a8r+ rqk sea, satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kay/r i+q2rd8kshe *a, g 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 of 82n-rf ,epwh* s 2 ko ,n1:n)gttshhoq5.50 cm and a mass of 0.580 kg. C-pn ,n1nh o* tst5ehk2,h:wgf o2sq) ralculate
(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, accele; ,ese/qbas2p7c cox6rating 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 tangentialszc ajx2-4 cu6ly on a small 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 andx2au z jc-64cs 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 10,300p 0-5vel1phjv rpm is shut off and is eventually brought uniformly t5hvvpj le-01p o 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 acc9v(d 7;-o v dk2elllzfelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solely pf( 5oswuum 9584rlzhgy7q*lby the action of the forearm, which rot5puz5qf7s*llu h9m 8 g4r(ywoates about the elbow joint under the action of the 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 considered a long thin e l*kd,ryjwbl4:n5bsao sjhaz 360h;b:( z3n rod, as shown in Fig. 8–46. nel 43yb;z3:wd: k( sb j5,0noazj brhhlas6*
(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 mass 2s .m2m h/qb) 7hl*rdcqbgp7kes, $m_1$ 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 r 8i/dzfhdz4 ;tx8mc; uest within four full turns (revolutions) and reledm h u;4z8fzd8tcix /;ases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inert:9vftj 2qls eyiq-z ru,b + jmko,-b*8ia 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 dex ctx/h 31l(paj5 p07pjx z4avvelops a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radius 9.0 cm rolls without slipping down,zwgd8u:2ql i a lane at 3.3 wuid8 :g,zlq2 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as thpw1/b mw m04n3 odwc/gn7*jd,qs ;sl 7py2rkte sum of t74ro0 clg2kbdw;pwt7 , dsnpw mj1n3/qys*m /wo 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 radp;6qar lgv 6h,(4uz aaius of 7.50 m. How much net work is required to accelerate it from rest to a rotation rate of 1.00 revolution per 8.06az h4gu(;l,6rqva pa 0 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts from rest and rolls without 8bs5fyuk ;f u08yq.wh slipping down a 30.08yf. 0fskq h5u8 yw;bu $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip. It starts to faykvavzt -is +m-k29e5ll and its lower end doee5-iym+ vsz va9kkt2-s not slip. What will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momentum of a 0.210-kg ball rotating on the end of a thingvbl(umwhf: 5gx g)f /z34mv 9 string in a circle of radius 1.10 m4 h gxg:v/z53mb(lmv )9ff wgu at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular momentum of a 2.8-kg uniform cylindrical grindinruqt *5z(70cn wtq,hp-f;c hrg wheel of radius 18 cm when rotahfcuhqr ztt-,*7wqr p;c0n5 (ting 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 plabxc5zeze-sx7rkwb+: (w3z h )nd1my6tform that is rotating at a rate of 1.3rev/s If he raises his arms to be(6nz-xyb1xm)zwhw5s+ k37: rd ceza 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 sgj 1):o5-wwawm u.bpshown in Fig. 8–29) can reduce her moment of inertia by a factor of about 3.5 when changing from th1aj.wmpbgswu :) o-5w e 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 3 lp27v pvk2durate from an initial rate of 1.0 rev every 2.0vp2uv3p 27ldk 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 - +nbe9.:xk xslz (xsna vertical axis through its center at a frequency of 1.5rev/s The wheel can be conside.s9bks x+znxe( -lx n:red 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, 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 momentt*n1eb:et-t oum 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 momentyo/ b(fo4g 3x tx1uji,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 tg) qu9ubjyt) 2:4+ad3ek, ;r lgbv icdisk of moment of inertia I is dropped onto an identical de; bt:))taib34yju,c 9 k 2g qrdulvg+isk 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 2. e wk)yx-uj2z6x2*ory4 $rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the center of a rotating meae4 y(mmg)v 6ah ,fk/irry-go-round platform of radius 3.0 m andvg6ke4/ haymf(i, a m) moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an adn+.5 x6 5. grjmujgpvcjf s.)ngular velocity of 0.g+.jm)6u.jdxpc.jgvnfrs 5 5 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 9ar 3ctjsbgno))3un* a white dwarf, losing about half its mass in the process, and winding up with a radius 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 intra9 tu3* c)o)3jsbngneger)$\approx$    $rad/s$ (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 ov7ez/m) qhm v.)ytt6rf2s*cq f 120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass 6 rz2k* ae6qm6b(-8bl ax ,rpu9 uclyx$ 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 l8x)f)z 5cvryp+/jt d.cl+ nyumq7t, at rest, that can rotate freely without friction. The moment of inertia of the persol)tc) t pl yuxf85 qj+dvz,.7+m/nyrcn 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 personr (w*5aqjlw iz4p;*jk w/-zmx stands at the edge of a 6.5-m diameter merry-go-round turntable that is mounted on frictionless bearings and has a moment of inertia of 1700xp5lwm*zj q-(;wkrjw/ *4i az $kg \cdot m^2$ 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 v bo-:21cuele -6egkeo;dx9 zon the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope ueeo-9 x1bk lz-;ecve o62d g:and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person without slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces thf: jska9(8l lo v/fmaor; gpucb(q4(9 e Earth. Determine the (fb:4(/vmkrq fjsa 9; o8u( g 9collparatio of the Moon’s spin angular momentum (about its own axis) to its orbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest a9uxd3bl* 35iukc iks0t 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 s3di-,t *57tp8cs 5lj(pfm rq.ybubs a uniform cylinder of radius 0.20 m acquires a r-t5rpm(3bpss yt7 jd i8lsc5 f*buq.,otational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the torque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical diqj+yhd t- 5)gvsks, each of mass 0.050 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 w) h+dqtvjy-5ghen 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 , ,2pjwh/ bypxspeed 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 +. yo wk -lmho7db6 e.icff.p5rotating at a speed of 1.0 revolution every 12 days. Ioemfw -ycdk.6plf5b7o i.h+ .f it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume 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-pollutiodvi.3tpj wn 9ww6ag+47v l mee/6o) dtn 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 27je+a3 down9 w6 ei46 dvpv mg)/wltt.40 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 illustrates5 uedv1mk .,ajyjv(/z 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 horio6v5xx d(7 cbyvz; z4e1ivcp9zontal 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 mass M and length L can pivot freely (idfwy;bh. fryv7t:l+ 4.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 acts at the center of mass of the rby;wfh7 d .vt4rly+f:od, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M ha4; 0wnj py ;)dsfmvrxl 00tqfvih6z4; s radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which i;d 6f0q v0 4vxs0)yj mp wznfh;4i;tlrt rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making a turn wij.nnzj-)3kg gs,k v2wth a radius The forces actinz)sw,-gk jj gnv3 2k.ng on the cyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rock into a sling of length 1.5 m and begins i0ku2sp 7ald ym)m-5z *kipg:whirling the rock in a nearly horizontal circle above his head, accelerating itdgl)ap ms5kiu2mk7 -*i zy0p : 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 b8p b 9/ cdm ej;n-:t5*llc rr,npoeg;sody as a solid cylinder and her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio ,pb -m c8d ll/5ensejn r;g9cpr;t* o:of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly1ec y ngyqt30* which consists of two cylindrical plates, of mass *yc1yg 0te n3q$M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ 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 rolqsql3 ti5** 5a qgc+tcls 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 i tl+35qgc*q5sct *qa of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not a9 rl glvw*a7i5ssume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reduce68ry2g vpqp omlv+0,q s its speed uniformly from 90km/h to 60km/h The tires hav6v m, r+qpplg2qvo80ye 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