Angular displacement is usuallr,d utr1rj(dar z;1uik8 m/c1y express in units of

  Angular velocity is expressed in uni9)iyu, gfql k-ts of

  Angular acceleration is exprett:z3fpsg8ba.nq q, u(+b )ums u,(1glq mze0ssed in units of

  A boy and a girl are riding0f4,h5xq, t p*dzm arh 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 h5 mrqd 4 p,x0*thfha,zas the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning j2tcxi1:6c u 5unxtd.at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater anui 5:d2c6un1ctjx xt. gular speed?

  A boy and a girl are riding on a merry-go-round which is turning at duh9;vca zn.; a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear.vadhc ;zu;n 9 speed?

  A boy and a girl are riding a merry-go-round w nr+6 (ng0jzejt,u- wvbp3n,v hich is turning at a constant rate. The boy is near the outer edge, while the girl is closer to th6nzj vjvt3,pegu wn,+0 -(bnre center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a d e tfpmj4-i)j6+s,t emerry-go-round which is turning at a constant rate. e,i- et f) t64js+mdjp The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which ofe ;,uwzd6 *y8jaf gjj, the following is an accurate statemen;,w,jd8 z *ugfje6 jayt?

  Rolling without slipping dependi f5; ax5c6ezcs on

  Two equal forces are applied to a door. The first forcdzlh w37o6 o fl.g*h;ae is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpe*;ghl3w o76ohaz l.d fndicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doore owgi2)b ;b.i:1i smpknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exer osw1p)iib;.m 2:iebg ts the greater torque?

  Two forces are applied to a doorknob, peg73.da5qv1t sl8xlu bxx1 e)arpendicular 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 oqe)3 .1vx5u 18lax s7bglt axdf the second is

  What is the quantity used to measure an objr2 v/ext1qe n21 1 u2el-mlohtect's resistance to changes in rotationv2 lht-lmnee22x1e ruo1/1 qt?

  Consider two uniform solid0 kp8*hcga .ba spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the largeakp b. g8*h0car moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the d9qs7cs+9d 9+lxk c0+nkh-mgvv su(q same mass, but one has twice the radius of the oqm+x(nsl90cdkuhqcv sd g+ks7v9 9+-ther. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice thqbm-k6 0 5wh2brc/ erde mass and twice the diameter of the ot 5-2m 0rr/hd6b wbkecqher. 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. I 6qtz)ujlf *7 45t* wezp)zj7f gsrub,f these are increased to 2M and 3R, wha 76z5)jslf)jr,wz gefu ptq*4* btz7ut happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object,s 6 ds1-65kv:a kcbtzh that object will

  The moment of inertia of a solid cylinder about its axis is giva/5f+1jp gd smen 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 whi3al8ptx 5 -(:elcn01yroi2cw ae :bvwch has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatio walla1w 2-:eicte:0 5o8x p3 bycn(rvnal 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 radius R rq rq a(;kb6tivod/n0,s /gk)aolls without slipping down an inclined plane sta kstkiqora/ qbv06)dg (a;,n /rting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without/anph4gy-y6 oqyb y (0 slipping down an inclined plane starting from rest. The angular vel6gyay/hyq ypbn(4 -0oocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles ch. hwh9byz8/y8frb sii(7 -nr canges when a net external force acts on h97 s -h./bi(yzf8wby8rr cinthe system." This statement is

  In what circumstances can the angular velocity of system of par2o z0;b+oybx xticles change without any chan2yx 0xb;zo ob+ge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which mary 3. cxbb;t*(o*2uy ii;;. luzttkid y be present. What happens over time to the Earth's angular momentum ab i i3d rl z(xyt.cy.*t;bu ;b*tkio;2uout the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves j9+d* k toh vw45nqi+d5ulc4a close to the Sun, then which of the following best describes the orbiting speed of t4vh u+54iqcjado+9lntw k5*dhe Earth about the Sun?

  An ice skater performs a pirouette (a y;3px2e)h0 de1h a (4irweywofast spin) by pulling in his outstretched arms close to his body. Woh ;e xri yy3ede42)hwpaw0(1hat happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pull17q 4x*7iwfpq/ m cg3bwj 7wyling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axblw*7jfp 7cig 1m w4/ 7qq3ywxis of rotation?

  An ice skater performs a pirouette (a fast; 6wcoce52u im spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia abw;i6cc uo2m5 eout the axis of rotation?

State the law of conservg/ rs9ujfg d i3rm7r8/ation of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly (xq3w sq:zufbqk(5 , ucircular orbit about the Sun with a rqu(bx5k u ,z q:fs3w(qadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 mpj)9m )eq q.uw9*vvrr . What distance does the tip of the second hand sweep through in 3 minutesvmjq. r) *uqe)9rpw 9v and 45 seconds?

  How many rad/s is 25 revolutions per minutr +ud3xj2yo -ws7my e)e equivalent to?

  A bicycle wheel rotates unifor g wn0q ;9elyrh;6se ,i,ady3emly through 2.0 revolutions in 4.0 s. What is the frequency of the wheyqi0rnh9deey;, e; l3 6g,asw el's rotation?

  A pulsar (a rotating neutron starx.z kvl7y5;fn ) emits pulses at a frequency of 0.40 kHz. The period of itsyfk7n ; x5.lvz rotation is

  A phonograph record rotates at 45 rpm. Throu)rbu-jfz8oayi xvi,1 4z fe 8*gh what angle does it turn in 0.20 o zx,vu*y i b4jfi8)zr1-ef8as?

  A wheel of diameter 26 cm turnsu:; op*oc ub jao93ngcc2( f,xgf zi;9-3mtr p at 1500 rpm. How far will a point on the outer rim move in 2.i ufop3 cgzcu 2,-cnb3*xfjo gm (pr;ota99:; 1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0t0 (jc ;xq+inci(lxg , s. What is the average angular speed of t0cq l jg,(ix(c+ xni;the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0hxp* 9e/,xifd s. What is the linear speed of a point 0.10 m from the center of thpdhx ief x9/,*e wheel?

  A cable car at a ski resort byv/d:o 7+bmpx pp** tcarries skiers a distance of 6.8 km. The cable which moves the car is driven by a ppyppb*tb7 x:*/ +omvdulley 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 with a c6qx )ic/ub2 5iixk3vf7 kdu5-1gg voionstant angular speed of 2.0 rad/s. Wi cdix/gx i i2kvv5q5 b g6)7f-k1uou3hat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If th5x ws:.jnz+ga6f*u oe 3btt 2be motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end ofn3+j2sx tb w z.ao:5* feut6bg the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/6*./)qda-ecbi hi-:p g hviofs. What*)iio-achieqfh 6gv: -bd /p . is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter ok+wx5fz -/smtmmwh6/ f a bicycle wheel of diameter 70.0 cm when the bike is mow mf/mtmwz /s h+k56x-ving 8.00 m/s?

  How many revolutions per minute (qw8 w-q60cm nkrpm) must a circular, rotating space station (r = 1000 m) rotate to produce an8qk- wcq0n6wm artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ofsymz(w3v9n6 b 20 m/s. The maximum centripetal f3myn sb( wzv69orce (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 curv),pwt.f qigncbsb+f 06gdk -rx52 v.ot 2p2pb e of radius 50 m with a speed of 20 m/s. The maximum ceng0 nkb +wctxp-gqpfod.ib r2)bp.2t65sf 2v ,tripetal 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 0r* bs:pex4w 5c.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 maxw4sr* xpce:5 bimum 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 slipr oxea(u6w;hadk +2e9 ping 10 m downedhxu 2 6k(;+wo ae9ar a lane 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 l an)a.b*,f/ppso xzm+ 6v7o sa constant 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 of ql(,9px /la eqeb0uu ;r6j. vs$4.5 rad/s^2$. 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 rs)9+z r;*m7c xuddhj6q cmlm+otate after starting from z ddm*mh)m;+ +xcqjc7u s69rlrest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and ha ts gx9c2e17jas 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/s deceler,dx0n:vpn4kce* ja, yates with a constant angular acceleration opkj: ayn 0e4 vn,xc*,df $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from xp j.4)puk8 jbox zx-.rest and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acckb)x.8o x4.pjj-p ux zeleration of the wheel?

  A wheel of diameter of 68.0 cm szxx .8ejetj1-t,s t-vlows down uniformly from 8.40 m/s to rest over a dist x1-8.-sjetzj,v tetxance of 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 fav6t7 q;z0kpom 8.40 m/s to rest over a distance of 115 m. What is the angular accelekptz 0fq76va ;ration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/5- vbiflydjj+y aq;.. 3 fj*yjs to rest over a distance of 115 m. .day-;qy3 v .fyij5+lj jj*fb 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.nh,7 xi;ljxkdjw0npq,say,m,ig zp8.e 0 .n 3600 rev/min. When switched off, it rotates 50.0 times at a constant an,p. jp g7e;hwd yq0k8,.,lx.inx,s z 0mn ajingular 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 luv7bcf*,nx- sg :t,fnd 4ow /a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requirxc,u/n7,tlgs *n -vd bw fo4f:ed when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torqueoeb ug :+t-m4u of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requib -uot: e4mgu+red when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerh4fjv8j8cz j;tia $3.00 \; kgm^{2}$ 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 orig+htdk so .rt55in, mass 2m is at x = a, and, mass 3m ist+ r.othd5s5 k at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass (ppwf flm:mbe 9xp/ : yyv4+1x10 kg is pivoted about a frictionless axis thought the center O. A rope wra: lx pm4fp w vym+bp(ex/yf1:9pped 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 thought the (fyfxq +us2 ,bcenter O. A rope wrapped around the outsyubq ,2 (fx+fer 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.q8 7f).y qemtmobz, 7j The rod is initially held in the horizontal position, and then released as the free end is allowed to f qomey78zmtqj.),7fb all. What is the 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 k0g5lw1up.;q:cgez v qruew8u9gg q/ .g. Neglect the mass of the axle and sprocket. If a force of 20 N is ap . gz810 5u:vlg;e 9qqgwqgc.u/per wuplied 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 wrapped around a frictionless disk pulleyr2 2 i)cuf7ggj of mass 7.07 kg and radius 66.0 cm. What is the angulaf)cg 27g jiru2r acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fricti36hrwvunh hh6eh- -v/onless disk pulley of mass 7.07 kg and radius 66.0 cm.-/nve-rhhv u6hw3 h h6 What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it0 d +t xahxwr9-,yzcp4 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 inq 8ved7bcp5j;j (ej9a eo*jy6ertia 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 an *o j3cfn8)0z oafh, vz-pt3ucd 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 r n-ofa)0op8* 3cj tzfz 3v,uhceaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolll2 xk ye6;.xjfs with a speed of 10 m/s. How high up el;.xk2x y6f jan inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fskfub3 k qqug+o742l1 rom rest and allowed to roll down an inclined plane. H blqgok3f1uq2s4k+ u 7ow fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg a8tvhv ngxx-o8,rkei( h-jm84fsr-/ ynd radius 15 cm rolls without slipping down a 35e incline that is 7.0 m lo -hr4jtvsx/-o y( -g,8hx irf 8v8nkemng. 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 ez+xi a4(+.)k a ipfhy)vcaa5changes 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 mome.* xoqxr7eym c(6t8hz0)sl p i)yf h4pnt 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 has a moment of inercdsdvr,ec)q+ +; 8vki02ot dztia dt;v082d,ik+eqs+vcr )d z co 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?