Angular displacement is usually express in unitdsr4i ngl3 z(1s of

  Angular velocity is expressed in unit qs+ijk9ke -2qjaf1a1gqp 12fs of

  Angular acceleration is expressed in uk 0vuy0-um vt(3 g:2xh0qp;. oz czpfonits of

  A boy and a girl are riding on a merry-go-rot2 9czdr jpv 6-x;t,caund which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to cpt d t;rjv,z269xc a-the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go2dvpz(q) 9/ zoxuh 5jw*6 )e2lf 1pictv1wgyt -round which is turning at a constant rate. The boy is near the outer edz )uv f5gl)ywi h9eco( */q 1tw1j vzp62dxt2pge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-roue7srp1/33q ) t:b4s4q2 vrxlayt wwopnd which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to thew r)wsxeatpo2 tvb3r/3:qls44 q71py center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is tue lf im30xe.c9/n*gou rning at a constant rate. The boy is near the outer edge, while the on/um9f .0 xl3cgi*ee girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridin1zbjk 44sjraie*+ ;o vg a merry-go-round which is turning at a constant rate. The boy is near the outer edge, w4e 4is+or1 kvab*jj z;hile the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid bodyd;*n pc 7+ gi4lox*men6(skcs that is rotating. Which of the following is an accurate statement;*esm* g 7sopnc 6(+kcxdnl4i?

  Rolling without slipping depen:vhuq() cansj 3yob. 4ds on

  Two equal forces are applied to a door. The first force is applied at the midv odbv0t4j7h)lku 0qijd5k77as1(j jpoint of the door; the secjvd q)v01u7(dj 5ktlhis0 bk47a j7joond force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The yiij/fe(p n:+u .( kkcfirst force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which(c/jn(f +iyk: u.pike force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Theer,tws 2coi zo*bh))5lp - +uw first force is twice as large asz2b5p+)eu ,s)r -oic*wwlh to the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an objea1g t -ks5cuq*o) qzc6ct's resistance to changes in rotati6* sgo)ac uktqc5z1q- on?

  Consider two uniform solid spheres where both have a ;eb.dno (ci;the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia t;i(a ob.c e;dno that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius oj+ abgjz jnetd .)/c/u/i9gd *z1gzo9f the othegdzo1u)*j9c z9/b/+nzg gtid a/e.jjr. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spherewwx ; :2 y:ydni:8xz7 mjmhjmf/ipy 3-s where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertiaxndwmm8y-2 xfy/m zh pjyw3::i :7ji; is

  A uniform solid sphere has mass M and radius R. If these *z3jp8g/r6 tmmqs ago41a uk )lbi4:jare increased to 2M and 3R, what happens to the sphere's moment 8k gtj* /ar:g mb4q1mazu643i)os jplof inertia about a central axis?

  If a constant net torqugy . zp24 ef5x:jjzc*pe is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis nlw0wtqg( 2lm- j- j9wis given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotationltwwljj90n-q( - g2mwal kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg an8)dyi t5e x0f5mid+zp d a radius of 3050ey 8p5 iit+ mf)ddzx cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M andbi3- ep(c ub67b7n jav radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at thb(-7 b6 caeb7jpivn3u e bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R roll xnyp8d(amgk)z/ 63 e3 5pv-hmm;sc kws without slipping down an inclined plak;mgdsm56 /w z3mcphx)v -py 8e(3kanne starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes y)p y o ypp.rt,w2o5v*htwu1+ when a net external force acts12yp p tw.5h,) yr+yvtwoo*pu on the system." This statement is

  In what circumstances can the angular velocity of sy mownhm4zvy(. 8-p. sustem of particles change without any change in the system's(vw-.8ms.zmuh 4pon y angular momentum?

  The Earth orbits the Sun in an elliptical orb7m(yn. o+gzi 61pbuxyit. Ignore any friction which may be present. What happens over t n1ixubg6m(+yy7 zop.ime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves cl)m(yh jz,,-ncs w0 bfzose to the Sun, then which of the following best desh(j,byf0z -) cs,zmwncribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pullin21f:o a2a 8zdtl+l tcng in his outstretched arms clna 2+to l:1tf zdlc8a2ose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedo ux2wm ( l(b4em/qnk7 arms close to his body. What happens to his rotational /w7emkxu2b ( (nlm 4qokinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in h0x-kn.m42eu lz- n3o d8 prsbhis outstretched arms closedxoz3p.-28 uebsrh m4n-k nl0 to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momen n.knhn 2re1yf1-yqh;qb4t1s tum.

  What arc length does the Earth travel in a three month period in its tl*/gvte z, e)b:/onpnearly circular orbit about the Sun with a rade)ev og/zt,/ lnbt: *pius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0. j0)oyww;av (pmcf9vpa;q )7m 30 m. What distance does the tip of the second hand ;wacpom m9v;jpw()fvaq 7y)0 sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutiswe 5rr9x+ sh o,8qgy*ons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W0ly8gyzgu. 0mhat is the frequency of the wheem0ug8z g.0 lyyl's rotation?

  A pulsar (a rotating neutron star) emits pulsew6yk+kjx*ga q( ln(2qfr q l)4s at a frequency of 0.40 kHz. The perq 6f(xj+ 4ylw( nqql*)2grak kiod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does c.oeu rb3o/epo3f+e4it turn in 0.20 s ueo3+oebf 4/.3cpreo?

  A wheel of diameter 26 cm t5h//vb.9sb ia.h cz cdurns at 1500 rpm. How far will a point on the outer rcd h9cvaib5/b..h / szim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revol:yv9aqh0u 4i eutions in 4.0 s. What is the average ana94uiy:qe v0 hgular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revo6nj:yetncs7a1y9l m0 lutions in 4.0 s. What is the linear speed of a point 0.10 m from the cj6y:l 0ny e9a 71tcnmsenter of the wheel?

  A cable car at a ski resort carries skiers bcqq 8; yk(gy;a distance of 6.8 km. The cable which moves the car is driven by a pulley withykqc8; (qby;g diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a coejj-j1 hl-bgdb 5rd :b5e:l vq77 sbltw9/5 aenstant angular speed of 2.0 rad/s. What is the linear speedd1w lqaej- e7d5rgl5j :-t/b blvh:5je 7b9sb of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter isj a 9)l09ng3 ug.wdzjr 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear r )aw j lz.ud93g9j0gnspeed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular spe ;f*8xm(fhn .;mesjii ed of 2.0 rad/s. What is the centripetal acceleratios8en ; xhj(;*iim mf.fn of a point on the wheel's rim?

  What is the centripetal acceleratio61g iokxgwc81n of a point on the perimeter of a bicycle wheel of diame 6xg1o1ic k8gwter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotl; z9 +6j.:l khqnjgrtv 7tm7sating space station (r 67+ ;hgzkj: tt vl7js.lrm 9qn= 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular ppmp /pn;xi32n7yid9curve of radius 50 m with a speed of 20 m/s. The maximum cippnnx;p9 d 3m/ piy72entripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radiusxg d4my cv +p18zh+in94yvo*biiw)i; 50 m with a speed of 20 m/s. The maximum centripetal force iw9)odyngh1m*ii +zvxb448ivcp; + y (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to pl7xrx3;-; vo;gkly fthe end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 2503 ;;voxl7;pfx l -rgyk N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m do8so)ghczm8y7 wn)gs 88hc7o yzm a lane at 4.3 m/s.
(a) Calculate the angular displacement of the bowling ball.   rad ( fill in numbers only)
(b) Calculate the angular velocity of the bowling ball   rad/s ( fill in numbers only)
(c) Calculate the radial acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)
(d) Calculate the tangential acceleration of the bowling ball    $m/s^2$ ( fill in numbers only)

  A wheel accelerates witlq :;9y*zcgci1:: wqs v6hw;6 vxv1ufg7kzpsh a constant angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angle the wheel rotates through in 2.0 s?

  A wheel accelerates with a co40dp )t*)wdxzd1 ogvr nstant angular acceleration of $4.5 rad/s^2$. If the initial angular velocity is 1.0 rad/s, what is the angular velocity at t = 2.0 s?

  How many radians does a 0.300-m radius automobile tire rotate after starting frofeun, e-6qz3 xm rest and accelerating at a constant angulane- 36uxqefz, r acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, ab3l1cp-sz9hjd+ uz5m u57afs 6+xy tznd has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a consta2l os+,4 hpmc,h-fcdn6m 6xnj nt angular acceleratioc,d smp4, nx62- mhj6c+lhno fn of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed oq+te;qgl 5i; sz,q +xif 6.0 rad/s while turning through 2.0 revolutions. What is the ;+t,+sxliqq q;i5gze average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s pexm.i/ d rvd2n zni);6d3e ;*pzz:puto rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to resivxm;d:urz2; n e/6)zddnp3 *ei.pp zt?

  A wheel of diameter of 68dmpre; eh*.7lnj -a,m.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What rhnd; lm.7e*e,m-aj pis the angular acceleration?

  A wheel of diameter of 68.0 cm sayv /x5c+zx10bja i/tlows down uniformly from 8.40 m/s to rest over a acy0 5//itxabx1v +jz distance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatji6uwib.q4/fmjw 4( hws1u.g);smm;*am ovoional speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratiovo;j6ifgw4 a .mb (m*iu jow)smm.u w;s4 qh/1n before coming to rest.
(a) Determine the initial angular speed of the centrifuge.    $rad/s$
(b) Determine the angle (in radians) through which the centrifuge rotates before coming to rest.    $rad$
(c) Calculate the constant angular acceleration of the centrifuge.    $rad/s^2$
(d) Calculate the time necessary for the centrifuge to come to rest.    $s$

  The bolts on a car wheel require tightening to a torque of 90 Nm. If f;-;b lktofz6rmq3+z a 30 cm long wrench is used, what is the magnitude of the force required when the folrz-f +z m kb;f63t;oqrce is perpendicular to the wrench?

  The bolts on a car wheel require tighteni5vlmgq ixtklp :*/3ewbmv.k qhu-50 +ng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required wh0vlkpqq5- .vh3 tx m5 uigwl/+:km*been the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of in: .rilfa2n qf7ertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: )en*eem 3u n1amass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia a1mn ne) *au3eebout the origin?

  A solid cylinder of mass 10 kg is pivoted8)jc9v3 *oz u 4mufxqf about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceler)omqu3v 8jf c4u*z9f xation of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless a)0n8,+ /uet6 ts emdbgvk9hdv8s+uebxis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts/+8+kgebun9,8em vedbvt 6ds0 ) uh ts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cylinder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. u 9eidgqua( d,s6 ;j6oyma9e7t7uo8 n(c5bav The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment oouo; gd9 ,5aqu7it6 8v(a9b cue mda(7ysenj6f inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mas4.mz hme+ p xj-gd*; 1pgyph89oy7ltss 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 c984gppy;g *dtj1y m-.h7x hoepz sl+mm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk+gc 3e3qi 0acr,w0/( qiuhtbr pulley of mass 7.07 kg and radius 6+0(ewc3i3h0qt au,ir/br qg c6.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlnuuthx4f-7 2kess disk pulley of mass 7.07 kg and radius 66.0 cm. What is 2hnku4u7xt- fthe acceleration of the mass?

  A rotating flywheel can be used to store energy. If it ha 21v0pazbk.4z2whxis required to store $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment of ine2z t 8cq;xgt;xt-z(bprtia of $5.00 \; kgm^{2}$ starts from rest and accelerates under a constant torque of 3.00 Nm for 8.00 s. What is the wheel's rotational kinetic energy at the end of 8.00 s?

  A solid sphere of mass 1.0 kg and radius 0.010 mk19 az hiott4x07 zz-x starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of zo0i 4z7-9th k txzxa1the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rollp4mw-/xhv6kezfxr:3 8h to) us with a speed of 10 m/s. How high up an inclined plane can it climb befou6/ kr-mpxz3hw : t8)evxo4f hre coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released frsq,wve*hoy. 2c zab,wt 4: ,ijom rest and allowed to roll down an inclined plane. How fast is it movtbv*sw yz,j:2iqc eo ha4.,w,ing after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm r+/ 95nvv1-2xhnd xg s3k,ncgl,oabj volls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momentxcn,gd/1 x2-lhvv5jno9 sa, n+gbkv3 of inertia of a sphere is given by $I = (2/5)MR^2$.
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere? Does the angular speed depend on the radius or mass of the sphere?

  An object's angular momentum quu ,)yqcy:gt9*iya,3r7qfo.8i l rm changes by $20 \; kgm^{2}/s$ in 4.0 s. What magnitude average torque acted on this object?

  A proton of mass $1.67 \times 10^{-27} \; kg$ rotates with an angular speed of 2 x 106 rad/s in a circle of radius 0.80 m in a cyclotron. What is the orbital angular momentum of the proton?

  An ice skater has a moment of inertt rm526d h 27ta1uc0bycrl 2zjia of $5.0 \; kgm^{2}$ when her arms are outstretched. At this time she is spinning at 3.0 revolutions per second (rps). If she pulls in her arms and decreases her moment of inertia to $2.0 \; kgm^{2}$, how fast will she be spinning?

  A figure skater rotating at 5.00 rad/s with armsv,r(opt9tx4im;9i ob extended has a moment of inertia vtp,4(r tb9;9 mxiiooof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?