Angular displacement is usuall6lcweeqluc *h:0kdo k2md( -pr2; +qoy express in units of

  Angular velocity is expressed in u.7j -m mnim)vynits of

  Angular acceleration is expressed in units (jc :0 vj:zl n5;emvsvof

  A boy and a girl are riding on a mgbm;7)ea x u*ucsn z3yj1.dx-erry-go-round which is turning at a constant rate. The boy is near the outer edge, and the gicazs e)unmx7. *g ujy;xd1-3b rl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a q6 */r p;qxd*nmwj1rk constant rate. The boy is near the outer edge, and t 1;dqm*wrx n r*jp/q6khe girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are kp e+v6w4k; h2rc(pwl-.oq aq riding on a merry-go-round which is turning at a constant rate. The boy -hkk. qeq+2l wopw(;pa6r4vc is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry*tvdm.(hv rs 5-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Wh. hmst*d (rvv5o has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant vym4bple2 yap9,)o-lohp +6e rate. The boy is near the outer edge, whiy h l+lb,oayep)2poepv9m-64le the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotah- p-bjo06udjting. Which of the following is an accurate statement6jjb0p- oud- h?

  Rolling without slipping depena,f5y4h)vb fuds on

  Two equal forces are applied to a do1hgdn vx(ccis v+.(p4 or. The first force is applied at the midpoint of the door; the second focp 1xg(.n s4(vid vh+crce is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applel p*:s5k)i-o;gxtrvvozs pq2 44pr*ied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door.oo)2 pp v; p st*-qrr44i:v*z ke5sxlg Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The 4t vfsdf2dp *p,sj7mw s43nz- : zu)vhfirst force is twice as large as 4zfz3tmup jf7d *sp4vs)nhs-dw 2v ,: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 changes in rot.b f42 tqbqp u..pt.jvatiouqv.4p.t .fb.p2 qj btn?

  Consider two uniform solid spheres where both havesx2 9 l1lt6h 6/dixe5ppxtv -j the same diameter, but one has twice the mass of the other. 6 h-ll2t9/1xx5jsvdpe tp6ix The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres hav ve:lm0lq3y )/bc9 y*pd m57lawjqi9ne the same mass, but one has twice the radius of the other. The ratio of th 7w i0*nale:ymjp3yml lc/ qd95qv)b9e larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solis) yx1 f-+loimnh;e*owq9h 0fd spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of in0hq;-i fl w+ x1yoome*sf9 hn)ertia to that of the smaller moment of inertia is

  A uniform solid sphere has marppmk; fqgtzx4bbk.d7m vl9.e 3 e: 41ss M and radius R. If these are increased to 2M and 3R:xedp. bvt 1k7 9pqg.rzb m3el;f44m k, what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object,69abmjioy. 8cic/ ( pjysy;t, that object will

  The moment of inertia of a solid cylinder about its /d;nfcc00xlp)fn1t a 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 om);n:ts2wv 7f fwd0q86jwn d rf which has a mass of 10 kg and a radius of 30 cnj ) :rftn;w2wmd80qw7f ds6vm. 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.

  Suppose a solid sphe 20n3llps6x ogixo:7wz-.a qhre of mass M and radius R rolls without slipping down an inclined plane starting from rest. o x3xqga 7sp.z lni0-2hl6o:w The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere o hv/ e 98c)rbxwl0d :/-wrtbxrf mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bbd trv)w/:rr /bewlxxh8-90c ottom of the incline depends on

  "The total angular momentum of a system of particlj1;, eiyd uoo2es changes when a net external force acts on tidyu2o ;o, ej1he system." This statement is

  In what circumstances can the angular velc9 2jz4 0 uk,ezlgdb)mocity of system of particles change without ak)z ,dg9mz2l40eujbc ny change in the system's angular momentum?

  The Earth orbits the Sun in an elli:c io l1kf48septical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum abokf8c sl:i4 eo1ut the Sun?

  The Earth moves about tft+( qoq)61q8zax rp0s k7msyhe Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth y61oz(t7m 8qskr+ )0aqxp fsq about the Sun?

  An ice skater performs a pirouette (a oy ;j ld65j znlli*7l-fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum abon*6jlli ;lod -5yz7ljut the axis of rotation?

  An ice skater performs a piro sns:-spdxgw7ek5 z1:j7h*9ry8 fjr huette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energns:rwks 9 5pr:gx -y 8*jsefd1hhz77 jy about the axis of rotation?

  An ice skater performs a pirouette (atkx6kepj mej(d408 09xmn +a is. +oib fast spin) by pulling in his outstretched arms close to his body. What happens to n0 (s9xpm+bxet ea8. k j0mk6i4ij+dohis moment of inertia about the axis of rotation?

State the law of conservation of angul3luv1jg ed9 c-ar momentum.

  What arc length does the Earth trav:)zfsw- n a:jfel in a three month period in its nearly circular orbit a j-na)::f wfzsbout 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. Whatm ds 8rf6: ka.vqcc.hta)3,pt distance does the tip of the second hand sweep through in 3 mi,th.)tk vpa . rqm 3c:cd6fas8nutes and 45 seconds?

  How many rad/s is 25 rercvnw3 wv5f 3k,rn2z ,volutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What iv 4 p)x.szqxaa3 tmo(3s the frequency of txq(4apza3 o3xsvm.)t he wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz.hgodo8 pn/xv9.gx71x3s* dk j The period of its jo1/3dskgxxxn7 *9dvp . 8gohrotation is

  A phonograph record rotat.+5fknuq rbl/fzs2 h(es at 45 rpm. Through what angle does it turn in 0.20 s?usfnzq25.fbh+l r k(/

  A wheel of diameter 26 cm turnhp52rfi3xys9*f g +6mw i 6oras at 1500 rpm. How far will a point on the outer rim move in+rhwsf3 y 69 ari2*5p6xgfoim 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolzrxduf82*j h+1 o8ke9 (e6ruv9 dns drutions in 4.0 s. What is the avddjnu o 89uxe6*( zsr198+ed2hrkfv rerage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.nm:eaxo y/i02w*yf 7fb2 z7+o dy(otj0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the fai*y oty o0yd/:n(zmjb7oe2f72x+w wheel?

  A cable car at a ski resort carrao 8u.6t98y qkbwud3bies 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 rot398tb wb 8ayduq6u ok.ate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a cons ewbz.8h+ 9gv bmyap3.f+e 9dctant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's8gbwed+99 + f.ev3 .hmczbyp a rim?

  The cutting cord on a gas-powered weed cutter ina.y8b -9 +p6 q/uie6simds nps 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of6.u bp qena id p-s9nyi/s6m8+ the cord?

  A wheel of radius 1.0 m is rotating with a constantfs-k 7(prkfa9il7h 1y angular speed of 2.0 rad/s. What is the centripetal acceleaf1-rsk9hy(7p k7f ilration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter ofd /3y)a2r5lx hwo7g md a bicycle wheel of diameter 3o / mw72ydh)lrgadx570.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per .z+p1,jgec0 q)josbt ,-tw twhqk;2e minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce anoq, tezj;b.pt -hqjk0w1,+)2 cegswt artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circuln+eh-ng3 :nc .zse m2kar curve of radius 50 m with a speed of 20 m/s. The maximum centrip+k shcnnm.g:- 32enze etal force (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 rl8t o5l3)+xxn3: a0tsdi wxsj1x uz2tadius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by l dxi3u1t +t03: alwxxx s5 8otzs2)njstatic 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 arounon ;vt5a)-9c3ohscowd in a smtnhc )-5voso3a;oc9wooth 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 break?

  A bowling ball of mass 7.5 kg and radium ayr7bclq15dxi: 98 ts 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/stq9x a 5ci7md8yrl1:b.
(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 acceler)if)ie6koc: y ation 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 const nclw7y.*rg;g bw2j5,m;df mkant angular 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 autou/38strbgh z/fwdiw)3 x7bv 6mobile tire rotate after starting from rest and accelerating at a coni wx/ 6 wzr8)vts3/ud7hf b3gbstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular ac ssotq/s/h. - xjv(gw,celeration 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 acceh.6qu.u e *gsjleration of 6.euqu jgh. *s$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaydsfn *pv .3k6ches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is thef6.sny *dvkp3 average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dow -utq) o,bfla8n uniformly from 8.40 m/s to rest over a distance of8baftlo),-uq 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly fr+gn+ uii v/.awg 28d phc5;v(va az9vxom 8.40 m/s to rest over a distance of 115 m. W d9+cvzw vvuii xgp5a+ah82.a /(v; nghat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oo -fbhwht6ln 3gx16l/ver a distance of 115 m. Hlf-g66/w 3obxh1 lt hnow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a ro(/ yr8y w .,ucyqa/ltvtational speed of 3600 rev/min. When switched off, it rotates 50y/vy/(r,qtwcy8. a l u.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 tighteni- z 3nrfqx i3-0g cijzgw80vb*9eeq m+ng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requwvg 0f+8iqg-i e eq zrmx9-*bn03j z3cired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a .;i1.fqzfwj b30 cm long wrench is used, what is the magnitude of the force required when the force applied at zfb jwf.q.i1; $53^{\circ}$ to the wrench?

  A wheel with moment of iney 0w(ox7pjt37* vgynertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as 3h8 bilmg*(+ yxco)h6 i8r 5( ssbuoejfollows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is35oy )g8bem8b(ijlrsu* c6+shi(oxh the moment of inertia about the origin?

  A solid cylinder of mass ts0jh35l1 eeh10 kg is pivoted about a frictionless axis thought the center O 1thl5seh3e0j . 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 pivoted about a frictionv g ckit(c,0i n:+93glpxecrm7y,:t d8 a3owrless axis thought the center70 9i3 o r,tmr ykge:vn:x,ig(cd+lc8aw3t pc 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) 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 e9b3qm 9ze:y+b6rn my in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is 3qe:ze +mm6 rn9byy9breleased? (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 vc,f/ ba71gpi 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 sp/i v1ab,fc g7, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs r4f lbl9r i35o9ecpx,on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and rapl fco3rlrx 59,4i9be dius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fri.a )r/qzjsa,9yvr 0dm1e8iv i* o7u yrctionless disk pulley of mass 7. 8y e9u.za,0 mivd *7s/j)yqrviroa 1r07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to stofk*u .kem+xzb/: 8l48yht9 nlymhbs 3re 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 inertiakbg ,4a)cg.e2gqp9fs u 6q mf6 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 m ot a* os( n5dk/txvo4o-hv,; q46kktkg 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 the bottom of the inclint*5o;vkka4sx,to -4oqhkt o n6 (m v/ded plane?

  A solid sphere of mass 1.0 kg and radius 0.010qvf6,*k c2:lcl4 czjx m rolls with a speed of 10 m/s. How high up an inclined plane v, lk:xz*6f4cjcc2l qcan it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from bmeg+k 8 r.e4arest and allowed to roll down a +b48 kaer.megn inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 1t p5ae4fj era j1tzir*/; 1eekg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mra1tej*ri fa4jetpe; e 15/1 zoment 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(zu2 l3ahmpt:)fkm09f wm rb* 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 inertlk2q1)c5) 4l+4f +xphckym r pvttx1 fia 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 rotathmzel*+r2 vka9cdu;m09 u gp:ing at 5.00 rad/s with arms extended has a moment of inertid 0lp r2+9kguauzmc9 e:vhm* ;a 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?