Angular displacement is usually express /owjiso9 g:it ip2s4- in units of

  Angular velocity is expressed in units pr1i2 r- -:qm+i 8( yy.1coqayzhsfgnof

  Angular acceleration is expressed: nn:gfq0rg9x fcdtp91 ca++ d in units of

  A boy and a girl are riding on a merry-go-round whicm* k*uqn eqtk,vlw974h is turning at a constant ratkn9,wuvqq4 m*lk7et*e. 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 aq*pw h7(tr 1pu merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has thehurp(t71pq* w greater angular speed?

  A boy and a girl are 0h z/mfdb;.ebriding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the zbhf; medb .0/greater linear speed?

  A boy and a girl are riding a merry-go-round which is t y2v1j;5 8xtix1j)0 y3desa fmkn,gzdurning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceler fxe0tvn 5x1)yddj8 ;a,1 sigm 32jyzkation?

  A boy and a girl are riding a merry-go-round which is turning at a constant p:wp *qvsi1hti 0/l -lrate. The boy is near the outer edge, while the girl is closer to the center. Wh:ppw1li0hi lqt*-v/s o has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the followxxqqd z bfyedm6p:j. hg279p60mq 7 ;iing is an accurate staf:qh;xpqi6q72zje6d p.bmy0m d7 9gx tement?

  Rolling without slipping depends fq0 2/m dpb3k 0ef:p i4+bgxev3afo;qon

  Two equal forces are applied to a door. The first force idwix e7mvdu 67n.gu5bj1 6ny7s 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 ex.gwj76und ydmv17x7b une i65erts the greater torque?

  Two equal forces are applied to a door at the doorknob. Tm;ez p7m zmcsk-8v*0i he first force is applied perpendicular sm0;mv*-ip7z8 emz ck to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to ym -w5,tsw2kv the door. The first force is twice as large as the secyv 5k w2stw-m,ond 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 in rot*syq( y m rkofucz-)3x)ki4q 5ati*u -3y q4k rsmk)5x)izqofyc(on?

  Consider two uniform solid spheresz, 2* sr neevho)d-r2c where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment ofcznvorrds e*2-e2)h, inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, u w3z10 antfm8k6s0 wbk6n ,ktbut one has twice the radius of the other.16tsn,tamu k8nf b3w60 wk0zk The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one h l7 wig .bptffwsj;6/4as twice the mass and twice the diameter of the other. The ratio of the larger moment of inert.iblg4/6 7w t;wpjsffia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and p05dkcnkeed;acs(y z+( ;h h, radius R. If these are increased to 2M and 3R, what happhhs ;dkz(d p,cna;0 (+eyec5kens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wih6r3a zlgc e8wxw(b.5h:0q t cll

  The moment of inertia of a solid cylinnhw 9. gj4cs1ej(6sgwder 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 of 10 *5.u2;p;spm cyrmkb m 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 mpr mb5;u;*mpkc2 .s yare uniform disks.

  Suppose a solid sphere of mass M and radius R rolls withoynkho)zua 74,v b 50 + em6jr tgf1(/pa(epkwout slipping down an inclined plane starting from rest. The linear velocityvpkfu0e +r,7()oenokbpy1a(twz agjm/54 h6 of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of x p za(51s vnu2tob:.k)9mbzsmass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends ons)bz:5x9pau ksvt.(nm1z 2o b

  "The total angular momentum of a system of particles changes +u-vm0 mrzw a,when a net external force acts on the system." This statement ,w u+rm-a m0vzis

  In what circumstances can the angular velocity of system of p o rmvzy0r6u *z.x-a)barticles change without any change in t m .x0-vo)rz*ayubr 6zhe system's angular momentum?

  The Earth orbits the Sun in an eld jq)wsct8mw e o7; (uul6dy3twgjw(p/ 9.2rfliptical orbit. Ignore any friction which may be present. What happens over ftm7 qwgp w ;/joww)j(.u6yd8d(u2lt9er cs3 time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. tqpq42bz3:j snc 0gy l6)bs(m As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth abos 34mypgj2 6s(b) :bnqcqz 0ltut the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outst0;t/f,v7 an aa6j4hmd wc9jkzretched arms close to his body. What happens to his angular momentum about the axiak6n tj,cfzad9 h470w;a m/vjs of rotation?

  An ice skater performs a pirouette (a fast spin) by px3 fhjeo:j5 5;zdrx:za( rzx)ulling in his outstretched arms close to his body. What happens to his rotdo5r:j z; xjxrfz:(z3e a5)xhational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outste2hfwgk8/5v2x5g u 6 ns*zkk vdz6n.*hot z-xretched arms close to his body. What happens to his moment of inertia about the axis of zw 8 -/zsv2o5kfgehu *65 x6hvt2dnzkg.*xn krotation?

State the law of conservation of angul39pzts-vk 5f zokvx 2(ar momentum.

  What arc length does the Earth travel in a three month period wwg; dh4 90b+fwe0q5pcwbb6xin its nearly circular orbit about the Sun with aw+p4fd5w6 0bqh; becxww9g 0b radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0y/* z0/v y6vvnxfmrm0.30 m. What distance does the tip of the second hand sweep through yfnxvy/rzvv 6*00mm/ in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions ph*fdx f,kz7x,zxk)m1 xpjgc(v:k x, 52mwl 7t er minute equivalent to?

  A bicycle wheel rotates unifh b2l ou5ua.j/ormly through 2.0 revolutions in 4.0 s. What is the frequency of the wh /uj .ohl25aubeel's rotation?

  A pulsar (a rotating neutron star) emitsprctz e tz):64 pulses at a frequency of 0.40 kHz. The pe t4tcr zzp6):eriod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it tur4bsscuj7iq l87 kp68+,t4csrh .r nld n in 0.20 sk 7duq7si48.+ lhcp6tb8rs sc4 nlr,j?

  A wheel of diameter 26 cm turns at 1500 rpm. Howa1 ,l/fmpywfey d((4v far will a point on the outer rim move in 2.1pde m1l4ff/ w(ay, (yv s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is sl kmmy814 a *v*kaoxw 720o8nxdatn, the averag t mkvda x*mnkaosw*any8,l4x0 o278 1e angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. gbn14qd-oh*v mt47dc9 ; :kep 5cdkge What is the linear speed of a poinh cmdtg5dbk1k4gn- odq * epe;:9vc4 7t 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable w9 vv9bhg:4p nof lu2mh yv,p))hich moves the car is driven by a pulley with diameter 3.0 m. Assumihv29 p)oy u9f bh,4v:)pglvn mng 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 rtl8oxjo.fwjlb d3ft9t m,3-c (pi3*gotating with a constant angular speed of 2.0 rad/s. What mtpxt-( *j l9lb.gj3c,otffdw338io is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. I(5 /scg3:l4f oopyu2 n;j5ts)u m mtuwf the motor rotates at the rate of 20 rev/s, what iotjn )tmlpw/s;4o:ucsfy 2u355m( u gs the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular 2q1byil wk+ b5b9g, gs3ihxm5speed of 2.0 rad/s. What is the centripetal acceleration of a point on the5sgh21 qm3w x9+biyglibk5 b, wheel's rim?

  What is the centripetal acceleration of a point xxc17mk(td. jon the perimeter of a bicycle wh1t ( .d7xkcjxmeel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station zjk,4 rbt h,;v(r = 1000 m) rotate to produ ,j4 ,vzr;bhktce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wi(v,c,q rs/y vy7f6fgr*v pnz:th a speed of 20 m/s. The maximum centripetal force (provided by static friction) isr/ ,f*vzqv7sf:y rp(v cg6ny , $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curld,sisb,0 mdrz1 19vwg+ k5apve of radius 50 m with a speed of 20 m/s. 9m1a5k1 w,,zgvp isd b +srdl0The maximum centripetal 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, -zc-ud0k4bf,a.x f pmis whirled around in a smooth level table. If the maximum tension that the string can withstandc,4m.k -0-zuxp affdb 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 with b*s2nyzx u),qout slipping 10 m down a lanz,u n)xy*bq2s e 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 ang/q 2+,(ha2ritd*wsmp1 c*zxa h* vwyiular 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 angular accelerat xe6/zpm gv)m .b0,ljos*r y;kion 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 aut l8l(j5a47f xojl;oal --- fhwjs n w)h2i6egyomobile tire rotate after starting from reslxl 4)jnf7( laoh;-ijgljoaf5 s-w-8h w2e6yt 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 a6natbexa8qsp 9-ph0p ,+nv)sj 94 mt 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 angular accelx 9tqa,h9o znrx03o(fkj-cx-eration of qt fcoxx 9anzkr(j3 -9ox,0-h$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular sp7ws3 rcugnl 4scgt46 if) ,7bub9+djfeed of 6.0 rad/s while turning through 2.0 revolutions. What is the averc79f +7bb4drugfsu6t n43i j) gswl, cage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to r xem0(lp.)tv nia f5d:est over a distance of 11ipmfv: txle an).( 5d05 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm sgndb4s,:qtc l3h)r/ zvv */j mlows down uniformly from 8.40 m/s to rest over a distance of 115 m. Wlc*/vmq jtr: dbh3g/zv4), snhat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest 9q icgiz,i9xir+ w3x2over a distance of 115 m. How long does it take forg9r +29xwqzi, xi ic3i the wheel to come to the stop?

  A centrifuge in a medical laboratory rotat(5s t.)vix0 a9 zdsbfv*nvks:es at a rotational speed of 3600 rev/min. When switched off, it rotatesis9x sa*d nbs(v ).:05vtzkf v 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 tightening to a torque of 90 Nm. If a 30 cm lo 78pnq l7 exbbc7v.0wlxnux2 z a(.x9ing wrench is used, what is zl82c0 axiq( pwb7v7u.nexlb nx7.9xthe magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque ofg:ef kdl+s*c * 90 Nm. If a 30 cm longd + **sckf:egl wrench is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner5xsjchke0 ;8 gry vfs 8.rvn**tia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows:+wvvg*uvw +cdzt :m7. mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x =.7+wd *mt: uw+vgvcvz 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about ak gzp :(kqkl6na) l(4mw /)zum frictionless axis thought the center O. A rope wrapped around the oute(4 zwma u6pk(kzl gq/mln)k) :r 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 abou7n rfj+s46wf zt a frictionless axis thought the center O. A rope wrapped around the outer snfz 7j +fw64rradius $R_1$ = 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 yr+ jj3et;u o)z v,3r.od6w1hojr u;khinged at one end. 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 asr1+uuzj;r.j hj6,;3vyrt eok )dow o3 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 30zywx 0w9q9fj6 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 radiww 6 yq0f9zjx9us 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 a 8dk y.e,t,bbxround a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is t,td e 8y.kx,bbhe angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around amnl07 3 f dk)g18csgqq frictionless disk pulley of mass cgf07mq 38s lkq ndg1)7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store en8rx).jafy9j s*v iov ,ergy. 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 inertisf o 3d /afgv3)s,n7 ;ofhu6yhqry vu(5/(wbka 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 f k-kltz70vk- *80cl jbjl(6gfys2s rh rom rest and rolls without slipping downh-*bl0c sglzlj0t vy-68k2 jrfk k(7 s a 1.0-m high inclined plane. What is the speed of the sphere when it reaches 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 mw7 4r;-ap6nth00 fu *anxzbut/s. How hig ap uxa04;b6ntz rwn70hut- f*h up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowxhsywh sb* 7v(y f+;h9ed to roll down an inclined plane. How fast is it moving after droppiyb +f*s7h9ys xhvh;( wng a vertical distance of 3.0 m?

A solid sphere of mass sq g5nk 7,h;w4k: bxrc *on:qn1.5 kg and radius 15 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 gix5b s*h : 7g4:orqkw nnn;q,ckven 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 momzlh; 77s h3lqmrpml) r/4v-dwentum 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 inertia c: m+w 0hn -bhog7*b;dm.xdhz 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 momeqx4 d*3m:ec7e+uhajknt of inertia of ed+ *xquj7e3cah:m4k
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?