Angular displacement is usually express in u)+f ty.l 0d:pxpdmo-d q q/y4anits of

  Angular velocity is expressed in qrjz e0:llr53mhiwc +5u5 gy(units of

  Angular acceleration is expressed in y,gmb6l)kt 7zunits of

  A boy and a girl are riding on a merry-go-round which is turning at a constant r)wh0n us./ qfoate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angularw uf /os)nqh0. displacement?

  A boy and a girl are riding on a merry-go-round which is turnin-teze v+0ng * djk)kz/ p-v/dw/3xwda g at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greaa-zp0vt-/ xj3v d+wk e g)e/d*dnzk/wter angular speed?

  A boy and a girl are riding on a merry-go-round 9e,ix992 txkgvd zgy a88bh7ywhich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cenegb9i7x,yt a98v kh9yg8xd 2z ter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a con g 5pg-spxc,x6c3cc:k stant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripep5ccg-xcp,:6 c gx3ks tal acceleration?

  A boy and a girl are riding a merry-go-round which is turn r7k,3iz ljj*zing at a constant rate. The boy is near the outer edge, while the girl is closer to th7 l,jzr 3kzi*je center. Who has the greater tangential acceleration?

  Consider a rigid bodiic1f6uihekcxk0f 0hi -9m2+pfgp1 )5zys.b y that is rotating. Which of the following is an accurate statemeihc0szeg+x.ky i0ck26u ) fi fb591hf pm1pi-nt?

  Rolling without slipping depends oeumc)4(ucma r :8h, wq:n *uxnn

  Two equal forces are applied to a door. The first force is appy47/*qr)fog fn0 cgcvlied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exer0g q7fv)/ccg *yn4 forts the greater torque?

  Two equal forces are applied to a dot/bnj/ :qll9wxxs 6(s (*i9csesbft -or at the doorknob. The first force is applied perpendicular to the door; the second force is applie:nl( * ej/s-sqlbt(69f9ws csi x xb/td at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a dzn .b18 77hm7jsn:u qep8yczdoorknob, perpendicular to the door. The first force is twice as ld7m1cnepsh 8 qb . :7zzy8j7nuarge 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 obj;h- sjqgpny2;kp5iops ac, -sn) m8*fxj 8 .gnect's resistance to changes in rotationjfp2 o qn s5pnmc;ygs-s na-igk hp8 *j;),.8x?

  Consider two uniform solid spheres where both have the same diameter, b tuu1 e j7hshecx4,7xmf 2we;/o0*unvut one has twice the mass 7*0o; un4ecx7vf ht,1m euj2xwsu /h eof the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have td)r 9lvew;f*,xja* o2x7kku hhe same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertv9 l *x*;dfx aowk,7kuh2rj) eia to that of the smaller sphere is

  Consider two uniform solid spheres wrn;ioy:nxi 0mlerk, (n30 *rqhere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia inryxo l3kr,;im qi 0:e0 n*nr(s

  A uniform solid sphere has mass M and radius R. If these are inc/0nnk ndop8 )cgt /qo+reased to 2M and 3R, what happens to the sphere'spg /ndq8c+ oknn0)/ot moment of inertia about a central axis?

  If a constant net torque is appliedy.k. x.w 3h ;2arrx.kr9s9-jo1pw*wvgchs xf to an object, that object will

  The moment of inertia of a solid cylinder about its axis is givenho)07jj-uidk+e 42mind gktw, ;lmt 3 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 kg and- 98sqpq +g*red4 eqkwf k/0uak,xe4 b 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? Ass keesp+grqdx we4kq4-/k*09 uq, fb8aume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls wit(lt+0sa+f wly hout slipping down an inclined plane starting from rest. The linear velocits+fwla0t+( l yy of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of m narjyj f0grpmh-z6q 0-z1 b0czq)q 15ass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at t1 5 hq g-rc0jpqf0zjr -qzzym)06bna1he bottom of the incline depends on

  "The total angular momentum of a system of particles chabe;pc4 ww ,q4o8uk mv4qv;b:gnges when a net external w;k 8 m 4qeugvw:b4;4,ovcqb pforce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles ch 8bkfrbdmd5; 8ange without any change in the system's angulabddr8kf85 mb ;r momentum?

  The Earth orbits the Sxbhv1i/hr b,cl67s ,zun in an elliptical orbit. Ignore any friction which may be present. What happens overhbzhb,v,7c x s6ril/1 time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sa7ey k2s; hv+oun 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 about ;kvo ye+as7h2 the Sun?

  An ice skater performs a pirouette ( rce1 b32sfh,f). iugd5wsb:+0bsca pa fast spin) by pulling in his outstretched arms close to his body. sh w as 0crbfd3 +:psfu5c.ie ,12bgb) What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedu0 )ly w1igbzn6e3ovyxnl(- 2 arms close to his body. What happens to hisbi 1u)2e3x-( gzw0oy nn vlyl6 rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a f.2 sx ijsvw33kast spin) by pulling in his outstretched arms close to his bx.vk jwi33 2ssody. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of i*xxu -,p 7vc;6eombuangular momentum.

  What arc length does9sc+uiqva7cif6kx. m; c n77 v the Earth travel in a three month period in its nearly circ7qfucc+. 69x a vsc;kivin77mular orbit about 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 distance does the tip1scw: ijw1w:hdi *8 ei ofj i:1i81e idc*ww:hs w the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 2572xr*:u(lfrjsvlfy7 revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutiortxg 19n+ tbk/u;xsn)ns in 4.0 s. What is the frequen u) nbs;gttx+r/9 xk1ncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a freq9f .kiith,v-g e 5txa4uency of 0.40 kHz. The period of its5i a e9igtk4,-x.vh tf rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.2-ts. ( 9s.ilqv 4ykyyy0 sv9(yyki l-4q. yt ss.y?

  A wheel of diameter 26 cm turns at 1500 rpm. Hotse/h bgg8ze k8m:s4: w far will a point on the outer rim e km88:e/zbh:tg4ssg move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What cg17vip v fl.2is the average angular speed of thgc 1pvf2.vli7e wheel?

  A bicycle wheel rotates uniformly through 2.0 revns5rkm 0y 9v yvdn niljd+da/f( 3*l3)olutions in 4.0 s. What is the linear speed of a poad9v3fl3yd mdjnn5* ys v0(li)+kr /n int 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 cvl.1 girhjbtye+; c zcd.16nk2tec/ he 02/lgable which moves the cgl n;. + 1 2c/1t0e6bkeg/ tz ivc2ercyj.hdlhar is driven by a pulley with diameter 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 yk d+ax0zdi o-s b(,o1lqkv.0 with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's v(00l.q,okibods1 +-dkyxz a rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the aw du. 5aml-m6motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?6.m-daw ma 5ul

  A wheel of radius 1.0 m is rotatod6/nf wk,5r4kh95r daay:e uing with a constant angular speed of 2.0 rad/s. What is wf6ek ,do9adruyan5h rk45 :/ the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle wh 2xryasxo fdi98 2)6lleel of 8f )lry9o s26id2laxxdiameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stati 3 ;fkx *)se w6u5qx9pi:dhxiaon (r = 1000 m) rotate to produce an artificiali hxqw3 s5u6aekf)ix* 9 d:px; gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curv8gqm; hc yahp374*-mo.oxmsq e of radius 50 m with a speed of 20 m/s. The max mmyqm. -h8co7o as*q4phxg; 3imum centripetal 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 radius 50 m with a s v7ye;zlb7jdmtcp(n +r ,1as/peed of 20 m/s. The ;r71m (y+zc /7s,vtnblejapdmaximum 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, attod s*eyl, l,8dached to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear *e sl,dd,8yol speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cmm*1+k h0*jlzsmp,ik96d xr lc rolls without slipping 10 m down a lane 1 *ksklr,d0x 9 zmcmj6il+p h*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 angul l+ 7; ea-zxy4 u9qhoodtes74par 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 witkb70ww ,2hgh0p0ol vyh a constant 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 automobile tire rotx9uh r-q , ,fbgdt*d1wate after starting from rest and accelerating at a constant angular accelerat h9*b,u-grd q 1ft,xwdion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerationsoyofri-l1 ), of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates k 9qvhkzy7d;+3t 0 dlhwith a constant angular acceleratiod +z0l dv7h;hq3tkky9n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from k jc,v,xv+s* srest and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration of thv+xc ,s*vksj ,e wheel?

  A wheel of diameter of 68.0 cm sloc;rh8w ; j45 bgq;ybv2yj*tis ws 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 comin5y s q b2*riwy4c b;j8;;ghjtvg to rest?

  A wheel of diameter of 68.0 cm slows down un1y4 - .sm6qcvjejs fo:iformly from 8.40 m/s to rest over a distance of 115 m.qfcj om-sje v4ys6: 1. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fromj 44g.4fra) df5xeeql 8.40 m/s to rest over a distrf gej.a)44q4de lx 5fance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev*k1qmet q+4l l/min. When switched off, it rotates 50.0 times at a constan4 l1+qktl *mqet 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 whexnw(+ xx5x tq4 8l5(kpxfp qz3el require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force rexxq8+(w n p(kxzq4xl 5xf53ptquired 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 cj9liopo 2-q3wbp -z ccil (d.(m long wrench is used, what is the magnitude of -(i3c p zojb pi qwlldc-.2(o9the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of xu i f+/xm5po*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 ap4epe a4j 3e1kjd+ :one+h 2gis at the origin, mass 2m is at x =+2 +opjha3j4g1pe a4ede :ekn 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 frictionless axis thought the 58tini)7h /hnin u)qvcenter O. A ron v/th )uqin75n8i)i hpe 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 frictionless axis th(9vj.ue hi+t 7fu6wqyought the c. u+6f(u 9hwjie vyt7qenter 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 o nzn;h(26zomwvbn:/ 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 released? (The n6 2w(hnm:/; oz ozbnvmoment 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 16w jlxo z/8n81x.5 wysggr) bck7ubj2.5 kg. Neglect the mass of the axle ans8b2znxb5 wu71yow) 6glkj/.j rc8gxd 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 does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope y9k-u(pm 4fks,f8 bvjwrapped around a frictionless disk pulley of mass 7.07 kg and ra,k 9pjkvumf84b-ys (fdius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a q2.tk2j;wn ps.w w 0obrope wrapped around a frictionless disk pulley of mass 7.07 kg andwq owk;2s 2p.nj0bt.w radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requirat )dd.1p f.rbed 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 iner.x* yyxbgw) hwb:/23jeuar9 7nxbkm ;tia 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 mb)v+x4p :: bguukn+v k starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere wvn +p:+ xub4kv:b)k guhen it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with afu h:)r e:xn*a speed of 10 m/s. How high up an inc rena:ux) f:h*lined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released ( 1v9g;y8olrzv m gv2jfrom rest and allowed to roll down an inclinzg;vrjg92 8( vvmo y1led 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 with4lm2 qxv0 oqoo5wb 4,fout slipping down a 35e inc f o wx54q0l4,oqobmv2line 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 moment. y x1mzz:z,tjs nh1+xum 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 o)yxzd)b hh + h-1s2wg13zmsr gf $5.0 \; kgm^{2}$ 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 arm23dn uwgh /bh6v.azt6s extended has a moment of inertia tuzdw6hva2b n6h3. /gof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?