Angular displacement is usually expre d/7 cip*8 lvm.uxgwo4ss in units of

  Angular velocity is expressed in units h3 0zzi bkx pbrl)o7x6pt/8)tof

  Angular acceleration4tus80 4pf uopu /atqr2eu4 )m is expressed in units of

  A boy and a girl are riding on a merry-go-round which is turning 1gejg. ce(rg 3pw ht+1/i-jnc at a constant rate. The boy is near the outer edge, and the girl is closer to jic+g-n1/cjt.gh epgr 1(w3ethe center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a con980shgl h grcc)c3 u: er06gqbstant rate. The boy is near the outer edge, and the girhc)ug : rcqge6rch s3l 89bg00l is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whic:s9,gd xa:tws1m u1t vh is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whowm1a9s tu,t: v sx1g:d has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is qu01- tamx/ nwturning at a constant rate. The boy is near the outer edge, while the girl is cla0 n/xwtu1q- moser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a consta+5skw bu9q mhec80cl7 0l t6cont rate. The boy is near the ouoe 8cw9bl5 s7 umch0qtc+6kl 0ter edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatju0 sv -j+cipp r315rhing. Which of the following is an accurate sp 0rp1rsj3jiv - 5ch+utatement?

  Rolling without slipping dfmi,siunp 78 g1c9l m9d yiufhv5 )k3(epends on

  Two equal forces are applied to a door. ( 5nc;dgdrsh(xfu3 g6 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 force exerts the greater toru 5(g (s6;drngx3cfdhque?

  Two equal forces are applied to a door at the doorknob. zxib.rrza4 +o )ir /wnm qy1+e-h1)zg The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Whi yr4e arr1+ +bzioiq.mn /)whz 1x)g-zch force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. mrf6j6sy a6p -jxyihkh ;,4z9The first force is twice as large as the second force. The ratiyaj i9,4 y 6sm6z-hk;6fh xrpjo of the torque of the first to the torque of the second is

  What is the quantity used to measure an objecto6d,kt,s-bq/c lksx q3fw0mr)d7u .z's resistance to changes in rotatirwmkq.uzs,,cq ofb) - tks6dxd 7/3l0on?

  Consider two uniform sov9al/v. 2) /ojn 80jdvnuy(8bxvk fvd lid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the s)( bovkfdn/90avvunx .dlvy2v 88jj /maller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius oob 8: 4( hh3iaf0ntz7jjhd1 sxf the other. The ratio n7ih1zj08hh t( a3:d f4jbso xof 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 and twice the iri/bs 6hx5p:ew6i+qs pv43wdiameter of the other. The ratio of the larger moment of inertia psiip646x:i5bw eqvh /3+ r swto that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these *f5+y o)lr qphmi9w13io 8mnf are increased to 2M and 3R, what happens to the sphere's moment of inertwp9fm*58oqr3olm+1 ifyh) inia about a central axis?

  If a constant net torque is applied to an object, t4sh16ko6 zc unhat object will

  The moment of inertia of a sostd5zao0zzl 2sy1 :(.g zam)( jq)frclid cylinder 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 massrdd p;- o;t. .f)uj/jyxlc0kn of 10 kg and a radius 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.)kn/pju. ddxf-y. 0;cojrt;l

  Suppose a solid sphere of mass M and raoz cq / wk.(+kxip42ah*k*uc2nr.mp u dius R rolls without slipping down an inclined plane starting from rest. The linzhpic/+xwak4(.cqkm*ku*pru2 2 .o near velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass 1o/m 3lpilma u6.)mo /pvw0jkM and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphl kvmop30 .ium//1wl pja 6m)oere at the bottom of the incline depends on

  "The total angular momentum of a system of particlesd7 uo:qt + dgcla1l2t2 changes when a net external force acts on the system." 2t:uda27qt +l1 o gdcl This statement is

  In what circumstances can the angular velocity oebd;1b;eh)ifz+5: t7f6 bo /qtep jwwf system of particles change without any change in the sys:w f )hb1jbbiwtp 65q feoed7t;ze/+;tem's angular momentum?

  The Earth orbits the(yzt.s0 )b-hzu i7cks g64tal Sun in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular a iytt-gu60s)cb hl7ks4(. zz momentum about the Sun?

  The Earth moves about the Sun inzit cw )43rzc/ggh:z7 an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting spe/ 7 hct4grz zig:3zc)wed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hisu cxn/oep e7e *0/oh*n outstretched arms close to his body. What /o nu h0*expcnoe7 e*/happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in -.yfaxuuar.m03/jsz cuybphk,7m6 4his outstretched arms close to his body. What happens to h 0/y3 u h.csfa 47xuzky,aju6mmp.r-bis rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by /smktqy (*ak uuk+1 290lfrfu pulling in his outstretched arms close to his body. What happens to his moment of m+ukt uq0/9s ur(yaffkl2k*1 inertia about the axis of rotation?

State the law of conservation of angular momentumvs5a, 3norkm4 .

  What arc length does the Earth travel in a three month period in its nearly circt9.l w s*cw1deijt0 d9km hlzjk +-x+.ular orbit about the Sun with a radz-l.j *tk j+dc1it .lxwm9dhs+ w90keius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of +z,yil *egco, 0.30 m. What distance does the tip of thzyeoi,c*+ ,gle second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute e/ 9teev q+5sxcwetsta9 cc54a .7jh 7equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions insm4zx2 p;d; fw 4.0 s. What is the frequency of the wheel's rotati2 px;df4sm wz;on?

  A pulsar (a rotating neutbdrja zoq(5zumx*z:(j 3 -bd 470pcwaron star) emits pulses at a frequency of 0.40 kHz. The p cq ardd30zx( 5b7bz u(azjmowp*4-:jeriod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle dor )cu7k ;p.iiu 62j(d(noe7 dkmnlkk-es it turn in 0.20 s?(cuku epk7nm(.ik6- )2dj kdl;iro 7n

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on t906l (48bz uifbez bnghe outer r( lef gibu4b 9zbzn068im move in 2.1 s?

  A bicycle wheel rotates unifor h2mb wf(.ql fa:rs2o:mly through 2.0 revolutions in 4.0 s. What is the average angular speed of th sl. r:fmh22f( wq:aobe wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What i1awwzn(d:;l:u/ 8tyt 9cl wz z0fk we;s the linear speed of a point 0.10 l1; zndze8 0;wkw:cwl9wtuy (fta :z/ m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Th67e:glq7f8hgb1spjz e cable which moves the car is driven by a pulley with diamete 6fqb:sj7hg1z8e lg p7r 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 angular spee43h,qddp lm9 ad of 2.0 rad/s. What is the linear speed of a point on the wheel's pd hqadml 9,43rim?

  The cutting cord on a gas-powered weed c,g.7ghr .ft n g:8r3x/hplaloutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear sprfgn/83 hp o7g.aht:l x.lgr,eed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of +( 20e skkdyf/3oadv e2.0 rad/s. What is the centripetal accele3s0va2 yfd( +kdkoee/ ration of a point on the wheel's rim?

  What is the centripetal acceleration of a point4 a4dwz-mgokc 9mfm 4dof0xi+b m11 )c on the perimeter of a bicycle wheel af19dcmc 0om44xg +w kb o41if dmz)-mof diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (r+9drh50nk q9 *tni -op.nsybq pm) must a circular, rotating space station (r = 1000p-9+qk5r soh tn*9nq.d b in0y m) 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 speed tlu dxlqu 9z -5vf;4d9of 20 m/s. The maximum centripetal force (pduuzf9ll t9;d- x4vq5rovided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating +s2)nnfn0q1m hv0(e n; 3n qdnfrqwa -a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum cen0v 0aedhn (s;2qmnn ffn)3qn-1q rn+wtripetal force (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, is whirled around in a- g b(imh;l2mv5zjko( smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed can the mass have imo 5v-im2k;l h gzbj((f the string is not to break?

  A bowling ball of mass 7.5 kg and rxqw(;ih 93;pg h9:g h;-iogwtd.b tljadius 9.0 cm rolls without slipping 10 m down hd( pxg:;9ww3bg9hj q;toi g. ihtl-; 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 with a constant angular acceleration o itbo h,0e;tr-f $4.5 rad/s^2$. 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 angular accele d8rlzw6ro0fsb8x 2)sration 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 ti75-qbs je.qpu s2qg, pov:wf0re rotate after starting from rest and acc:v0bj7 fsu,.o5p qq qpwe2-s gelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest,qein v r(93 pow,go;c5 and 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 constant anrad13t02z cj oq dq0leh t+x62gular acceleratirlq3e d 2d2qj0ttoxha c6+0 1zon of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and rm f k)cvewt12v)*a 3 mff5qst:eaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is)c3 q1f2 ktvwfem:amf) 5t v*s the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m4cbh/;sw7l t c8,q u+l hi-be xnlmq06/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates i/h7l+0,l qe4n;l-w cq8chs i u xbtbm6n coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to res5vf5w h,y03b2b ml(jo:y zzg,f pmg8g t over a hlogz50 z y gw83j:2vmy,m,g ( f5bpbfdistance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/ssj 8gx/vqhtbt*wi3. (/w fgi. to rest over a distance of 115 m. How long doesw/*q .(j/gthxi bit8v.wg3sf it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 revjj4(89+ hro c5yt-ko zsg9m1 bgdc6y n/min. When switched off, it rotates 50.0 times at a constant angular acceleration mhyc9 8nb(z 6-5j 91o+ ry4sgj cgtkodbefore 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 a 30 2ka9 n 85jvphmcz /uzj(i0tm1 nxp1vi7l9kw2 cm long mx81 v9mnzvnptii1/k29 kjph(7 c5a0 ljzwu2 wrench is used, 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 )q0fm9hmhj:ga 30 cm long wrench is used, what is the magnitude of the force required when the force applied j9ghfqh: )0 mmat $53^{\circ}$ to the wrench?

  A wheel with moment of inertinho48wxr9vsd 7s e*.pa $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule isgom;w6 pc)bl0 modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the ogl bo;w06c p)mrigin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought pvs ny x)kh us: /0z7iuh+ox,8the center O. A rx i/v8usop: ,zhuhk0syn+)x7 ope wrapped 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 max b-j i*ovy+f,0;9zh741aknj plyjw mss 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer fa1bpy 7-j*hwjn0+mi;yokljzv x4, 9radius $R_1$ = 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 w*p*phoyk +kqwzrr6.83vkrrd c09 q *the horizontal position, and then rewc pr6hr kr0k3zqo9 **.vqpr+d 8 kwy*leased 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 7b9 gm0fusmt9;ukpbg 8 xvh07of radius 30 cm and mass 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 cm for 4.1 s, what line70xvf0 mbgts bkpm;h9 g u9u87ar speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictio p : anpir1m3s:-gx/nfnless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration /1gxa:inpmn : p-rf3sof the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless681dam5mmo6c/ 1s jpnlcf ::l ypkbj8 disk pulley of mass 7.07618skadpjm :m1bpnc6f8 5/jl:cy mol kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to storennrsvm. *vz; 8lq5 4dw $1.00 \times 10^{6} \; J$ 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 m8ix83 3zxedb1iyp6zinertia 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 qnv(dnf/xz5t.q. iz 9f2cf+ h1.0 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 reaches thct(q nizf +2v.hq.f9znx f 5/de bottom of the inclined plane?

  A solid sphere of mass 1.0 k-5w b 9znxq*bim)3:xsc5gpu i g and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climbcsum )9nqi5 g*-:bxi5 p 3zwbx before coming to rest?

  A hoop of radius 0.50 m yt3r2 d3g ktw:k85*pk1izxpt and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?3pt *:1 5kk2wt3t ipkz8ygrxd

A solid sphere of mass 1.5 kg and radius 7ed48q t rtp5c15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given 54p 8tqd7cterby $I = (2/5)MR^2$.
(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 changes by l+ m; ib-znflj0 kaw i*a1m).e$20 \; kgm^{2}/s$ 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 inertia of4p u51k*pvj fl $5.0 \; kgm^{2}$ 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 5vm(eav 1) y;+ex vu,sq.00 rad/s with arms extended has a moment of inertia of qevvuv);xes(ym1a+ ,
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?