Angular displacement is usually exp soy( s+;o(0 uzk24gqv)mxgam ress in units of

  Angular velocity is expressed in uni8o .(yhof,v jw59mesets of

  Angular accelerationb z5n,77hw-re-ws tzr is expressed in units of

  A boy and a girl are riding on a merry-go-round whics)aadpvf :mhb5 7gp: *h is turning at a constant rate. The boy is near the outer edge, and the gi )bps:ph gam75a*f:vdrl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a coh0d/:kxei92 f7pu h2tl-ib89gx f ezbnstant rate. The boy is near the outer edge, and the girl is closer to the center. Whx9i/x2ti ekbl8z gu92f hp :7 b0hed-fo has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is tuxifn.y +fbf5 ;rning at a constant rate. The boy is nfb;yn 5x+ffi. ear the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding o9k) vca;fj bnuae-j, * hh(4aa merry-go-round which is turning at a constant rate. The bh o4aau-(,9n)* a ejj;vckbf hoy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which i9hsqu-/ ar:uz j+q/ jfs turning at a constant rate. The boy is near the outer ed/rq 9h /-azujj:qsu f+ge, 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 an acgbz-7.2og 1v+ stit,eqz 4zpmcurate stotgg 47eq +v.t2 1,spmzz iz-batement?

  Rolling without slipping depends dsi++43xea hmdwn ;vp)a:t/lon

  Two equal forces are applied to a door. The first force is apot5tygk hde32 r +0;qhplied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the grt3hh2tdq0o5+k ; eyr geater torque?

  Two equal forces are applied9 5 5t+czoyt ap/6rfsc to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30efp9azc y5oc /65rts+t to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular lfoz0v),ou() i ej+vpv u09b lto the door. The first force is twice as large as the second force. The ratio of the torqv 09vf 0vzbl +leu) uo),jipo(ue of the first to the torque of the second is

  What is the quantity used to measure 95oskdm. u zu+an object's resistance to changes in rotatio+s5ud9ou z.k mn?

  Consider two uniform solid spheres where both have the same diameter, but one hn lscos3o+zvc0,uj3j -oo8m7p *e8 rtas twice the mass of the otz*v+ m8l ocpj0 8n7r, o3- ut3osjseocher. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice spk8 zwmd;zzdh0wi d . (b..a5the radius of the otherww0hz;masi(.db8d.zz. pd 5k. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass an7y,chrr c-; mrd twice the diameter of the other. Tcrrc7;y- ,mrhhe ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radiu 1nbhrk+j+z)5rlt+sy1blth5s po) v7s R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertiabs5po ) ++7lksl +b1vyht1)5tjn zr rh about a central axis?

  If a constant net torqdrkv-l9a uy4bxb an.jhq/sq23 k44/g ue is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is giv u hq/ nqfblk:yn1r.4no.4b60ja(rr e en 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 15un5deiuerdg)03 hm: 90 kg, one wheel of which has a mass of 10 kg and a radiuseddne5r 0)gm9ui3:u h of 30 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 and radius Rna+;6+arfah xm ds/:-fim;iz rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depend+idx;+aim a s6m :/-hzfafn;r s on

  Suppose a solid sphere of mass M and radius R rolls withoufkoszor.w ba1c -3 d.8t slipping down an inclined plane staszboakodfw3 r1.8. - crting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particlw 2enp .bdg/m4es changes when a net external force acts on the system." T4 ngw.pdmb/e2 his statement is

  In what circumstances can the angular velocity of system of particle42t6 kqn9 ueq-22v vgatjc9res change without any change in the system's angularea22t6te qv9-4n9u crjg2 qvk momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignoremn17pcqu 7m /fv4ddn 4 any friction which may be present. What happens over time to the Ea4c m1 dfqmn7pd4n u/v7rth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves cloy (vqs( 5zi-bese to the Sun, then which of the following best describes the orbiting ss- ezvqi(y( b5peed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche8yfs9zx db73xc9 y7fz/ 4c q2m rntx9td arms close to his body. What happens to h7q9/xt7snbd 39 r4zt92f yy czmc xfx8is angular momentum about the axis of rotation?

  An ice skater performs a pirouetteb/;k/d-iy /wd* i.1kcwf slc26fg kld (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy abou2cl kd*.w / by/fgci 6-w/ils;1kdf dkt the axis of rotation?

  An ice skater performs a pirouette (ag*7ili9q sbv38i( y j o)bclk1 fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of ii*7ysbvgo3jb ll ki (8iq19 )cnertia about the axis of rotation?

State the law of const4dda zrh jwo67.s s52zucu5uht14f0 ervation of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly c 3v 6txxd:pjk;ircular 6x j:tx3p;k vdorbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does the ti/0-oyw3am2 qs qy lgj7qe*n c5p o 2mj3g sy e0wy-/onaq57cq*lqf the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivale4 x(38v w7) 4i kdiych4yrqiqunt to?

  A bicycle wheel rotates unifm/s3),qrt)wb7ru ww aormly through 2.0 revolutions in 4.0 s. What is the frequency of the )/a)w, mtu3br7qwwrs wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.svvb. s4n/k1fd( u+wn/1wa mryn ,rh1 40 kHz. The period.ry/41rf1/ks nnd n( , sab +wwhmv1vu of its rotation is

  A phonograph record rotates at 45 rp.ydprf+,c pcu/l z:7hf;*n)v mm-y psm. Through what angle does it turn in 0.20 s*y mnld .ps/p, hyp c);:m+7f-ucfvzr?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on 2lmqq)lh m( tv-ek*k(the outer ri2e*t -)vqqhm( klm l(km move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. ,rd dihqi -x+juqe /3/What is the average angular speed o/-i udrj hdxe3i /qq,+f the wheel?

  A bicycle wheel rotates unifothv lg,:7qnxi q4.g2 armly through 2.0 revolutions in 4.0 s. What is the linear speed of a poinh2 ,4qtgg7ax in. lvq:t 0.10 m from the center of the wheel?

  A cable car at a ski re 9:1i izz7 lu3:vjoluhsort carries skiers a distance of 6.8 km. The cable which moves the 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 tr 1u:3v7lzz ihju9li: oip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a consiq3gach r*f *:2v5n dotant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rimi5: 3rqo2advg*cn h *f?

  The cutting cord on a gas-powered weed cutter is 0.16 m i/ncnrh;h/t 62r.xd usn length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord.6 n2 d;unchhr t/rs/x?

  A wheel of radius 1.0 m is rotating with a constant angult yfmv:-,b*zg ba d,n+ar speed of 2.0 rad/s. What is the bty ,* :fgazb-,dn+mvcentripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle ja2 *;gskmn x5wheel of d5gxs*2amk j; niameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotatim 0u2wjihg mn0 h4w55hng space station (r = 1000 m)4w2j05mmwhgu i n0h 5h rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speede ,f * mrg6uhiu6f)fhlha5b :) of 20 m/s. The maximum 5f f,l6):af * hig)hb 6emuruhcentripetal 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,,v9i uvauk- x m with a speed of 20 m/s. The maximum centripe9-uu av,i v,kxtal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attachhloi1/;0 jzjy*z6j9vvpt ti+ ed to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum1oj9*zvhtj6+p/tj0iv ziy ; l tension 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 without slipping 10 m do 7-bxe:;kv ihcbeu *m;wn a lane at 4.c;ki-ve;u h em x:b*b73 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 adgi( x bap1w dth17m/8-vfvr 3 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 constant-7c7ynr6 7drm:3ocg j pqv 7pf 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 startind7li2dlf1t76ffv ) 6zw 3isvpg from resvl7p)i f36wsi72fd1f lz6td vt and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accel8;m .pt4mqv dy 7u9-i ui1q+ahru9yh7o yiy6xeration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating aty/nw*vo*- hfs 20 rad/s decelerates with a constant angular acceleratio y-v*s wh*/fnon 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 of 6.0 r u-ulhh4x8pb; ad/s while turning through 2.0 revolutpb ux4luh;h-8ions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 can6,u. hujm p9m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheelm9 u,jpu6n. ah rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows p e ws60gcbtf eh+jbsr5hf5h/*j *00qk8 -bhkdown uniformly from 8.40 m/s to rest over a distance of 115 m. What is the ahgk+sh0b*he bcs5ej-wpfk 6 /8r500j*th qbf ngular acceleration?

  A wheel of diameter ofz x+n1q( hinwc)+* lbc.1rh6bkrh 7qk 68.0 cm slows down uniformly from 8.40 m/s to rest over a distann16 x( rzh kq1crb)+ 7qbikw+l hn*ch.ce 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 rotational speed of y yb)d.f09ajf 3600 rev/min. When switched off,.f0)bjydy9 af it rotates 50.0 times at a constant angular 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 tighteni w/l/ap)lb9o eng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is pere a/p olw)9/lbpendicular to the wrench?

  The bolts on a car w/ v vb;d rxi6 7fsl0z0gt(9s wydytz36heel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the fo/tvb06x3;yzwz6sr fdgil y ts (d709 vrce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine.ax(l(h2rnko (yj9 eu3uly4 f rtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mode-, wd ac*r kw3 xuvg07:yk yp6e(fih6yled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. 0cwf7 ye dgp *3xk-6w(yri6kua:hvy, What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axwh (bd2 q6hgxaa: .(;x9ynvrdis thought the center O. A rope wrappehv9(w2ay g: ;6b qd.x( nardxhd around 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 abouc9 t4hb jq,:vct a frictionless axis thought the center O. A rope wrapped around the outer c,c9jtv4 bhq: 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) 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. The rod is initially held in the rpr 7a/rxs:(nq2wuq. nn vm * lrd93*vhorizontal posn*vx v2 u7.malpnw3:r*q/9q rd sn( rrition, and then released 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 lt te0o3/* jgtbe a ring of radius 30 cm and mass 1.5 kg. Neglect the mljt0*to gt/3e ass 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 wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictu04kng qj1:8bug7 foi ionless disk pulley of mass 7.07 kg and radius 66.0 cm.14q8gib0:uk7jg nfuo What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rop5q1o9 z6aqbjtxw-+ ff e wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 -j x15+bfofq 9q6atw zcm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is req3 ds;1( tefvtq.i8ez 2lxzm,quired 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 )eaz -6x;byx cinertia 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 179r4dlp ,6xsx cw,m m7 dhb5gk.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reakps65b9,r gx 7xhdm7wmd l c,4ches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/ r+lr 7wmcsvf- i6twcy )tu.)0s. How high up an inclined plane can it climb before com)tis )0-t+6u lr7y wwvrf.ccming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allow lfc 3n4czb9p0s i4*ys nqqp;:ij.ygtm xp8:5ed to roll down an inclined plane. How np nc9 :t;ixm0:8qiypq b5lcjg.sys4z3p 4 f*fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cpdz4ud8bg+gef2 ng1 .m rolls without slipping down a 35e inclineu. db14p2fn+ggd8eg z that is 7.0 m long. Assume it started from 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 cqb n)vr2)c tl.hanges 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 inerti:nu)r+ qjjld1ku: +cra 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 extenda:;jj gbvj4+8sf2 ei ztjo.l0 ed has a moment of inertia i08je24b +g lvjt asjj;z:of. of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?