Angular displacement is usually express in units odk6 xwpwf7w9q-c8w s*f

  Angular velocity is expressed i;z b53t1(wdpfwwwv1j n units of

  Angular acceleration is expr2wjtjg 3ge:t) essed in units of

  A boy and a girl are riding on a merry-go-rouvehrxq2-c-r .08aodund which is turning at a constant rate. The boy is near t0. r q-xuv2dec-hoa r8he outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ricn yfn4oszu vc8*;x, 6ding 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 tn;y f8s ozxc ,cv46n*uhe center. Who has the greater angular speed?

  A boy and a girl are ri weg09tk y6z5lding on a merry-go-round which is turning at a constant ratewey9 65klg t0z. The boy 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-go-round which is turning atkcf ,/q/- a xvonk/zo. a constant rate. The boy is near the outer edge, while the girl is cl n,oko/afz./q/vc-xk oser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ri;v4pa /dchqs 3z vt4 imnzexn-e;g85)ding a merry-go-round which is turning at a constant rate. The boy is near np 3x8gqzsci4;m) h zva4vte n-;de5/ 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 ofvyx *n3fs e8bj)2r:w9o55yisyi7w q j the following is an accurate statement?fv 3so2jrw *yy y)n8sq j9biix5we57:

  Rolling without slipping depends one7 1vlbshxz df7a1nib2 ,2f0x

  Two equal forces are applied to a door. The first force 8*z f i8ur)meys. kq+mis applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which forci+ *mk ur8qf8)szmy.ee exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is applf5hfuc3 . 4*3cwjaqljied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force h qja.cclw j5uf*43f3 exerts the greater torque?

  Two forces are applied to a doorknob, perpendicul ufukxil5x 9 s ldgl3:78+nu r0ch91vbar to the door. The first force is twice as large as the second force. The ratio of the torque of 8u719gusv5 x r 9n+ch fbul:3lxk0ildthe first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in r1jvs9ci + f7iar iwsh03vjd5d u 8t1n.otationci s d0f15j 9a+i v.uj3d8sitw17rn hv?

  Consider two uniform solid sphern2k7yl h. 4rxces where both have the same diameter, but one has twice the mass of the other. Thec74ynr l2xkh . ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mabj/(2 d2ahlz3 bzdu/g t40mm;tnh.dgss, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the g tmzdgdh nmz d.0 /2a(3bb ;u/24lhtjsmaller sphere is

  Consider two uniform sole- 47f s:(9yzeqpgu grid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to tha4s-zer7u(y pqfg: eg9t of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incr6wkimubv;60o7fl1 / wmml 9rn eased to 2M and 3R, what happens to the s 6k;fbm 61lwri/vw9n m7 m0oluphere's moment of inertia about a central axis?

  If a constant net torque is applpjb/:+1lyg7 hz vv1 znied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given byoe tkvw4ivz n 1zg:.3wr8+ q/g9bvn.j $\frac{1}{2} MR^2$. 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 v4+ .v,pn0iach.kno3ea -sed 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? Assume thshvneai-c n0.4+ae k,d pov. 3e wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rollsq29gx mzhd7svofx, m.w(8vc: without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of t,(w:zo 27 g qfhxv.smc9vxdm 8he incline depends on

  Suppose a solid sphere of mass M and radius R rolls withjdyu7)av 9ft)tqt d+w 8)xp 2nout slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the iy9+ n)7dvf xdt)p)wt j8utaq 2ncline depends on

  "The total angular momentum of a system of particles ch0:uk z znsvz28anges when a net external ns8vzk: 2z0z uforce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles chan0gmw9 -e4v epozj+ar 6ge withv0g6w4zrj o mae +9ep-out any change in the system's angular momentum?

  The Earth orbits the Sun in an:6bqzkp(e6z7h- mtn y elliptical orbit. Ignore any friction which may be pres qy:6hbzt (ne7k-mp6z ent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Ear,9a*i i pnqojd6rpw k1/5h- bjth moves close ppbji,d6r *kj5a1/wq9-hio nto the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by,q uaw9w4ggq vhng32( pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rota 2a,u943ngw wgv q(qghtion?

  An ice skater performs a pirouettyxi4)( c5ui, fh85rnz v ;b-mcys-alfe (a fast spin) by pulling in his outstretched arms close n au- 5-fxvbir8i5m,fsy(4;cch y)lz to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hij1hi:bao5 lss;k, 6 ius outstretched arms close to his body. What happens to hi5oush,s;ail j6 1b:kis moment of inertia about the axis of rotation?

State the law of conservatiod0q8ut-ci; jb2j a35uaq -h:9tyrrj bn of angular momentum.

  What arc length does the Earth travel in a three month perioo5zac(+4 o+ttqvg pvo ;8ir n2d in its nearly circular orbit about the Sun with a r8vp4t2og i5q;a(v+zo n cr+otadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length ood3zbdg6nor-5 5i3d53uthf o )*rttb f 0.30 m. What distance does the tip of the second hand sweep g3t5t 3ri drfu b5d ohn)o5tb-63zo*dthrough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutionkia y er5asau.7 b35-5wgfj8 ks per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the8zd uu6p0xy) j; eeqw4 freju;86 xywuzq0pe4)dequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits puls 2;hb4 qq*hlbb +hjati-)5knaes at a frequency of 0.40 kHz. The period of its rotatih+ 5;-njklbat2b4 h a)*hbqqion is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0vnm7 lg c*6l r 76.z;5lephrvq.20 levqnc.rglr6*5z7;vh mpl76s?

  A wheel of diameter 26 cm turns at 1500 rpm. How.7jyv* 0qommte0 5ia a far will a point on the outer rim move in 2.1 05 eommj aa*yt7 .0vqis?

  A bicycle wheel rotates uniformly through 2.0c7 vlfy7o7j0ultsrq8 v2 87co, f -vjo revolutions in 4.0 s. What is the avvfq t,07r78v o7-8 jfsyouv 7j2lcolcerage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutiw acg9 9xkmg9eb(6-vxpmg8 /v ons in 4.0 s. What is the linear speed9 g apv/xe 9(mkwb-9 6cvmxgg8 of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 k+jx -uncobw b)b8bf- hzzm )74m. 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 make the trip in )-of)w7b-hxzzb4jn8 m +ub cb12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular s5kl7i of zvc -s6n2x*npeed of 2.0 rad/s. What is the linear speed of a point on the lfv2z-o6n*iks 57nxc wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If t.skv* dh 5paxbl m9)e6he motor rotates at the rate of 20 rev/s, what is p*k)sd 6vmeh9. bxal5the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular som0i m3i s6aa)peed of 2.0 rad/s. What is the centripetal acceleration of a poinios)aa3m0mi 6t on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a b g eh )bbmyc:*9i2js*ep ao/f,icycle wheel oi*9/osa:eyg *,bjmec)pf h2bf diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minutg(so6fafl7,ec- ;8 xov csx(s e (rpm) must a circular, rotating space station (r = 100f6oeag ;ss(c( ,8xf-vxs7l oc0 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radi(pnp n 88zt1jxus 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) isz18xt (n nppj8 $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of rad8jarj/z,yp bh r(- u3xzx ;n5aius 50 m with a speed of 20 m/s. The / xp(nx;j ayb3 rujz8-z r,ah5maximum 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 0.75g3 8d,+87lw ( unp-qiymzuhtzl(g b/fwyt 2a40-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+4t p8fl8,ht2ugl((minza7u w3wz d yby - gq/ linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and ra sqyaw5( 4obd,0fo/v,gm/ qvqql 8ac 1dius 9.0 cm rolls without slipping 10 m down a g/qd8ysaf c1ao, 0mqb5 q/ v4(vowq ,llane 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 c fwzk 9enne:y9cep:r (, k5g3vonstant 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 accelavey : w2)o ucb4/ks*beration 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 rotate adgkl j3ct(b3i5ik0 0/ rso aa7fter starting from rest and accelerating at a conscj/50 okd3b3a t(gl0rii as7 ktant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, v2:7cyonkg;land 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/s decelerates with a constantzq9-m5 wvbutq,c7 nt * angular accelerati 7b95nzc* uvm, qwt-qton of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and regk:osw8ek)2 hea(kfcjm39(l aches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is th9 2gc8k kjm:law3o e)(ef (khse average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down udbnwbr 94i) ;yniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotyb;rb )4nwd i9ates in coming to rest?

  A wheel of diameter of 68.0 cm d msc6k tem 2;lcaxu /9z-4:ufslows down uniformly from 8.40 m/s to rest over a distance of 115 m. cut9k m6s / ezc-la:ux4 df;m2 What is the angular acceleration?

  A wheel of diameter of 6dy x/- n10ke1qbw( nto8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take fnb w(/1n-1qdtk0x e oyor the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3/v -qlot r w0x8a0nt)s600 rev/min. When switched off, it rotates 50.0 times at sv -lt/wn o)r8q0t0xa 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 requyb3yj1 z f*d4jd se93yire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicdy3y zfy9 d*s43 je1jbular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm l.j4m xtzkn27k;zaa 6wncm )j6 ong wrench is used, what is the magnitude of the force required when the zm76.)m axw;kn6jj2 an4 tzkcforce applied at $53^{\circ}$ to the wrench?

  A wheel with moment *kls/*bu4p ykv)zqn z 4 qf.vv/z*:lqof 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 is at the 0lvr;j zy.uw6origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia z ryw0.vl6ju; about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionl g) puk0q33du wmhkhh5c6*so7 ess axis thought the center O. A rope wrapped around the oo063k *)qhpg uu5dh 3smw7hck uter 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 kvsv hl(xx d;h4:- )lxaxis thought the center O. A rop x( ;s4lxhv-h:vdlk) xe 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 atl jknbl9bl;+ 5)hiz y* 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 moment of inertia ofnillk+by* jz9; l 5b)h a rod about one end is ML2/3.)

  Consider a bicycle wheel to be 3qo2ey,klwa j b7 w0y/om8 eh6a ring of radius 30 cm and mass 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 f8ol/yoamw7,hqj0y3 k ew 2b6 eor 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 ag y8y-g2j:aph j9y-m z*h.jg sround a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of ap9 myh8g jg*y-:jgjh-.ys z2the pulley?

  A 1.53-kg mass hangs on a rope wj7i dk/*fldes) :vit;rapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the massdd /v;selk*ji7i:) ft?

  A rotating flywheel can be used to st-g j7t/s6yb3 y5rhfwpore 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 o 9nean4,3rf wo zrb,/bf $5.00 \; kgm^{2}$ 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 rest and roll r52z 1kyn-,v;kgutq8 s-d fyls without slipping down a 1.u ynyk58tf1v;l -g-2z, sk dqr0-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 r3m1(msib1 t2 u;n cqnaolls with a speed of 10 m/s. How high up an incl bq1(3m;maniuc snt21 ined plane can it climb before coming to rest?

  A hoop of radius 0.50 *dz+.n jv 3 4,qsz-z8epjx rji5(b-jcv:devl m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertp-je3j,z idbxz cv(zvjjl:5+rs nd *-q4v8.e ical distance of 3.0 m?

A solid sphere of mass 1.5 k cb/wbk *4whyk4n3z1qg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from re1/4kc b3*q nkhww4zybst. 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 cha )vk 8ux ,+65ftjqc7eu( ltphty*,bs anges 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 mom3zg5wrp 9pgi)p60 jq dent 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 ejh**,mp25 w, gzkwqeo xtended has a moment of inertiamp *wj,z2oqwkge*, h 5 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?