Angular displacement is usually exprr0 qj sxo s fzb8z0tpn:(a k.eg1z2uu+//h,ttess in units of

  Angular velocity is expressed in .s5a1w j w 2p-k)fi5y,pr2pkjiv4vrfunits of

  Angular acceleration is expressed 9j xncc6 - zuzk/ ,:vqg0lr,zbin units of

  A boy and a girl are riding on a merry-go-rou*dy*gj9a jjnat/k 87ond which is turning at a constant rate. The boy is neaj/ j 8otndg a9aj*ky7*r 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-rouwudv2w/e 3p8abid7 /wnd which is turning at a constant rate. The boy is n 3 2w/wpb/u8veddi7waear the outer edge, 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-round d 9f./zjho01cfapz1lwhich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the grea 0zzc9aj 1. folhfpd/1ter linear speed?

  A boy and a girl are riding a merry-go-ro q1p 3th)/sjlp2d3 h 0 tmr76kpit0uq qdrie:6und 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 acceleratk0r:pd3)16 it q3hrtqh st p7 lqm6u/d0ipje2ion?

  A boy and a girl are riding a merry-go-round which is turning at a constant ;;:/q ajyfacd: 6 igfdrate. The boy is near the outer edg ;a ygf:i :j6fc/d;aqde, 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 ai;e. f4yzxkc 3n accurate stat4.c3 xz; yiekfement?

  Rolling without slipping depends o3wxd k3t mpv /-v.6lrtn

  Two equal forces are ap1htm / n6ab. f3m(mhfjplied to a door. The first force is applied at the midpoint of the door;m(f1mj 3b6/ma .hhf tn the second 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 first force is f:f+a1 mtopl-applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater:f+1 am f-tplo torque?

  Two forces are applied to a doorknob, perpendicular7l+ +n(uman;z9 j rxpy to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the su9pnnrz axj 7(+ym;+lecond is

  What is the quantity used to measure an object's resistance to changes i6:. d*wozj9 gnl x(gvnn rotationn x*j:d.nz9 6lg vo(wg?

  Consider two uniform solid spheres where both have the same diametyin)p n -/yx 8hx-riv7er, but one has twice the mass of the other. The ratio of the larger moment of inertia to that ofxyyp -rv7/i - nxni)h8 the smaller moment of inertia is

  Two uniform solid spherezikrl-xcmsx t6 : 37c i,wmfggn,-o/3 s have the same mass, but one has twice the radius of the other. The ratio of the larger sphr zci7-w/f3o,km3 g:,tg- n6cismxl x ere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid n6hnrcv0g qrm que1 xi 0:3;nn +f:ie1spheres where one has twice the mass and twice the diametem 1gce e;0i+0qr:f6q nnuh1xr: n3invr of the 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 inoxreb731; uah. s;wdvcreased to 2M and v;d.x a 7e;rs3 bwo1uh3R, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an obj44lu5udx l1;sv9. u5ommt zbrect, that object will

  The moment of inertia of a solw 4zi-en ob,.red0/ vwun7 o7g23nuqgd:ta6vid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slippin.7et/uud -n6nge4gvz3d ro 7a bo q0:nwiw2,vg, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of me1:b(:v4fvm *ne j ostass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to th(mvet :*onfj:vseb4 1e total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radi5xr fq9g ext b1)wgbomo6-ms0dt h.46us R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom)5wm6edof9hbgx 14 g6 bq.o-xt st0mr of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippinha +q/t6mwojoz 4 1*;yc,hsktg down an inclined plane starting from rest. The angular velocity of tm j*;yzoh1, t w+hocsa6/ 4ktqhe sphere at the bottom of the incline depends on

  "The total angular momentum of a syst37wg 17lwguyucjtb*qy1s t,5 em of particles changes when a net external force acts on the system." Th77s w1lgy t351buqtj,gwy*u cis statement is

  In what circumstances can the angular velocity ylc7 uo jlea0x ;k6.h-of system of particles change without any c c-j loe6.yk hua7x;0lhange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whichd; ub/np vdz p1-th05j may be present. What5zd1u;p0/hnjtdvb -p happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellip+7(cps jh li/zi ;vm:btical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Ev ;lpz/c jm7ih(:sbi +arth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcl)rxphx:*.15 watvp ujb57 uahed arms *.7uppatjv5ur:ha1blw 5 x)xclose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirb n4.l;wpc,3jypsol6 ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotac o;j3 6,.p4lblysp nwtional kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstredq0 x3t0xde o9:*h u xwpy(nx-tched arms close to his body. What happens to he:hyqnxp0xdu- *w3(tdo 90 xxis moment of inertia about the axis of rotation?

State the law of conservation of p3o f(sxblrfb) 2p53v angular momentum.

  What arc length does the Earth traveh5b)z.in wq00))tnud2wb l owihhs /6 l in a three month period in its nearly circular orbit about the Sun witho)uzhiw2hn b/ q)nbs0d).twih056 lw a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dista +pwfxj )rx:0aji6.ypz 2l+ qance does the tip of the second hand sweep through in 3 minu+a:0 .2xi+xj)wa 6pfrjpq z lytes and 45 seconds?

  How many rad/s is 25 revolutiiz7 2dli9om39gnk j/ztk m*4mons per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revo xme)ous191 n+xic1lz;u3 tpxlutions in 4.0 s. What is the fro9)3cnpx u11tsu;lmz iex1x+equency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thh5*p8z6et5 c. b fnb4zk6fnl pe period of its rotation i fek8l55t 6bz4hz6 b. nc*nppfs

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0;w fr*nm sq2f t+17dkmhwo72n .20 n n t7w2d; f*k+mh2w1forms7qs?

  A wheel of diameter 26 )v 38 .npid d/m)4akm5::ve h ylcooyzcm turns at 1500 rpm. How far will a point on the outer ri 8k.v4o) lidzn5cvadh py: :o/ m)my3em move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutieawu gh6 3e8k-ons in 4.0 s. What is the avgw3ah e6-euk8 erage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions l l*pb+ k38i0fdpt6pvvu) 4eh in 4.0 s. What is the linear speed of a point 0.10 mi8 )p0vb l*+vf3ltkeu h4 d6pp from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cas j:xr4/rzhtt -4irj *uoc+)jble which moves the car is driven by a pulley with diamt xt+4jri suh:zr-j4 c*/jo)reter 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 spee7 9v:tol ctl5ed of 2.0 rad/s. What is the linear speeevcl o 5:l7t9td of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.)d5e; e38fge tl(:fwi/ c,evvesk lz816 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed wl feeev()v8/t5fcdk ;8,3 ez:isegl of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular spee/yj8qzj0ys( gm n:6n5n yxkz*d of 2.0 rad/s. What is the centripetal acceleration of a poi(5 g/ s6*0 myz:ynx8ynkjjzq nnt on the wheel's rim?

  What is the centripetal acceliwo atutu/9u78 7 +jlphx if *r(x5k:seration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm wf 5ihr* /kx7ju (u+xwis:al 9pt7u8othen the bike is moving 8.00 m/s?

  How many revolutions per minute (rpmgg-k-gd2 b9ew6tv ee m7( d-z3unbpm,) must a circular, rotating space station (r = 1000 -d ,t7egmbe-gmbvk29 (3wzgn 6ed-pum) 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 of ri7tkj c2 xynqf9g)1. 20 m/s. The maximum centripetal force )q2rg7fn1ty9c.jik x(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 ra;2lc t*9c zy7q kpaot-dius 50 m with a speed of 20 m/s. The maximum cen ;y-oapk*l92 qct7tcztripetal 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 adqy dm2+v3 u)h 0.750-m string, is whirled around in a smooth level table. If tdum2+y dq v)3hhe maximum 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 sliv06s sk7p3 wq9kn 3sag4xv8q spping 10 m down a lane at 4.w476ss va 0n3gk8xvps93qkqs 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 ac6fo;pn3umtpi5 sdwh.;n,s 5lceleration 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 *:e*dspfa 0f j 8m6xiracceleration 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. x0 ;w *+xxies2f/somc300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular accelei2oxe+ss *mc; /0fwx xration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has anu w++smw9.yhkky;z2 d 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 a( -lb*fal5 koconstant angular acceleration o kf(-5ol*abal f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed ofyydaoy9wl q1n5l dz5bd((6x+ 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of the lqydl z(5oy19ndaw (d y56+xb wheel?

  A wheel of diameter of 68.0 +*r9xn(taldycm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wtd(alnrx9 + *yheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly dsg),.xym4s2x sr+w xfue x*9from 8.40 m/s to rest over a distance of 115 m. What uwrfxy sss 9 m4*d )+xx.g2ex,is the angular acceleration?

  A wheel of diameter of 68.0 cm slows dowgd.yeto;uei : v9+lh*n uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the segi+t.: ;h9yeu ldov* top?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3jg td 80d61-6wrj n fvaf9mki/600 rev/min. When switched off, it rotates 50.0 timewt8a imf/dvg0n9 kf6r6jj 1d-s 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 to s5p0tultm:4 qrque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force stlm4tu5 pq0: is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of vv5 acs5hs(d k-z,i:w90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the cdivs5v-khzwa ,5s:( force applied at $53^{\circ}$ to the wrench?

  A wheel with moment obb. mw)or7 ngp5-bk4if inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mass m is at the origin, mtb*e4y(j.q wjass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia *yejtjw . (qb4about the origin?

  A solid cylinder of mass 10 kg is pivoted about n *w yg t)m0ns5dt+g2za frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.ggtyd 0nw2z5 +*s) mtn0 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 acceleration of the cylinder?

  A solid cylinder of mass 10 kg is kiomb dv:.t-eg2 r1: spivoted about a frictionless axis thought the center O. A rope wrapped around the o krbie.gd m1-vots2::uter 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. 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 horkhlq6,ycr a)1v) 5u kbg0x9taizontal position, and then released as the free end is allowed to fall. What is the hac09rl,bv6t) 1 g)ky5 qkuxa 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 kgr+rtlcz18a xt0 3mh +v. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket of radiusr+lcxv1r z+ha0 tm38t 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 frictionless disk tdf 2 *i4ua9hqpulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the puludf9q *i2tah 4ley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk rb8yz1ip1l cuo5kf--gdj 9 7ppulley of mass 7.07 kg and radius 66.0 cm. What y9b-p1 o-1luz gcifpj 58r7kdis the acceleration of the mass?

  A rotating flywheel can be used to sto-c8g0 uxxr*3ly p)ctn re 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 inertia ig;kj ea9r()b2jck(u 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 aam j8gs),5 jnnv90hl z(kr /dcnd radius 0.010 m starts from rest and rolls without slipping down dj0,(m8s c/n rlgak j95hzv) na 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 andc nr dj5)icgrt2 +x6m+m ;e*v inhd/10ms qh1l radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rest?sdr+21nrx;t*hl 5jm+m n0i61/q)me vihc cg d

  A hoop of radius 0.50 m and a mass of 0.20 kg ksf(3u(vlv+ cn 7fh5sis released from rest and allowed to roll down an inclined pln7vs (uh+kls cf(3fv5ane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 smr.c3yz )l i s,ti 1r2*tzr8vcm rolls without slipping down a 35e incl2l)t z1vctmrs,ii.r s8 3y*zrine 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 changes 6c8gwyi 5 b* yf.mi1kx ety)/kby $20 \; kgm^{2}/s$ 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 ineln)la3k dizm 2 uu+-j)89a nvvrtia 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 rotatingagh x0zv9 k/6c at 5.00 rad/s with arms extended has a moment of inertiaz0ck/9 avg xh6 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?