Angular displacement is usually express in units ofwp;3ccmzg1t yuzt )il8bk),y/ru : 7a

  Angular velocity is expressed in unwvbg -ydy a,y3+ut7(3 v;sbv sits of

  Angular acceleration is expressed in unitz fy)zr4)l 6px 45mg.ajj.hu us of

  A boy and a girl are riding on a merry-go-round which is turning at a constas 0z9cp0vi85 wbyd8c*b-clhant rate. c9lza dy cpi85ch *0w0 v-bs8b The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round wxnnb; aj8a lwa66n+ w6u0hac3hich is turning at a constant raten6aw wun8 6anh0l3xa jc+6ba ;. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ridingxyuaq-o1ws/rz7c -,o on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer tow7x -aozqr/-1,oy csu the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go , +1dtdy;qhar+ uads/yb fq36-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal accelerad/bdrt+fu 1qays+ 3 a, qy6dh;tion?

  A boy and a girl are riding a merry-go-roundyq+5.wpq6 us*fjh2tjo+ qkk ) which is turning at a constant rate. +h5kk.*ow +jtq jfu2q spyq)6The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is qx +6j;v cqf+kpwly5, ) p;bmlan accurate statemevqcp;p yb 6jw5+k ,lm;ql x)f+nt?

  Rolling without slippi7 ib4k5b 9qh5nxrgrp- non*a.ng depends on

  Two equal forces are applied to a doom lu1 r ai6ftd6ld,13vr. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which forc6lf61ma3i,vtr1u dd l e exerts the greater torque?

  Two equal forces are applied to a door at the doorkno//oywomp3 :ktq w/x rz9gpa8oh7 e:, mb. The first force is applied perpendicular to the door; the second force is applied aopa:oe//o 9,py/83qrg:h m mz xkw7w tt 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicularc/pi qtc0w0 9g to the door. The first force is twice as large p wqc0gct/i90as 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 object's resistance to changes ex(dfz8/ t ) .fla i0fzt.hf+kge5qe3 in rotati(hiqe. e g+d)f faf l.t30e /85ftxkzzon?

  Consider two uniform solid spheres where both have the boby/;xv p9 ;isame diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia x;p ybbov/9; ito that of the smaller moment of inertia is

  Two uniform solid spheres have the samemht, 6md8tju7ws ed/ 5 mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smallwt mds,je6 /8udm7t 5her sphere is

  Consider two uniform solid spheres : iwd7kqdl;*rwhere one has twice the mass and twice the diameter of twdrkidl*;7: qhe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are in,wdb2vg3n 1 ( aio2twocreased to 2M anoi tv3 da1o ,w22g(bwnd 3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an obcx6 l 73nv:pevject, that object will

  The moment of inertia of a solid cyli dapy d7n7( oj:p3yjrxw.8,jhnder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass 3f.ju*jo uo;7 kyll8 pzy b5y(of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the whzb y. o5yj *8uo3juy(f lp7kl;eels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius v- uomq6 +;w9bbdc7 rn.vu 8hjvlio6*5uqc; qR rolls without slipping down an inclined plane starting from rest. The linear velocity bvod9 vcbj8 l+6c;o-qh6 quq.7r; min*v5uwuof the sphere at the bottom of the incline depends on

  Suppose a solid sphere of ukef :ac( 4 ie+1f3v)uqdyc /- tywp8(v4gndj mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom 1v(jveq (4nia+ fg/ y ey3)k-cd dpfwut8:cu4 of the incline depends on

  "The total angular momentum of a system of particles ch ss,v43skvjf)yfis ,*anges when a net external force acts os,fsvky)3j ,4vss*fin the system." This statement is

  In what circumstances can t i rn5 /gedun-7*r5dit7fepv9he angular velocity of system of particles change without any change i5en7tg5rr9v7/dii *npe-df un the system's angular momentum?

  The Earth orbits the Sun in an elliptical 8 yh5vqn ix j7x:)qcs)orbit. Ignore any friction which may be present. What happens over time to7yjq q5 cxniv:)8sxh ) the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves clos8kqt/ /l.k:h oeu j3gdx2 q(zxe to the Sun, then whichutz 8l :eqqh/kx/ogx(j2k. d3 of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pu* llbjh5 a9.malling in his outstretched arms ll* jba59ahm.close 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 outstretche6yzt-) e(se hdd arms close to his body. What happens to his rotational kinetic en dhs6 )tey-ze(ergy about the axis of rotation?

  An ice skater performs a pirouette (a fast8(oi; 7akmqtm 2izm7 jah :;nbd(:d tn spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the ax( d2nnm 7i:jkzham;8 ba7:iqd(t;motis of rotation?

State the law of conservation of angular momentuzq) *rb ,o1ruvm.

  What arc length does the Earth travel in a three month period y z mciu:4447i u,nfxtin its nearly circular orbit about the Sun with a radiu cm 4u:i4f7 x4iynz,tus of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m-pc,zwfu3 93 8otktez. What distance does the tip of the second hand sweep through in 3 minutes and 45 secfp3ctt,w-oz 8e93u kzonds?

  How many rad/s is 25 revolutions perkhd 50 c w;+xlteus:l9 minute equivalent to?

  A bicycle wheel rotat, i enix8r4z-oes uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wh 8zio-n4eix,r eel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Th w r7kq9tvu (x4,mwwvx+(sq5ye period of its rotayswq4(uk,v5qw 9 7 +w( mrxtvxtion is

  A phonograph record rotates at 45 rpm. Through what angle does it tur;(r vikbet0;b n in 0.20 sr(;it 0veb;bk ?

  A wheel of diameter 26 cm turns at 1500 rpm. How swelee:c c6 f;3so1,sfar will a point on the outer rl13,esf ;o ses:c6cewim move in 2.1 s?

  A bicycle wheel rotates unierat )l (d521u ,ga*ga;wsr kmformly through 2.0 revolutions in 4.0 s. What is the average angular speed of the*s1g, ; utl a5m2adarw(grk)e wheel?

  A bicycle wheel rotatbb93crxpil20 jl* *( wo,pxe ves uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the c vw0, c joibl rp9*pxxe23lb(*enter of the wheel?

  A cable car at a ski resort cadd/4b2by41 vbpcyuvpbb.n2 r.t) vx+.cvc- a rries skiers a distance of 6.8 km. The cable which moves th+2pad)4bbn2yvdv cxt 1c.pu4yvc v.r/ .b b b-e car is driven by a pulley with 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 constant aa/rwn6mb7 d/ ;csm.s)qdc 8ogngular speed of 2.0 rad/s. What is th8mwgq67 c/a)sd/cdm b;.o rsne linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 9amw/m3zw q n;06drey0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linea/m9qz6anm0r ;d wew y3r speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2b*gak;p twj4*lg+5-v zo,hrl-toj +q .0 rad/s. What is the centripetal acceleration of ,j4* wk*ol-pzra hogvq+ -;g+ jbl5tt a point on the wheel's rim?

  What is the centripetal acceleratif5zpi :q:mfg/ 7azqq1p 8oc (qon of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when thezp7gm15paf:o q(c8qzi q: qf / bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stationqa g 8my8yb2y7 (r = 1000 m) rotate to produce an artificial gravimq ya728ygy8 bty of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with ,2dwdo; ndwzbeq4; e0a speed of 20 m/s. The m 0dozbn ww2d; q;e,e4daximum centripetal 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 radius 50 m with a speed p/p*ntwtj fh-f q*x(f*,h 4si l:c j-gof 20 m/s. The maximum centripetal qp*:ts (t/ p i4xjfjwcfn-fg* l*h,-hforce (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 the end of a 0.750-m string, ii /p6xa 4ji31hu+kpqws whirled around in a smooth level table. If the maximum tensix pi kiwpj6ua /qh+134on that the string can withstand is 250 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 wilh2a 4/lad,w7u)pq sqthout slipping 10 m down a llp4l u haad,q2)s7w q/ane 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 with a constant angular acceleration ofnl0 1-x f zne3b(0apit $4.5 rad/s^2$. 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 (k8*z.a/pd ht.:ndb yctcs0o with a constant 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 ys fu)o8 eo,rtg:pb6 jv;o91t automobile tire rotate after starting from rest and accelerating at a o1r ,)obtoeyg;v:tp8fu96j s constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular -fgkml6 9y6k saassr3dc, b8i/vnbf z6ov8:-acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerate osph 5qkuvqvg22. ghh;st1qy** n)-rs with a constant angular acceleration k- 2gq ytvqghu)rvq *h52pn*1.oss;hof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from reswdbe e0 uarxj(,b*/vr98fa t)t and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average aa)vutj 0waeeb r/bdx(8*9 rf,ngular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniforxl2fe45j5w evmly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to re x fv45e5w2jlest?

  A wheel of diameter of 68.0 cm slows down uniformly si s4dru)qewx0z x.m/ (8jh/bfrom 8.40 m/s to rest over a r0u w8zhxebi./qsj 4s(/xd)mdistance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down qyw/thmnl2- ,uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take n-hw/qtyl,2m for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at2:: frgewt lu0 a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angula:rw ft:e2ugl0r acceleration 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 rsuvi4 40vk(0jem zw 1x:n;wo. If a 30 cm long wrench is usxsw:4ro n00m4ezv iwk 1jv;(ued, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a zs1 )-cyb c r vx/8xn7o2x9gds30 cm long wrench is usbn2zs y oxgdxrc8v/x c9)s7-1ed, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of im/ wf osxa)3x3nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modelv slv,sm2lk;f)97+x ;w *o grmm(dtcped as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m;ltmgs,29vlc wd o+m k ;()mp7f *sxrv is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionlese3ol-d)l rfw 1s axis thought the center O. A rope wrapped around fwdor-lle)31 the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted aboutv/tr1e4f+*z.sj b,t u ftg u1w a frictionless axis thought the center O. A rope wrapped around the outer r *vtrb+t4w/u ujf.s1z gfet,1 adius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 ygt+ 6dx 8z(dwuj4s* lhinged at one end. The rod is initially held in the horizontal position, and then releaseddt* +dg6u8 l(y j4swxz as the free end is allowed to fall. What is the angular acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Neglecb9wnkb8 tz(6r.sik 2yt the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the whbk8nsz 6.k 9bwi2(rtyeel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangsl ltvf 4g/(9sk on a rope wrapped around a frictionless disk pulley of mass 7.07 kg andl9/vk 4sflt(g radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless diskd.,crohc82 ok pulley of mass 7.o, o crk.28dch07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to st;1)amud;(8gvx: y(ddwp k j geore energy. If it is 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 inerm0(53gk g+kjyrt9 x bttia 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 m starts from kdc6x: v wz3520m wy gnxl+eu(rest and rolls without slipping down a 1.0-m high inclined plane. What is the 5l2 zx vw0d6wmn:+yeg(x ck3uspeed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and r:rg7qi v5ugj*,mn79t rz sue0adius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to res0nrs9g 7g* ier,u u7q5zm:tjvt?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and all.q,kr4- mls6ewdn0 htgbu* 4b owed to roll down an inclined plane. How fast is it moving after dropp4-e nlgrhb, 6*kmwusbt0 .d 4qing a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls 3 +lxi 8iqye(na 7y/xewithout slipping down a 35e incline that is 7.0 m long. Assume it started froil+ya (8qi/xex7n3y e m rest. The moment 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 1;kw9xmzl.i w 2tboce/z4 s :,b 4bubrchanges 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 i2 ;gv +.cn gydaq4)ksa (wju+gnertia 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 arms extended has a momex3 a-4c6 mcrront of inertia aomr4c -r3c6 xof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?