A bicycle odometer (which measures distance traveled) is attached near the wheehb 4y+)ek bgah6jd:k8 l hub and is designed for 27-inch wheels. Wh b6k:aje+h bd84g )kyhat happens if you use it on a bicycle with 24-inch wheels?

Suppose a disk rotates at constan2 tvns2w do0/5ijlg ah q-oc1zl4 e80qt angular velocity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, doeczso/ jg2daitlwl 045-0n 2ehv q8 1qos 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 singlkh9ek/cf w5 4le value of the angular velocity $\omega$ Explain.

Can a small force ever exert a greater torque th+20 fonep)e rd/task.plk -:ran 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-/k4pq s is(mk)up with your hands behind your head than when your arms are stretched out in front of you? A diagram may help you to a)m k/(kspsiq 4nswer this.

A 21-speed bicycle has semu ,was 7h(d+lven sprockets at the rear wheel and three at the pedal cranks. In which gear is it harder to pedal, a small rear sproma+hw7 dl( s,ucket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lower legs with fles e-qu7ov5ua *t9x *bolh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotational dynamics, explain why this distribution of mass is adt9 q* 5axlou7-ov*u bevantageous.

Why do tightrope walkers (Fig. 8–35) carry a long,gv oevlkt6.xfc1+ +apof j2/2 narrow beam?

If the net force on a system is zero, is the net torque also zero? I ajs0dn.h *eq 7)uoum9f the net torque on a systemqde m uah)7o0 j9.*nsu is zero, is the net force zero?

Two inclines have the same height but make different angles ub 4v tqk(z13bx1;zqo with the horizontal. k31z; vb tbqu14oxq(zThe same steel ball is rolled down each incline. On which incline will the speed of the ball at the bottom be greater? Explain.

Two solid spheres simultaneouslyj0 h :6w19huz+nh mbzv start rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the+nhuw0jv916z:h zhbm other. Which reaches the bottom of the incline first? Which has the greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder have the same radius and the same mass. They start fgibh:, x cw6ey7bpbbt6 +*gf *rom 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 y:gbx6f*bp*7wt ecb gb+ , 6higreater rotational KE?

We claim that momentum and angular momentum astm1af*u7f;ul5d wn j+48z byre conserved. Yet most moving or rotating objects eventually slow5s84bj nu*yf;dfw z 1atu7ml + down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how woul:/2i58 ye ixx ctipc7ld this affect the liec:yp 8 /72lx5i xctiength of the day?

Can the diver of Fig. 8–29 do a som; chq)uqowye2 u+:1jxersault without having any initial rotation wuue; 1o: wqq)hcy+x2j hen she leaves the board?

The moment of inertia of a rotating solidc86 rt)/dgtkyba :wq * disk about an axis through its center of mass abr qdt8wy /ctkg6:*)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 stnsnaa*f .osx6 e*0)he ool holding a 2-kg mass in each outstretched hand. If you sufaneh0* )xse6* anso.ddenly drop the masses, will your angular velocity increase, decrease, or stay the same? Explain.

Two spheres look identical ansuwd(q9 /q5h zd have the same mass. However, one is hollow and the other is solid. Describe an experiment to determine which is which.h z9/w5 sqqud(

The angular velocity of a wheel rotating on a horizontal axle po om- b/wd:s;v0 9wgb 35uaqfmrints 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 tr05vdogw9u m qaw;3m/b : sfb-he wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on pl :idjvjzb8 :bqka6l34 ;7 /gnw3aglthe edge of a large freely rotating turntable. What happens if7g;zdig3 b b8l6aa:q/3jwll4:v jp n k you walk toward the center?

A shortstop may leap into the air to catch:9f*6cvmbf kdknl/r )7 nh gd2 a ball and throw it quickly. As he throws the ball, the upper part of his bob:) f*c27dl/m 9g6fhrkdkn nvdy rotates. If you look quickly you will notice that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law of conservation of angular momentum, discuss why a :b 7ztq j;aq+yhelicopter must have more than one rotor (or propeller). Discuss one ozb+qty j; a7:qr more ways the second propeller can operate to keep the helicopter stable.

  Express the following ang(;5h q oi/wgleles 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 Earybc(l2i -g 2txth because of an amazing coincidence. Calculate, using the information inside the Front Cover, the angular diameters (in radians) of the Sun and the Mo-t bc yxl2i2(gon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at t r8cjr, u.+budhe Moon, 380,000 km from Earth. The beam diverges at ardub +,cjru. 8n 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 6500 rpm.q o.0(qz0s2 dd)s:ybco upsd :z qjv0. When the motor is turned off during operpq. .o00ydq) z2qu sojs:dd 0 sb:zc(vation, 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 k 4faq*m5y hbi9vbt //a level floor 3.5 m to another child. If the ball makes 15.0 revolutions, what if/h5a9k qi4*y mbvtb/s its diameter?    m

  A bicycle with tires wlev8m nxg.7/ 68 cm in diameter travels 8.0 km. How many revolutions do the wheels make?wx .el/gmv 7n8    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its9(eq ww9zmldf.1 l eq) angular velocitzm(ew.9 f9wqdle )1l qy 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 sl;jpj13 7pfxup 6joekfn8(zj3)9 u ya (Fig. 8–38). (a) What is the linear spejj6 (39up j;ap8ln3y f1k7jo)xfz upeed 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 t yk3z 7ab,vcy;he Earth (a) in its orbit around the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speed s ve w7/zmddu;:u5 i+h4i -cuvof a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a ce4l vxo 9 vcs-vt5z0pq6ntrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration of q95xt-64v0 solpvzcv 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accelerates un7k.zcq 2fa/vfy:tmf )iformly about its center from 130 rpm to 280 rpm in 4.0 s. :tf afvcf2ykqzm7 )/ .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 6t;f+np0uz *mvh*sn es $R_1$ 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 spaqjw.g3 ,67;cnnq(pvahlsna 1cecraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. The spacecraft can be th.1(qnc6 a 7v3janl,sw q h;pngought 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 acceleratebj2-thrl(leqh5,, r r8nry o.s uniformly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in this ti ljh2n,(.qbr tre r8o-yl,r5hme?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate7ol6aies ww -fh6r81n
(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 jz,(h:d/0s ,ew 1dx c gj 98vtqmjdm;uof flying highspeed jets in a whirling “human centrifuge,” which takes 1.0 min to jed:cux mq/8 hgjwtv;0,1j9dd zs(,mturn 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 accele 3/klkaqjw5*yrates uniformly from 240 rpm to 360 rpm in 6.5 s. How far will a point on the edge of the wheel have traveled in this time? wkl*y /q3a5kj    m

  A cooling fan is turned off when it is ruc g1 m8j*l+xiwnning at 850rev/min It turns 1500 revolutions before it comm8x1w* c +gjiles 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 uniformly h d9e vsnr *(aazx7(w9from 95km/h to 45keza(w9*nh9sr( xv7a dm/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 grffeoo- .2slnyh 5., uniformly from 95km/h to 45km/h The tires have ag2.f-on r5hy . olesf, diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts all her weight on each pedal d uc,vf1xn-)p 6t exm+9qcg)twhen climbing a hill. The pedals rotate ix-e9+ f1) d tpv qccu,m)xgn6tn a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 cm wide. What yxp(,bl:i5 kj 61fjzdgo8 b c;is the magnitude of the torqu , pyfl 815:gbbz(;6kcjdiojx e 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 torque0t8 h0yajf,yc about the axle of the wheel shown in Fig. 8–39. Assume that a fri8yf0 a y0tc,hjction torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mass m, are attachedps ypz4tk sch)4z20p7 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 2hcsp0zpskp47 t)y4z this system.

  The bolts on the cylinder head of an engine requa6t/ 4t s0shi ro1hb5x 63ckwm3cry1uire tightening to a torque of 38 6 5ttws 0x4coacshh6m1 r ik/3b1u 3yr$m \cdot N$ 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 r6tlt ds, 5a:roy0l(bx*g3k h:an z-inadius 0.648 m when the axis of rotation is t*:kl0nyr6lsgixno (ba- 3h 5,z dtta :hrough its center.    $kg \cdot m^2$

  Calculate the moment of inertia of a bicycle wheel sus +ni4tq5sva0 18ye dnb33u 66.7 cm in diameter. The rim and tire have a combined mass of 1.25 kg. The mass of the hub cae n3481 vs0q5ta3ub+s usnydin be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ball on the end of a thin, -vw*pm.o)*bt h1fdyt light rod is rotated in a horizontal circle of yb*vtm.d-)h potf1* wradius 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 bow-ja duhkk9 0,p4oh +hvl on a potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between her hands and the clay is 1.5 N tou d +-pkvh h4,k90hjaotal.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of th/ni ,;lo -f1t 5y:mr rx8oid x v;srxr:ptuc,:e array of point objects shown in Fig. 8–43 a- x trprs;cr,1: dmi ,;t o/x8:lyo:funrxvi5 bout
(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 of5f ;xh8 xvyz3r84kmhf two oxygen atoms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform cylindrical satebnqdo2 vo (;/ellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min?;q/nd b2ooev( $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radit52(*qa 5tyaj30sv7ybn e w dzus of 8.50 cm and a mass of 0.580 kg. Calcuy y 2e a5 t5a*zj(wsnqd0tbv73late
(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 rest 2:fd1+xy9hjrgoqigg6e92 w u 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 h6vgzbz; 6xxrql4)j0t and-driven merry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acv) zx;6bzxr j4g q06ltceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300 rpm is shut off and is eventually broulha( x 0:birv3ght uniformly to rest by a frictional torque of 1.3 vrlhi:(bxa0 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 ac wyk+4 c/gb-hnyn 69frcelerates 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 by th8kdom4,wg v6 u v:h6d/th7rjpxq10 abe action of the forearm, which rotates about the elbow joint under the action of the tp td1 w7vdx m ja,b4u0qh8v/66:ogrhkriceps 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 rod, as shown a i1fbfuo 1q -u2i o*y;8g) ,cxrszys/in Fig. 8–46.uif, * c2-1xfrgq u;ioys o/a)1 syz8b
(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 x pdl.,0)gnfztt*l8 3gw/ h ofe(0bd bconsists of two masses, $m_1$ 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 fule7g.qm93+p : f,grzz 9zmouwsj c+/t kl turns (revolutions) an9/: rwgtozqj+z 3,9u.cme fpz sg+k7 md releases 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 momenffe7-1oy ltm t zs2i3*gk)-rvt 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 develops a torque58c7g:xrz6xu .u,8 1texon (d ahus dx 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 ze-(a*ue v1wnslipping down a lane at 3uwezena*- v1( .3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the S8 1l:yaipliabc2u qi f v7(8z+y0 ga -hid16axun as the sum of two terms6 11iilipaax(+giz:cv0-lb8f782ad u qayhy,
(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 7.50 m. How much,yg s:fy7 p 8w* hechkjoan7/- net work is required to accelerate it from rest to a rotation rate ofhyskh7 7g, ao8*/w:yf nj-cpe 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 20.0 cm and mass 1.80 kg starts iee:*zir/ ;bo x dpg/ nb,;lu0from rest and rolls without slippin0rzp d;i,n e/lu;o :/bie*bx gg down a 30.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

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

  A 2.30-m-long pole is balanced vertically on its tip.qr7l)f;tbgc*pc9 rpz aoy,3(aez 12 ponr 4f5 It starts to fall and its lower end does not slip. What will be the speed of thqe4tn7*cz; fyg paro)r9 l, 1bfc ppz2(53orae upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momensft;x1igd obw 1nr4r4( wo(oho)-q)y tum of a 0.210-kg ball rotating on the end of a thin stobwy (ost-;h(qnox44dfo))wi gr11 r ring in 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-kg uniform v7pky ,y5(j+ xqp5hyqcylindrical grinding wheel of radius 18 cm wh,7j5p5y xvh+qq ( pyyken rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a plfm pe1m()+e-k7kluau atform that is rotating at a rate of 1.(eu )lu1pk+m7ekm -af 3rev/s If he raises his 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:djt)d w24nw7 q mv0vq. 8–29) can reduce her moment of inertia by a factor of about 3.5 when chavw 47qmnjd2v:t)d q0 wnging from the straight position to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rotation rate from an initial ratv x7t7vqya7(h e of 1.0 rev every 2.0 s to a final rate ov( 7vah q7yx7tf 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 a fre +bl2g2r k psxldl8,av0g5 vf+quency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, approximately shaped as a flat disk of raf, av0 gl rdl2pk+ +xg8vslb52dius 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 figi2bp p7()p5 fbb +n.ay)kqukqure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the t-j(txquwr:+8 orvapi7n,6m kf7r) aEarth
(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 dropped1ve8 qs 8od;jcob6wc9 onto an identical disk rotating at angqjeccsbo88owv;d 6 19ular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2a3 0/u (okhtmdh)g;s +i*nta q.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 yobejs 1i m4a/yzl9 ykmnk017qqs4/7 center of a rotating merry-go-round platform of 9sqbjsy 414qzimy/yl7kon7 0ak 1/me radius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angular velocity of m26xs)g2vyma; )h jru0.8yjua2xmg mrv;)62) hs $rad/s$ 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 about half ipvlb3u0d1j c//-md wx ts 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 woulb cvlxd1-/mpjw /3d0u d 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 3g vv) mvpgm;v;ha9vnkc-1 r *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 /vzlkun03cuf( hyibao 20(b6:en uo i(:w,c a$ 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 platfor gpj ohb574-emdt7jcg 6b+t,rm, initially at rest, that can rotate freely without frictibcg-b mt5g p,+ 4redjj76o7hton. The moment of inertia of the person plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m diameter:jkfoa zy1a4 8 merry-go-round turntable that is mounted on frictionless bearinkaao4f j 8:zy1gs and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls on the ground with the end of the rope lying on t.ih,t +0gizrq -2hhan he top edge of the spool. A person grabs the en-i2ag,ih hz.+ 0r nqhtd 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 spool’s center of mass move?

  The Moon orbits the Earth suy 3w,fxt crd52ch that the same side always faces the Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its orbital angulad3f, c52 yrxtwr momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest .g7/ a ,lkrocp im-7td (qj;lzd;fwz4at 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 ycb7+ i5ygx n-shape of a uniform cylinder of radius 0.20 m acquires a rotational - ygxicy+n5 b7rate 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 sdzyj mhn 1a3g490r3d8s h n1nfolid cylindrical disks, 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 sszng84nahm 0 hd1dfr33y n9j1 peed 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 angularve+q lh, s7m3l speed of the rear wheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the size of our Sun, but with mass 8.0 times as great, were rota 2)-xzwo,y jg6ej y3cq*vfk94e p(qndting at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what wo)o2nkx 4y6e ef zv(9-qjd,gwcy3j*qpuld 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-pollution automoe6,*es ; fps ez7-osacbile 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 diametzf7eo ss; e*-6sa,cp eer 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 illustra 5es *l/gzhmufzlr015 tes 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 t2sy+ c6 fzlnhk0 gr8/rolling on a horizontal 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 (i.e., we ignore fricti9sso o*xe4 g:non) 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 rod, as shown. [Hintogo: xnses*4 9: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically aoj9. :bn/ vhd2ojlo5+ k6 shxon the floor, and we want to exert a horizontal force F at its axle so txk 2. joad6jnobvo s5h9/ +l:hhat it will climb a step against which it rests (Fig. 8–55). The step has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat road is making zp gj15vv8icz;6l x:vy vwv:(a turn with a radius The forces acting on the cyclist and cycle are the vj :czvyxv :lz51( ;wgpvi68v 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 0.50vg /;6+fuxy qb du:v,p-kg 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 to a rate of 120 rpm after 5.0 s. What is g: dp6, u xuqy/b;v+vfthe 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 o)lt2b n 6ar6oic3 5tqher arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with 3l2 tqob5o6n 6ic) traoutstretched arms, and with arms held tightly against her body.   

  You are designing a clutch assembly which consists of two ipz sysct dx, )30+4vxcylindrical plates, of mczst d0x+43)pvs,y ixass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough track of 8b1 ctb tu3/klFig. 8–58. What is the minimum value of thu1 t/8kcb bl3te vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do not assu 8;nsw)6egvku nlcj06w*ii (bme $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the car reducc f7samj+ eb:m e;mpj3d e./j)es its speed uniformly from 90km/h to ejj p)b a fem:esj.+d3;7 m/mc60km/h The tires have a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s