Angular displacement is usualm-xo q 9, k6zx*wkdb piztg345ly express in units of

  Angular velocity is ex(hwu-1g- w kpspressed in units of

  Angular acceleration is expressed in unitsik8z0r q.r /t,al3psm of

  A boy and a girl are riding on a merry-go-round which is turning atctuk w;gtd8k()urk3) gaq ,6n a constant rate. The boy is near the outer edge, and the girl is closer to the center.uu)c(,8t;gkd 3)tqkg6n k war Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-rokd;i khaa 6 shh4ty1xy5wu+13und which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the1;xw6 4hiy+ask h ytau3k5dh1 greater angular speed?

  A boy and a girl are riding on aw..nw scuq(.h merry-go-round which is turning at a constant rate. The boy is near the outer ed( u.wc.h qnsw.ge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridinga u j,;l-l0lkb5fq f7l a merry-go-round which is turning at a constant rate. Th;fa lf0jlb7ukll5q ,-e boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turl6ow.:p2htq zb rw0ity4/im,ning at a constant rate. The boy is near the outer edge, whi0wqo2i/lbyp. :mi r,64ht twzle the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whc 7ixwv q5t) )wtjzf81ich of the following is an accurate statement? c5jqix)vf wt8w17tz)

  Rolling without slipping depends onvx;vkyt5 k-p0*fp o6( ikknrf1)/f yy

  Two equal forces are applied to a door. The first force is appliv3n+3h,: otl;ejlet sed at the midpoint of the door; the sec ten3eh;+v ts3lj: l,oond force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorah fpqc4.t7tm( 2 ajoxi 1o(5aknob. The first force is applio2ij 7tc.qpoxma5a ( 41aht(fed perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applie2o d+qf/ skhvsem:84nd to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of th /+sqed8mfsk4ohn:v2e torque of the first to the torque of the second is

  What is the quantity used to measur8sh.2,4ani- pi cdpi(wk 1b vme an object's resistance to changes in rotationbp8. mi 1id vi(ch s42-pawk,n?

  Consider two uniform solid spheres where both have the same diameter, bn -jy*s5l z ( ;br1z:vwmlie9xut one has twice the mass of the other. The ratio 5(mrz-lv i*:1;syzb w xe nlj9of 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 uh,0 ft8thqfx,f+au-twice the radius of the other. The ratio of the largeuff, uqf ht-t8, axh+0r sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheresc:okj oibnzmjs,:(4w8 gl7 v ; where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of thlgo ; nbs w(m8jv,o :jk4zi7c:e smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. I/pyu zbsk m*pl e 4d434mht8w;f these are increased to 2M and 3R, what happens to the sphere's momenpmhz* d 44ewu3m8/t;4y b slkpt of inertia about a central axis?

  If a constant net toe: *bd:9vpvwurque is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given( 8nxfw/f5ruqfu e3:n j,;xtq 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 oe4pu(rl4i5p 2pizu a7f 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 roppzr(4la u2e7 45iuiptational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphezgq 6g 8)cuo+vve0mzr,d.9pure of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bozgcv, om8qgd0u 9z).prv+eu 6 ttom of the incline depends on

  Suppose a solid sphere of mass M a)au0l x+s bg7s6ap +yjnd radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at thb++)aaj076 upy xsgsle bottom of the incline depends on

  "The total angular momentum of a system of particl;j6egxyt q 0kpnkvx 2-4rmlg k+al 05menp07;es changes when a net external force acts on theyt kpjl5k xr0ege;x04mg0-v;m+ kl 7p2an 6 nq system." This statement is

  In what circumstances can the angular velocity ofa/ cu9anv(i1dmo ,ok(b0t)k p system of particles change without any change in)/v9n(1dcip aokumka0bot(, the system's angular momentum?

  The Earth orbits the Sun in an ellipwa/.y de1i 3vek:dh 4ztical orbit. Ignore any friction which may be present. What happens over time toh z.:ewdi/k1d43yav e the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mojv/u )qx, zfrpi6.m0fluk:(s ves close to the Sun, then which of the following best describes the orbiting speed of the Ex qklj,u.ivmr0 (fsup f/:6 )zarth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in24)q a1ok5i+d; jf peu9 ehrcy his outstretched arms close to his body. What happens to his angulheo519)rjeikyu;2dcf qa 4 + par momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by ueo bhfxt) .u2b08x;bpulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotation?ebhb uf0 8xox2t). u;b

  An ice skater performs a pirouette (a fasd4qju78 nr vk8u: tw/it spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia aq i8t/kwd8 4vurn7uj: bout the axis of rotation?

State the law of conservation of angqdgm nmw9i ;gj+0*-ph:zvu i8k ue**xular momentum.

  What arc length does the Earth3w 6dvugo2, t nlqyv:4 travel in a three month period in its nearly circular orbit abw:ot2nquvl g,v6y d43out the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has6 8vhuib6/ -tpl; vuh e8cu4hq a length of 0.30 m. What distance does the tip of the seconducvv6pt8u il6uhh/ hb-q; 4e8 hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revoa6e)rn4xzmia)1 ff az(nx4 y i. o8;kulutions per minute equivalent to?

  A bicycle wheel rotates uniform7w- ewz4m/k fpwisuo37ti.z jq:)sr 9 ly through 2.0 revolutions in 4.0 s. What is the fi .) ejz-:7rqw kw9it sop/mw f7su34zrequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a dbgs.(ebaydf7j 8 7f /frequency of 0.40 kHz. The period of itsf.7dy8fgjb ( 7/dsa eb rotation is

  A phonograph record rwe ;x9+g5sr q swxx(+xotates at 45 rpm. Through what angle does it turn in 0.20 +xxw;er 9sx+x qs5(w gs?

  A wheel of diameter 26 cm turnswt e5.z *tckkovm,-1 cx0jb h- at 1500 rpm. How far will a point on the outer rim - -,zw 1 v0ek.*jtctckm 5oxhbmove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 .6hyi- f0 (epe)cjf lbs. What is the average angular spee0libfhj6ec(.-f ) pyed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the:em nis3sbd7f* 3k;me* tre1h linear speed of a point 0.10 msf b 33ehd*r emmet7*k;n1:i s from the center of the wheel?

  A cable car at a ski res,);93b4eqe g bnpogsupc8128 hi. rz kvq(iwsort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Av 9;4psg hr,ows2p)(3uqbe8.8ci1z ie kn gqb ssuming 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 constant angular spe2e5sze2rs z i.vg z; ;agn1;oxed of 2.0 rad/s. What is the linear speed of a p.; vz;g5xa1z;2ie n2zosrs egoint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m iny1xlpsl l 6257 y4ckop length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?llps 2 1lxc57op4yk6y

  A wheel of radius 1.0 mwf rsr6jwmo4(fq;zw1b , 9re+ is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the who+f,qsem4r6 w;br19 wrzf (wjeel's rim?

  What is the centripetal acceleration of a point on)5ce+cwdn.)9erv 1r yhx-r s 6(ecssk the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.1 r+9(ech )srdc. vc 5sn ew-)krxes6y00 m/s?

  How many revolutions per bj 1 (ik,zemd.minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravitiz d1,k(jme.by of $9.80 \; m/s^2$?

  A car is negotiating a flat cirsmh)/npw b73)kt dxdr3 qpy -3cular curve of radius 50 m with a speed of 20 m/s. The maximum centr/bxw3kr)hdy )3d np7sq 3ptm-ipetal 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 f 9vx3:z4cmnkqlat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal forccz3 vn4mkx:q 9e (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, bo1ryy421krogp 2yz0e-1zr+z kowy5 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 have1z -ozopg yr1k r14yyz5 ob22+rykew0 if the string is not to break?

  A bowling ball of mass 7.5 kg am(5o0 va4evq /h*yilp nd radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/s. 5/ol*m4e 0q aipv(hyv
(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 6s7t2a l4apeya 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 wg *pdpcv:(r c5ith 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 nrqywzhfd5vfa + ,7x1u:)sj 2 a 0.300-m radius automobile tire rotate after starting from rest and accelerating at a constantsv2nf:u1r a+5xdy)hwz ,qf7j angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angul08hw rw0;gn l6lt g:moar acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotatingx ,.1o pda8gc-iy trqm1 k,,xg at 20 rad/s decelerates with a constant angular acceleration 81id ka o,g , yqr,xpctg1mx-.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)nm:kdy *,too mgo; ,t of 6.0 rad/s while turning through 2.0 revolutions. What i;mk oy ogt*:d,,mont )s the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slo 1fax+pquh:1h7z;oder: x .uaws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of re r;o1x hx.qzaude1p:h+f au7:volutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down un.) 7 e pp rcdjgha16o+jc6qw8xiformly from 8.40 m/s to rest over ajw6o.)8 pge6p+jc x71q darch distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tetniv 0xjkwu6t95+d dh7l*g2( 3 apwgo rest over a distance of 115 m. How long does it take for the wheel ti tuw5 6p vxagj lk+923(d0*gh7nt wedo come to the stop?

  A centrifuge in a medical laboratory rot0zbd bxnm3k06 ates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular a6 z0db 3mxkb0ncceleration 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 a torqu nj6eytvurqnfs3zc9 xe0:;3/ e of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the e30zq fn 9;e6utvr:3scjn/xywrench?

  The bolts on a car wheel requi 8(38a*tdn w/ phldkw.zlt-msre tightening to a torque of 90 Nm. If a 30 cm long wrench is usedkm8 8.s(dtwh/ ln*l wazp-t 3d, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner0 o9 81xomp/ f9oznqy ju:as(ltia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule/+a l 4mf k)*k8bfg,azaivpr0 is modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia af4/a 8+kgpa*)zmk, ifvlbr 0 about the origin?

  A solid cylinder of m.4;qgnu.y69nmfjbmsmu: bk2 ass 10 kg is pivoted about a frictionless axis thought the 2;my bj gknq.b su n.m4f9u:m6center 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 pivoted about a frictionless axis though **7nmc/ oeubq7cwk1wt the center O. mocw7*qw7c1nek *b/u 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 initial ;0haotz;k 3x 2lb. wlt7edzpg*p; 9vcly held in the horizontal position, and then released as the free end is allowe k pt; zxzcev20p;adlot;3hg.b9 lw*7 d to fall. 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 ka cjr5:5c7px dg. Neglect the mass of d:c75acjr5 pxthe 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 does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped 9)e:u ve 6)z v w*mnva4r8ib h gxeyo/wm((;ezaround a frictionless disk pulley of mass 7.07 kg and radius 66.0 vm;uz bv9e(/m6r)(4)nxe*w :ey w e8vohi gza cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a ro ixh **4ogakn.li5bv z77go2q pe wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acce57a7z v2ixg ihg*ok.l 4n*qboleration of the mass?

  A rotating flywheel can bwuc9q8z9tmpb c3 kg3 5h67x- n vmh(dje used 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 inertia ogp1kh/dqt f -7f $5.00 \; kgm^{2}$ 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 0.0109 rqv1(f0gcs*dbzb2x m starts from rest and rolls without slippin0 *sb1 9fzdv2xrc(bg qg down a 1.0-m high inclined 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 rolls with a speed o yoo0(m:w /;zyig;lpof 10 m/s. How high up an inclined plane can it;oy go; m:l0y (/zwipo climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest 1/t,xm3rbsa zoc(8xv and allowed to roll down an inclined xr31 x(tvbm,c z 8/saoplane. 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 rr2:xewa sul+;olls without slipping down a 35e inclar 2 e+xwsu:;line 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 momentum chann(e*axf:m u a9jab*-pg5* eauges 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 q5 )hlb.7l lz2q.ilsl 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 wid6rm4y8sxq5e th arms extended has a moment of inertia ofxmd6 5r84qs ey
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?