Angular displacement is 86 cig694hlm-uoc wf kusually express in units of

  Angular velocity is )+q eim02msmr/jmi4 +rf+g dm expressed in units of

  Angular acceleration is expressed in units oq:nih,:lz9*uwnzij6.o v ); fg af ;fuf

  A boy and a girl are riding on a merry-go-round which is turning at a consmaq 9cm 6ge1t+l(zh;c tant rate. The boy is near the outet6cmeqa(gc;9+mh1 lz r edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round8/6jo0 vb qan uvamn );*ild2hu.n ks+ which is turning at a constant rate. The boy is near the outer edge, and the girl is closer t mqu)in +aldvsj6hk0 ob8.nau2*;/n vo the center. Who has the greater angular speed?

  A boy and a girl are riding on a mexu4 ludau-y,j;ah a4(rry-go-round which is turning at a constant rate. The boy is near the outer edge, and the g h-u4yud; x,4a aa(lujirl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is tur 3)cf9blpbmt-y-/xs8 je,f+tikwhfr r s6y40ning at a constant rate. The boy is near tkh 4bti-fyr6 83mpsbwc/t -+x0r,9je fy)lsfhe 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 turning at a *uu) 29ykpp ipconstant rate. The boy is near the outer edge, while the girl is closer t2p ip9)uk yp*uo the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whicdm k:rd7*r9- s2/hd epum;j aeh of the following is an accurate statemem2a-desd/ :*ud ;7mjrrkp h9ent?

  Rolling without slippf k /kle4oqd67a.hwl u8c5p w-f8dqy)ing depends on

  Two equal forces are applied to a door. The fir*b;vzalxd*2ug :z go )st force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied pdzgl;2:uz obv*xa) *g erpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the dooe5 5wowp8 m/ 5db.0gpdds5l:tzngtq( rknob. The first force is applied perpendicular to the door; the second force is applied at 30e to td(w :t 5ng5p5mzogdd ps5/bqt 0 8ewl.he plane of the door. Which force exerts the greater torque?

  Two forces are applied to a ds*u wfo/ sx*2poorknob, perpendicular 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 of tp wos/**2fusx he second is

  What is the quantity used to measure an object's reschz;qr nhjyb1x li 6a- k )-b+,9trf8ristance to changes in rotati+zb6r1 lq,xtni c k ab-hrr)y-h9;fj8 on?

  Consider two uniform+-ksmkhozaxtw -rg*1sr.9k+ z+ ev *x solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio -r* hwgks1a vkok*s t.9 +mx-x+e+rzzof the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid sphereis*-fyhr, 7hg s have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertif s7-yigh*hr ,a to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and t vc8u )d+sfua ptrtbw1 jow.e v++2,(ywice the diameter of the other. 1)vu+sta+cjtoww p.fv2d+r8ebu ( ,y 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. If +aunhr qktc2 8vi0u5:j * 8shqthese are increased to 2M and 3R, what happens to the sphere's momn:t80 2uksqu8+ca h jv5riq*hent of inertia about a central axis?

  If a constant net torque is applied to 2z2ik mj+ x(vsan object, that object will

  The moment of inertia of a solid cylinder about it w2f/is/u++p fia5fyjj;x (mh t9e (wys 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 of which has agwh lk;os s;:, mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translationh;w,l;osk sg:al kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere7u 48fgyvoyh(s6; r z;bwww 9d of mass M and radius R rolls without slipping down an inclined plane stayr9w8;w s6 h dv;yw4g o7uf(zbrting 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 r;r(sj 9etw3di olls without slipping down an inclined plane starting from rest. tiwdr(sje 39;The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a *r 8 xhm/x)i6hj1mjmssystem of particles changes when a net external force actxh18 *rj/hmjs xi6mm)s on the system." This statement is

  In what circumstances can the angular velocity of system of particles changjt g2 -39ipfdb 1e0woye without any change in the system's angular momentw0ftje gpoy-3di b 219um?

  The Earth orbits the Sun in an elliptical orbit. Ignore any-g(hvycr1u 2 u friction which may be present. What happens over time to the g2v uu-hyr1(c Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical or5 0vq0s(zv pocbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth ab0cv( 5vz 0psqoout the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his oulz cjwsh:8dmdo 3(p2 5tstretched arms close to his body. What happens to his angular momentum about the axis of rotation:hsj d5zd2lm(3c8pw o ?

  An ice skater performs a pirouette (a fast spin) by pulling inly9/;)kzuav (l1f rwa z0who1 his outstretched arms close to his body. What happens to his rotational kinetic energy about the rawh19zo(z wful;l yv 1 0/)kaaxis of rotation?

  An ice skater performs a pirouette cu -o9dn81odk(a fast spin) by pulling in his outstretched arms close to his body. What ook 19uncd 8-dhappens to his moment of inertia about the axis of rotation?

State the law of conserva+iyim9lx+29; iq kmz mtion of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly circzh19qtqe r6z0 6udkz. n+dc.aular orbit about the qzz9e+d.1r6ck0 h a uq d6nt.zSun 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 nh0c)3w a ykx)1b/i9 +egb y56scvxvktip of the second3 )s6y ca1bi90kgxcy hvw/xbnek)5v + hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutiomes 8upm5 rg;m s avl-9 v+n2cg,1ibz+s*8r cjns per minute equivalent to?

  A bicycle wheel rotates 4+ka7g x ucjc1l4m8oc uniformly through 2.0 revolutions in 4.0 s. What is the frco8ua447xl+ckm1 cjgequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency bu 7zwavb rxa8h4-n1d 9r-;gr of 0.40 kHz. The pax81rav brd nb- zg-9r w4u;7heriod of its rotation is

  A phonograph record rotates at 45 yh2 mcyf z7l )0i2yt1rrpm. Through what angle does it turn in 0.20 stc 2 r7f)mh102lyziyy ?

  A wheel of diameter 26 cm turns at 15tidi ,ddj* /w3t30fkc 00 rpm. How far will a point on the outer rim mt jdd3dwfi 30c/ikt*,ove in 2.1 s?

  A bicycle wheel rotates uniformly through 2k .8n( 4mq *hrdbycij2.0 revolutions in 4.0 s. What is the average an8.hyb 4nkq * d(ircmj2gular speed of the wheel?

  A bicycle wheel rotates unyq* y:7djuy-l /vo8ko iformly through 2.0 revolutions in 4.0 s. What is the linear speed o dyy y/- ljukqo*v7:o8f 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 kf v7 v1wk0if226nb qsyi;0q ejm. 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 is 0jy6wkb2veq2v 17ff;qn 0i12 minutes?

  A wheel of radius 1.0 m -t oq1p tgo(v-18al tqis rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a pointgap-8vo1lt ( qott1q - on the wheel's rim?

  The cutting cord on a gas-powered weed cutt80lm 3wdhj btnb-+ fd7er is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate li78ldhw3+ jmd btb0n-fnear speed of the end of the cord?

  A wheel of radius 1.0 m is rotatgnnp0+mn i.kixb:5to.1 bo2g ing with a constant angular speed of 2.0 rad/s. What is the centripetal o0.1o mkn5i +.2gxgpnb:bti n acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a poipeg t g7q58dwb 2-pu b/e;o-acnt on the perimeter of a bicycle wheel of diameter 70.0 cm when the bik eud ag 2ebo q5g/-bcw;tp-p87e is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statibcw(p8 w dt2px prb+ 01w5czo1on (r = 1000 m) rotate to produce aw0w2+tpzw1d5cc8bxb 1p (p orn artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speq543tvs(t ib dai.l5ttkb-7pt,yi0nw nj:2 led of 20 m/s. The maximum centripnyaw ,t.2ls53v-7n0l4(i bpki j tq dttti:b 5etal 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 n*knxw*go )i/t.i ,ttflat circular curve of radius 50 m with a speed of 20 m/s. The maxikx n.w,ntioi tt)/**gmum 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 v2;(vhq-mtx r7knkwynq r)9) 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 speed(x7 9 -n) m)hrqwk;n2v vqtkyr 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 sy(9n(6ixw 5n rjgqhcy:4 bl2mlipping 10 m down a lane atilm:hcx4j q5wyr2 g b(y9n(6n 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 angular 7or ec3 x9z 0bdqd,/do(0iklxacceleration 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 az*cjh)b 9j, ea 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 rotate 2irf7i ;/4n(b 1yduaugrln9 qafter starting from rest and accelerating at a constant angular a 9b1ndni4/ 2au (ylqrrgif;u7 cceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hhyzt8 t+p1jxsma*)u2 h4tm *mas 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 constant angular acceler.1 mmnka yw8xxnhi5 .gem;(a ,ation of 1,gm nimhm(k. xew 5a8an ;xy.$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from r ; lkknq +3c20hzuc2mmest and reaches an angular speed of 6.0 rad/s while turning through 2.0 revoluqck mk 03uc22mn;l z+htions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to re.1dqnfsg 4 (syst over a distance of 115 m. What is the total number of revolutions the wheel rotates if 4q.sysd gn(1n coming to rest?

  A wheel of diameter ofon5 (j wc77d0q sx+3asf tg3tf4gewx+ 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance t+o07 g+sxtsan5 jx4fg 3w7fe(cqwd3of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over hcs(hz0 /tc: hebmvbqh1:*7b a distance of 115 m. How long does it take for the whe b:*c:h ctbbsm/vz(1h0eh 7qhel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational spdua66; 0z uskheed of 3600 rev/mi 6a; hzusuk0d6n. When switched off, it rotates 50.0 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 tightening to a torque of 90 Nm. hsbq o). (odl2j7vmx ; If a 30 cm long wrench is used, what is the magnitude of the force required when the force islj7m( ).d qv;h2oxo bs perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 3 1e+nx)vf +lbb0 cm long wrench is used, what is the magnitude+ bf1b v)xel+n of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of 7;mcv;im s t70m9g;:dfo6 7hmtqnjdxinertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic moleculeh :m8bcf/,yi j is modeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What f:8mb,/jcyi his the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a loc(i0n ci+;ffrictionless axis thought the center O. An 0c+;o fliic( 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 aikw+2xsl -3 wa4ga, kjbout a frictionless axis thought the +a xlk-w,3 w4k2aisgjcenter 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 h w,ba9jk6)x kainged 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 moment of inertia of a rod about x6ajk)9bw ,a kone end is ML2/3.)

  Consider a bicycle wheel to be a ring of radiq7:f*gaurc6cm 9c h0uh wr js0;o(a1hus 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 for 4.1 s, what linear speed does the wheel ach:aom r0r j(76;fca sch wuu1c h0gq9*hieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped8r )g ,pwkcd74edh. el around a frictionless disk pulley of mass 7.07 kg and radius 66.0kegddew )h .p874lr,c cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frihf3*90c o zghp6: *fdd:wu lqpctionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the mash3qhf 6 c:: p*p9uz0odf* dwgls?

  A rotating flywheel can be used to store energy. If it is requir0 osn7)f tjc5zqy 3,zned 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 inertiae c g6:w hs u(ppufsdkh5f:.74 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 m starts from rest and rolls witynn;5 tv9 3k5x s,cqmahout slipping down a 1.0-m high inclined plane. What is the speed of the spymq5nv cts3x9;k, n a5here when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rol lzxd 068zu3m i2pdq(kls with a speed of 10 m/s. How higi 8uxp30 2qkzm6( ldzdh up an 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 from rest 94ao 6tf 6e:6vvrh bxoand allowed tovb atfe6:ov r66o 49xh roll down an inclined 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 without slipping d5d fh1x zros39 *;fotgown a 35e incline that is 7.0 m long. Assume it started from rest. The moment oof;s* 1 hg59xzrotfd3f 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 changes0x ax)0okrfx8 4yzpfv b5.kgv//k bt 6 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 inerhg u8:,vj gr tn(/xm xy 7-)+rtxyhke8tia 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 a8f smwt ob608e,yi:gf :gg:cxrms extended has a moment of inertia o:myt:0gio c8febx, fsg 68g:w f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?