Angular displacement is usually express in unix.0nck ,c; qsets of

  Angular velocity is expressed in unitsgx+ee.xi;bbygv0 y4h )5q)s f of

  Angular acceleration is expressecks*mp, -54vpmk6 g hcd in units of

  A boy and a girl are riding on a merry-go-round w 9b awm:ptq0.rc8. ttnhich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who hm.tnctab qr p 890:w.tas the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turncst )yo dksn4tmsku5o*1p,tul 5 ,5.eing at a constant rate. The boy is near the outer edge, and the girl is np1 5,dk5uo ,e 4tms5*o.k) ytsctluscloser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-roundo1r 4/lbcbio8i ux/,z 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 gr,bcizul8o/x1ib 4/r oeater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constfy:2 c/ j(g7b cqdmhr7ant rate. The boy is near the outer edge, while the(7/grhj2 qdbc fmy:7c girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round g.xy-8) ,znq3kv485isl.y lomeejvewhich is turning at a constant rate. The boy is near the outer edge, while the gire)se.gqyo3z4-xv klv, n5yi8 mj8. ell is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following )m ja8,+xpn5k+vszoz is an accurate stateme) o8z+ jpn ak,xsmz5+vnt?

  Rolling without slippia 4k abna3p;a;ng depends on

  Two equal forces are applied to a door. The first k d + /))qmnkt.bz*nxz9nk)ikforce 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 tor /)i) kxnmkzd)tqk+ bk9z.nn* que?

  Two equal forces are applied to a door at the doorknobm l2 ,1au6icae. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the eu,1 l6c ama2igreater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firs/um q51nfbl b 2-5ukpot force is twic 51f /2o5-u kblpnbuqme as large as 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 ck wa7tzupy),pg(*0r khanges in rotationak,*p u0tp) 7ygk( rzw?

  Consider two uniform sozeb45rzu j(t ;t3yo. 1 gk)sx,.cfsojlid spheres where both have the same diameter, but one has twice the mass of the othekfj ,4x uy1s( .cg. beozz3trj)sto;5 r. 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 the radius of qhrbe/6lthp,+,cwt ) gyi0ilu (e.e 3the other. The ratio of the larger sphere's momlet. 30 ytbw (,i)hp+qrih/eceug l6 ,ent of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one) 4r3g.eaxkxjmax / (vny )jm* has twice the mass and twice the diameter of the other. The ratioxxx )*e aja).4k rnvg(jm/m3 y of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M acvv /)y; sx.3fr9:ige2hcv a0hu o s:knd radius R. If these are increased to 2M and 3Rsv: hvi2re/g a h:c9c3uv o;fy.0sxk ), what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, onp;6:5 zui/sa7a rci+/ de dzthat object will

  The moment of inertia of a solid cylinder aboutqzn1ipa (tr; h udh54c8 *i3fp 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 o,(4laz 7lpngwt7d,q8u j) dexf mass 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 ) ( t7znug8dwq ld,xjep47a,l energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere nmwpypbuz3* limp 3a9 c5794dof mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dep97*a3p d9p 3un5mzbpiyc4wml ends on

  Suppose a solid sphere of mass M and radiu kagn23d2moo)ne;t .vs R rolls without slipping down an inclined plane 2 ;23novg)d.naemtk ostarting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum ojcf7 v4;-64 nb jdigmif a system of particles changes when a net external force acts on the system." This statement ig4 mni v;j4d jc6f7-bis

  In what circumstances can the angular velocity of system of particles chan dj c7):+hytx outa.ska-:k*kge without any change in the *k-)atktxou 7:yh .+ dscja:ksystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. I8y3lf :cy 7 d2 5(ba5wrkbcxkognore any friction which may be pa kk d xfwc:7cr3 (5l28bb5yyoresent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moveo dhni7n ;t)--5bcqd cs close to the Sun, then which of the following best describes-dq 5c7c)n;t- hdboni the orbiting speed of the Earth about the Sun?

  An ice skater performs a pi rf8) j.oc+bxga5mt po*s8h6zrouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about theb8.at5zm 8fcohsgr* j xo 6+p) axis of rotation?

  An ice skater performs a pirouette (a fast spin)4xdyv35j .aa u by pulling in his outstretched arms close to his body. What happeajvd4.xya5 3 uns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hiwh bf(isb cf.90:uu:ss outstretched arms close to his body. What happens to his moment of iner 0wucs :b.hf(fbs9:iutia about the axis of rotation?

State the law of conservation of angular momentum8fkkwd,481fh0pbb miu1yks 9 .

  What arc length does the Earth travel in a three montpjn34 j 0r2 gc9vp .jhaj78k.abduvu* h period in its nearly circular orbit abouu*48b k07n ar9.ja2pjp3vh c.ujg djvt 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 dis4: c cv-qeor;) nn8ur0hhd(l stance does the tip of the second hand sweep through in 3 minutes and 45 secucnhdvq):er s r 0n4 -h;c(lo8onds?

  How many rad/s is 25 revolutions per minutey eiunf9bm91 n*(9wqc 2rov e: equivalent to?

  A bicycle wheel rotates uniformly through 2.01gwvqj + i5e(vkfnb5+s1:z6yj6ssxk revolutions in 4.0 s. What is the frequenj:xz (5s6+ 6 fnq1v gewkji +kssv5b1ycy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of cow k: 7zb jeu- p73zhk1vbt4;0.40 kHz. The period of its47; k7:bzh3eku c-vj t zpbow1 rotation is

  A phonograph record rotates at 45zim 1/ r5 )fu2kc1e+meqo; vnv rpm. Through what angle does it turn in 0.20 s? 2k5v1e;zc uq1 fi )mrv/omne+

  A wheel of diameter 26 cm turns at 1500vmvb9oyz65zzk, k7ux lk8j ,, rpm. How far will a point on the outer rim move in 2.1 z, 7,m6 b kzlx8zyoju95v,kv ks?

  A bicycle wheel rotates uniformly through 2.0 revg 1i*e8 t8nqrtolutions in 4.0 s. What is the average angular speed tr e*818tgiqnof the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ia5q ksqo( ibmjc 51u8-s the linear sp1 jaubmqc-sq5o(5i k8eed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distanb c*/+3k -m6r 1tugzxz.mngcx ce 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/xxbz 3m1rn6+ g u.ccmgzk- t* car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant 1y8 hoec0k1un angular speed of 2.0 rad/s. What is the linear speed of a po1 0cnk8e yhu1oint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0./rl ly;( 6n wvn1cwc2r16 m in length. If the motor rotates at the rate of 20 rev/s, w c; clvr( ylrwnn2w16/hat is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant anguladad(i4)p uh( vr speed of 2.0 rad/s. What is the centripetal h(pvd4(uid a) acceleration of a point on the wheel's rim?

  What is the centripetal accelerarjuk :,a2qv zl fu/ba16wtg 0 pw4*y*btion of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movin :p q* 0*waulk g6b/b2vw4u j1zfyr,tag 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (8 mayt,c1x jry+z(fju;0.dztg c- wo(r = 1000 m+j,g0 ut( c(. oar8jm fz- ;wzt1cdyyx) 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 speed5do4-y/7)avy pbodtk of 20 m/s. The maximum centripetal force (pro )v7o/ o dbpt-yk54aydvided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat dwaqf*x/*g/r circular curve of radius 50 m with a speed of 20 m/s. The maximum centri/rw *df/xag*qpetal 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 2u .vt4piz,qo around in a smooth level tab.o,qvu p4z2 itle. If the 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 slipping 1r1 cz89ejxji js6 t2sl,ql 0x)0 m down a lane at 4.3 m/s.8s t)isj qzx0rje6 92jl1x c,l
(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-b wjr4lmyp4: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 angularczhwp *: 5hd.;lore -h 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 *w cf dzf+f+mp5ie.6t rotate after starting from rest a5 c pdmf+f*wf.+6 tizend 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 acb5snx*pz-; 7,yk i nltceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelera2ly3ivmj p2b ff;+nl1) ky cj*tes with a constant angular acceleratj *2;1i y jncm2 vfkl)3lbf+pyion 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 rc kh tek4y(n: v;cvqor4 s(dmm0w+g +5pw g1x3ad/s while turning through 2.0 revolutions. What is the average angular accel mkvc:m+swh;npvy 04((ek wdtc1+go3 4x rqg5eration of the wheel?

  A wheel of diameter of 68.0 cm slows do ;c,:kw o/kpjswn uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotatwk,s/:cp; jo kes in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 hsvt k z/38i/im/s to rest over a distance of 115 m. What is the angulhv3z /iktis8 /ar acceleration?

  A wheel of diameter of 68.0 cm yhho j7ef;+sk1p7 m -pslows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to c7emks ;1p+-py jhfo7h ome to the stop?

  A centrifuge in a medical laboratory rotates ad2(to +p m0pxhw)f. x6p8cr jit a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a co+)rh(dwpo pc mtx 20if6x8.jp nstant 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 tig(xy up(e ;v 3ojc6dnd/htening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forx dv /3e;dcouj6( n(ypce required when the force is perpendicular to the wrench?

  The bolts on a car wheel requiiiqc:w 8g * .wy)11ss4t7dm x5tqpwp fre 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 f s)8 q id5tppwxyfw7 4m:*g11.qstwic orce applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertims z;t9mokg0e2 rv9+o a $3.00 \; kgm^{2}$ 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 8+k/,hxxgj te,u6gso the origin, mass 2m is at x = gxo+jts 8x/k h ge,6u,a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionkjdyv j5r7i-1less axis thought the cevd5yri- jkj71nter O. A rope 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 mass 10 kg is pkl2fl6;x )o4)rzh mefivoted about a frictionless axis thought the center O. A rope wrapped f6rm z fkel; 2xo)hl4)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) 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. 8 coebb qzu e4a+-o),j 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 as it is released? (The moment of inertia of a rod about one end is q+ ,8ob -ea)ceobzuj4 ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass z4m6j6neugn+ ;sdd5 e1.5 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 sg +nmn e6jed z5d6;u4cm 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 frictionww8 qzuvzue l1+,37 cwless disk pulley of mass 7.07 kg and radius 66cz w+73uw 8zuevw ,l1q.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a f+qwrq9ifiax b2c 1e4: rictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Wheiwfq :b4+2 x 91racqiat is the acceleration of the mass?

  A rotating flywheel can be 45 e sj2t p3qub bng49hujrk71used to store 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 tv0)u9zp tt(b inertia 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 0.9cgy2x78r;4bc bynq v 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 the bottom of78 yqxbn2 rc;4gc9 bvy the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m g(m-1ru(b racuran6gf v- 9 z:aby/b9rolls with a speed of 10 m/s. How high up an f (au/bmran99cyr1b( rz6 :a gu-bvg -inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a6ltgia7s6 d gln7il8f ,r g/s (i+j9.fx; rlzr mass of 0.20 kg is released from rest and allowed to roll d/i68ntd6i g7lr(j9ls+gr;g s,xafl.r7 z lf iown an inclined plane. 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 cm rolls without slipping6, c8y19bgvump qv5nt down a 35e incline that is 7.0 m long. Assume it started from rest. Tc,9y q6pt5v 1ubnvmg 8he 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 chaqcup)jf c ;0t3ia+)kuml/dmv87g5 g anges 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 mifm+ ea/e*d8/5n 3k bj )ibdnvoment of inertia 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 extende3f)v zx.8xgxv15og tfd has a moment of inertia ofxgv1zgtv8x)of 5 x 3.f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?