Angular displacement i9e8i q -1qa.f *ra;lgdmtcd4 us usually express in units of

  Angular velocity is e+tmroaq1 0r6kxpressed in units of

  Angular acceleration is expre5i)f8bwccn: -9bgz+ qhmizj(ssed in units of

  A boy and a girl are ridingmg*zwg u 9ul:kht-jv4,w 3f9 e 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 gr ez f ,tw9-9g3w:mu4*hgvul jkeater angular displacement?

  A boy and a girl are riding on a merry-go-round whiczita mu2;l;6q/4lnl-o5d taa h is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cenm-z;alult l64d2 atoniq a/ 5;ter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-rouqx:kh m-n3 k:j u58o yjp3 1njinz8;bond which is turning at a constant rate. The boy is near the outer edge, and the girnhp :qzunn 18jo;k 5-3xmo8jj yik3: bl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whid; (ubahzv6fn(7m,i hch is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the c ;,zibnua6h(v(f hmd7enter. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round whiczv2g7/-1u0gya ; ikc e/ dapuvh is turning at a constant rate. The boy is near the outer edge, while the girl is closer to t1zk e-cai/ vdyp a 0;u2g7/ugvhe center. Who has the greater tangential acceleration?

  Consider a rigid body that is rota(pfcnw/- 1kc ufu 3tx09k/agrting. Which of the following is an accurate statemep1 (f3 tckf //w-uunx0g9craknt?

  Rolling without slipping dep+qu*pql71 he t4d0z rcends on

  Two equal forces are applied to a door. The first forced8(6n9jweq ey .lo- ch is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door.deq he9n j(6o-cw.8 yl Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is app0u+quh3p o l38no3zjnzqp q-.lied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the grejnup8 qz+3-oloh u 3zn 0p.3qqater torque?

  Two forces are applied to a doorknob, perpendicular to the doot9q rq dz7c1+loe. bh;r. The first force is twice as large as the second force. The ratio of the toretr+;q7o .czbdh9ql 1que of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to change)rpf8qm-y(fkw/ f37ez zvzr*em*n r 7s in rotation?(-rvr8zr 7 e3nz yf*)memfz*f kwq7p/

  Consider two uniform solid spheres where both have the same dia 2*pir(pi agj9meter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of ipi9 p2ajr *ig(nertia is

  Two uniform solid spheres have the same mass, but one has ..a:on xg e1ogtwice the radius of the other. The ratio of the larger sphero1.:.agoengx e's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice thek2css pk,3eh+ -8j ujg diameter of the other. The ratio of the larger moment of in-jh+c2p 8ekj k3sgsu,ertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increazh; oj 3mpmu*r/ : u talu;n73k14dwctsed to 2M and 3R, what happens to the sphere'suhaw1p7 * und;crkzm34o m/jlt;:ut 3 moment of inertia about a central axis?

  If a constant net torque is applied to an o q(brh mi2uu0/7w x3bwbject, that object will

  The moment of inertia of a solid cylinder abi.z cg)ha sgp;k0d7r39n ql(vout 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,kt./t0o meu 3o one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the raokme.ut 3o0 /ttio 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 no8bu,st3u d 5radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere atsb,nd85 uo ut3 the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withxec)dtuf9 xyubqh7 /qc,j5jmh 0-y7;out slipping down an inclined plane starting from rest. The angular velocithx7dy7 )tj, f ejcu;09xqbym/ 5u-hqcy of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of pmmpt3pga6voc / kt7 i8 /j47hg-btaf 9articles changes when a net external force acts on the system." Thiscpt/ aa p83- h6v/7bmgom49gkt 7 itfj statement is

  In what circumstances can the angul 2*onth; rw t47r3atehar velocity of system of particles change without any change in the system's angular momentum ttah273nroh;*rtw e4?

  The Earth orbits the kyd,ps(5j k0dSun in an elliptical orbit. Ignore any friction which may be present. What happens over t,sdpdy05 kj( kime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellip2 9h(kqevd8vsg )3uj mtical orbit. As the Earth moves close to the Sun, then which of the following best describes th(ue3kmdj9v gvq hs)28 e orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) tiqf. (y.0* idq95e9oyspj a mby pulling in his outstretched arms close to his body. What happens to his angular mo5e aptq99fj0si i o*dqm.y(y .mentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstret. u/ dj8zua g8j2up2; yty)yc0)i7/db jbcchlched arms close to his body. What happens to his rotational kinetic energy about the axis of rotation?bc lh)d8z/ucatd/yij;gp2) bc. 2 uyy 07juj8

  An ice skater performs a pirouette :p+ ty:,e+fxvipm k -x(a fast spin) by pulling in his outstretched arms close to his body.+ x-p:,e:vyixp kft+m What happens to his moment of inertia about the axis of rotation?

State the law of conservatioeomur. 6cj,br 4h-x+hn of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly cip25fcgk2c)bo*a h (z,8 kf jljrcular orbit about the Sun with a gjf)k f2b c(kazcop2 *5l8,hjradius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length qss xx )tii0a308l:-x .vyn:xxlhid5 of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes aihxxs 5aq8siid-0v.nxx xt0y3l:l):nd 45 seconds?

  How many rad/s is 25 revolutions per minute equip xg68)kw ho*dvalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whacc eng9 zjv82x 5 y*nz;b:8+vqzxoxz +us9r*pt is the frequenccnx9*;: x5eubzpjgc *zry 98n+so xv+82zvqz y of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. us.3v09x)ctt(yjli)hs mv 9 r The peritsjl9 ))yvs9vurh t (m3. c0ixod of its rotation is

  A phonograph record rot3ej z2mysbdsbu3q7e)9ud t+ 1zjm l2;ates at 45 rpm. Through what angle does it turn in 0.20 s?23+bus2m;ju dtqes1mej ) bydlz z379

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer9i-6vqqb y pj+1 drc,2v *g-6spkkuwp rim move in 2.pi vycb -1p-+96 2qvu, ds6wkkrq *jgp1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the q /bpcnea+5uh.zx(y* a/uqxyh* ec+5b .( zpanverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. W)h; ,ugnvr h,hqg49 *szaa :xrhat is the linear speed of a point 0.10 m from the cent*:uh gag4; v9)s,hzh,rnqrxa er of the wheel?

  A cable car at a ski resort hs pap1z n9qsll,u6d2i; ug5,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 ma6zsgpu9l,a5;u q d,ip 1n 2hlske the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 0lbxb yuc,ch+:/l a m7ll/p*r2.0 rad/s. What is the linear speed of a point on the wheel's rim?+a *lmc 0b,urllp/ y:bh /lxc7

  The cutting cord on a gas-powered weed cutter is 0.16 m b aem2lsd*99n in length. If the motor rotates at the rate of 20 rev/s, what is the approxima a9n*9 2emlsbdte linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/sqgz*:d4 5 )3arj.7y w hwiufwm. What is the centri )dwyq 3 w hg.w:zuim*rfa75j4petal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point o6( g1sahl*vavi jcn x +c*t-whsr:y 18n the perimeter of a bicycle whex1 -c8s:ni +ravl61vwsjgt *hcahy (*el of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions 62ows -z(tfttxu/n/ fper minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produ f(u x-/ttwt2 /nfosz6ce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curvei(wmv.)bok-k:.s r sz of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frirkvwos .:k-.z( )mbsiction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve qgp9 t yz+-/5tspp e4oof radius 50 m with a speed of 20 m/s. The me /qop5 ps4tptyz9+g -aximum 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,lt*rbro 2, *+ipj8 iia is whirled around in a smooth level table. 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 breaka*i 82li+tipo*jr,rb?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls wi /q,l6n fkve/7sx5k lathout slipping 10 m down a lane at x/v6a k7,/5f nqklsel4.3 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 3+ v il;tinni: em:ckx0.dvg3constant 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 angular acceleration o r51cypg7 f,b vb0l9mvf $4.5 rad/s^2$. 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 automobil-4pxorx j07mt: fa:jbe tire rotate after starting from rest and acceleratinj:-0tf:bm4 paxx j7rog at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and s8 oulwv5-,se 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 j6uba2ae2lcsq( j+* f j4u(pn/s decelerates with a constant angular acceleration o2jj n(cl2*faqap e ( u+s4buj6f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of ii 3*3ftz8y;lp cxa:t6.0 rad/s while turning through 2.0 revolutions. What is the average angull:t ;pxyti* 3azi3c8far acceleration of the wheel?

  A wheel of diameter of 68.0( ppk(k)cj73rj bbcv/ cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming3/k(v 7k)cjprp bj (cb to rest?

  A wheel of diameter of 68.0 cm slows down uniformlyj7azupp3; c 4w from 8.40 m/s to rest over a distance of 115 m. What is the angular ap; 3cjwz 74aupcceleration?

  A wheel of diameter of 6 .8nd l,e )t:h0oy hxral3wpw(8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115,pw:)h3er oy.na d 8lhx(tw0l m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medsc.xgvq; 2/rv ical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 timevc v.s /rqgx;2s 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 b67iup)sr 7ory5h0wvu, d i3dtightening to a torque of 90 Nm. If a 30 cm long wrench is used, whor7ds 3iy d,uu7 h5pr6)0 vbwiat 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 a 30 cm shmu.q 9; w ga32(ndmplong wrench is used, what is the magnitude of the fo gmm(3q2dna;wush 9. prce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment o 9yaf enjgqms/e)w+8/ ns/ o7bf 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 0 *9lu4xb:) ye gg,0vyqtzmstm 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 origin?tb 4 esvt9, 0mxgq) uz0g:lyy*

  A solid cylinder of mass 10 kg is pivoz3- ,wv 7fbxr1a tdzm7ted about a frictionless axis thought the center O. A ropevt baz,7zxd 1w7f 3r-m 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 pivoted abc ;ba.avi:0qn*7; xuoldaf)mih y9 i8 out a frictionless axis thought the center O. A rope wrapped *m0yxq.a lh ;ii:cnf;7a8bau)i9ovdaround 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 hijbz jd0e+)(6fvr5l zr nged 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 as it is release v) fjjr zb+l0(6drz5ed? (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 kg. *hxfwi2 68 o hlyd,y;uNeglect 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 linear speed doeyhi yl hx,62fu*wdo 8;s the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped arodi/lmw./.gme;vb /w)2 hsdyw und a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angu/ g wim he.w/l/d;.)w2dvm ybslar acceleration of the pulley?

  A 1.53-kg mass hangs on a rogk*3g/apdt):w e*ec gpe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratioctke) * gp*gdew/ 3ga:n of the mass?

  A rotating flywheel can be used to store energy. If it is requiredmxadxl(f .g, 2 r8kkcpq0 ;ban(h2lb7 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 inerti: h*eke;u: ga,qn 6s(pv+ue zra 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 from*rn ha 3zt/m)q rest and rolls without slipping down a 1.0-m high incli3h*mrzqn/) taned 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 roll fa,fk4y5,+7r t rzlgzm0;sy vs with a speed of 10 m/s. How high up an inclined plane can it climb before com,+lyzfgv4r57 msz ,rf;y 0kat ing to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from restu,d3 o 2y6jw7o zs/evu1s- qff and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical6/ f z3w2eqosvosfy,d 7uj1-u distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius /-s 3c:ei bv(x6ocvoq9gswe+m e2 sh(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 givencgvs (v(ob swh/cse 29+ o6 -qex3e:im 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 gtc/5 2 a rag/xv+hd4qmomentum 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 mo( wj ,jve+q;ahment 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 extended ha 3:wpfu(p0 9psunw4d bs a moment of inertia op3 wn b9wf puusd(:40pf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?