Angular displacement is usually exmco)6q*ijvkm v268 gq press in units of

  Angular velocity is expressed in units td9(b-bwa3pbnkr ( j 8of

  Angular acceleration is expre kp2ca0 hk:a 88ld42 cpnt8bvmssed in units of

  A boy and a girl are riding on a merry-go-round which is tl8ufh gv2 +jdapgszs+ ;/h)x4urning at a constant rate. The boy is near the outer edjhpux)8v+ dhs/;gf4z2la+ gs ge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are rif4b y+mbju 04tding on a merry-go-round which is turning at a constant rate. The boy is near the outer mbtbu j4 4+0fyedge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning asp;5)b qb5 gupt a constant rate. The boy is near the o5p g; q)ub5bpsuter 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-ro8uy7 4o+cz(sh.how n wdd s+7 )gwnl/kund which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater 7wg7wd+.c/z d48yosuos lhhw(+n) n kcentripetal acceleration?

  A boy and a girl are riding a m,7;y(peu6w4 ;lqo bu mneh ufpfy.8 2terry-go-round which is turning at a constant rate. The boy is near th p(m ebluequhn7yfpy6 ;t8; .u,fo 24we outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the fonjso5hl9u4 yo evv32sb m+k/- llowing is an accurate statemen3bm h/-onv l2osvj5e9 4usy +kt?

  Rolling without slipping depends onfls e:bg1ku.n f(x:yq7h yj30

  Two equal forces areu n2q8rt : wlnv+(ma-s applied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknobn qw(+ t8u2:- rsvnmla. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is appko n*7qk8 3niolied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the gn87inq 3oko*kreater torque?

  Two forces are applied tox7m tu8ni8+j 5hol7ilsw5 e4w a doorknob, perpendicular to the door. The first force is twice as large as the secon lse5w7874o wuhltmni+5xij8d 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:vg tu dbj(06eect's resistance to changes in rotation(vu:t 0bdeg6j ?

  Consider two uniform solid spheres where both have tfs))cp )8yewb yq a4 qcdwqb()hd- 2x7i:-jzphe same diameter, but one has twice the mass of the other. The ratio of th)dh) wp8z d4)-qb -2q7a)sei:by fqywc(c jxpe larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius oxsn;*a zffraia i01 )3hmq))j (a8zwa f the other. The ratio of the larger sphere's moment of inertia to)a qw1am*fjazfr a0;ii) h )8(n xzs3a that of the smaller sphere is

  Consider two uniform solid spheres gad-l* tes rerqn03+1c w:h-n where one has twice the mass and twice the diameter of the other. The ratio of the larger moment t1r wd-hn0an3 * :q+r gesl-ceof inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M ar1 niw o;tny,)nd radius R. If these are increased to 2M and 3R, what happens to the sph wir1ot),yn; nere's moment of inertia about a central axis?

  If a constant net torque is appld bs3hkq)t.82 0e k:rgdcsu;lied to an object, that object will

  The moment of inertia of 2ab 4twlxuccz:h.p 9/a solid cylinder about its 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 whe9oevf-j*4 ,x 94u zasx8/dnw ftb kx3eel of which has a mass of 10 kg and a radius of 30 cm. What 3f 4-a n/df, xwxt sekez8u4* b9j9xvois the ratio of the rotational 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 rolls without slipping down t1s89ah9it 4duo0wug5so su :.yw+jaan inclined plane starting from rest. The linear velocity of the sphere at the bottom of a.us th: 5saogdwiu91t 9s 08j+wyou4 the incline depends on

  Suppose a solid sphere of mass M and radius R r0,j9b aca(e7( tmei xnolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depea(ejc 0x tma,97 inbe(nds on

  "The total angular momentum off )pi99g-ndi xng /n:a a system of particles changes when a net external force acts on the system." This statement if pgxdn:-/ agin) in99s

  In what circumstances can the n188mv.4hep2g ,smxg 6tmozpugf70 nangular velocity of system of particles change without any changg 1pvztg.hgm8 7xueso0pf, m84 n6n m2e in the system's angular momentum?

  The Earth orbits the Sun in an elliprdhrfk . q,fy6f,(fv(tical orbit. Ignore any friction which may be present. What happens over time to the Eh,,f(6(drff yrkf v.qarth's angular momentum about the Sun?

  The Earth moves about the6mqtno2x l2clmx. 2y oiz2;3 qp3dt+s Sun in an elliptical orbit. As the Earth moves close to the Sun, then which o oxl2+c3odq qn2mt3; ztsyx2mi.pl6 2 f the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spxwhar42ky+*8 *vw:irw/w aa q in) by pulling in his outstretched arms close to his body. What happens to his +w:a8*r4ryw*ax qh wiv 2kaw/angular momentum about the axis of rotation?

  An ice skater performsly/xjdp -9ck3 a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kineti y9xl3k jp/dc-c energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin)gkpexle/n r s1+kv*8d 0c*er n/n0kq3 by pulling in his outstretched arms close to his body. What hp*rkn e83vxlq0c +enk0 *er// snd1kgappens to his moment of inertia about the axis of rotation?

State the law of conservationi0 /nb;wq83l z(qhn iq of angular momentum.

  What arc length does the Earth travel in a three month period in its neabarop/x,7bhpws v) , 1rly circular orbit about the p/wb b1p ha,,roxsv7) 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 tip uau09 6)t/vguif1 dl-0fdl gsof th9i d6sud)ffuv/ulg 0alt01 -ge second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per mka.g0rgs 1nm q8s6t e xp;z4i5inute equivalent to?

  A bicycle wheel rotatesh p5ba4b/mma/8y v f9i uniformly through 2.0 revolutions in 4.0 s. What is the frequency of th54/9pmh ivb8/ yf baame wheel's rotation?

  A pulsar (a rotating neutron star) emits cc i;tes68f *qpulses at a frequency of 0.40 kHz. The period o;*6ictesq8f c f its rotation is

  A phonograph record rotates at 45 rfz4q+ m.a zlgh2.i+ dtpm. Through what angle does it turn in 0.20 +i ztq. hm+z f42gla.ds?

  A wheel of diameter 26 cmqpn,ypdz y069je0;i / ie fdjx csg;)5 turns at 1500 rpm. How far will a point on the outer rim move ;p0 5fq egd/ j0y9x nzd,p)es;iicy6jin 2.1 s?

  A bicycle wheel rotates uniformly through 29a y0qx:s9 foxa n39ul.0 revolutions in 4.0 s. What is the average angu0sxy9l o9q9: fx3n aaular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions ix5ykxx, .go 0.rpptp,n 4.0 s. What is the linear speed of a point 0.10 . kgox p,r5xxt,0.yp pm from the center of the wheel?

  A cable car at a ski resort carriehb, ste*w1 80aw,bvv xs skiers a distance of 6.8 km. 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 f*vwhx,0vt1b , aw8b seor the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a:9 (j3j dfnjsf constant angular speed of 2.0 rad/s. What is the linear speed of a point on thes93:fnj(jjd f wheel's rim?

  The cutting cord on a gas-powered weed 7vd05 bjr.qp.,h g3do;:2pe2nf.rf ymko qt g cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is thvoqrd2.2hpg5fbm 3n;g.qk,joe f 7dr:.0y tpe approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant as9xf7p/c- qnvngular speed of 2.0 rad/s. What is the centripetal acceleration o-s9vp/n xqc7 ff a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bi) ;u exghp77m p8neqy4 l8k845nhxzkzcycle wheel ouepypk8mzn5h 4kq;74ghezl 8 nx 87 x)f diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cirb2v1jler / rybo7wy: 8cular, rotating space station (r = 1000 m) rotate to produce 7b8 /ewrrj2 l:ybo1yvan artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat 9tln q6 ,tyhh3circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal fort n,93qy6 thhlce (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 speed of 20 qbg9os5ws7z7 g,zj)upm4ze. m/s. The maximum centripetal force (provided by static friction) jm 7zgp7. gu zow)54ssq,e9 zbis $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the e2c8f csey5;k and of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is fsck 5 2caey8;250 N, then what maximum 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 slippir0f0 f g8wlgam5w2h6 i.fkqx(cr ; u0ing 10 m down a iru0 iwf08qf2ax f;klw5mgrc h.g 6 (0lane 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 constan6/i/y 0(vf6hiajo u cjt 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 acyu mpx89 7mw)nceleration 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 automobile31mdb *h7l q c;eo;foh tire rotate after starting from rest and accelerating at a cond;7*l1 cho3e fqohbm;stant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration 9m/dzh0ue,0.nuxq lzof $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at e sedjdz1vc )l-2n6q7b,w 5by20 rad/s decelerates with a constant angular acceleration oe -c5 vwn2d,7j6q) dslbyez1 bf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.f*- 3u w7kehmu0 rad/s while turning through 2.0 revolutions. What is the average angular acceleration ouf*mu-3kweh 7 f the wheel?

  A wheel of diameter of 68.0 fu(z8s* ht3qmetie ::cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Whattsm(*eh3z iu8 fe: q:t is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly p26 pwcrjadf4s,s/ 3 pfrom 8.40 m/s to rest over a distance of 115 m. Wh3,6 pjcpa2/ fswdsrp 4at is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest oij8oj4(5y/ qpra nk3ug r-;o uver a distance of 115 m. How long doe-ryu8n( 35ig opjark uo/;4qjs it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of lnd3q dc*wy e4jd2h)s b6+0an3600 rev/min. When switched off, it rotates 50.0 times +0cew y n6jd)2a4*d ql3bsndhat 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 tighten yx*/:wvsn9 hcing 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 perpendicular to the w9ns:* cxv/y hwrench?

  The bolts on a car wheel require tightening to a torque4a8e .e)rtn cm of 90 Nm. If a 30 cm long wrench is usemaecn4.te)r8 d, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ot fs u .j.41z/t,+qixxov/ egtf 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 mod f,n0 s-b azqgptv7z*(eled 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 about the orpt-vgs0*7 fzz,nbaq (igin?

  A solid cylinder of mass 10 kg y+/qpis 36 zu j6n-lpqis pivoted about a frictionless axis thought the ceq+zp/yjqp iu-36nsl 6 nter 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 pivofa0xq rrp -v8(cg.pe/ted about a frictionless axis thought the center O. A rope wp.x/qfrg(c0 var-ep8 rapped 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 initially held in te+6cpw/na ek( he horizontal position, and then released as the free end is allowed to fall. Wha+p/ ( c6nkaeewt 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 i (,fht;1ric ty xpx-6a 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 tangen;xxit(ci 6, y1tp hfr-tially 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 frictionless8bdyc03 og*dx ck8j5 e disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the c *dbe5o8g x80dkc3jy pulley?

  A 1.53-kg mass hangs ono lbff/2nn 5e4o0aa t0 a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleefn 4al0o0n 2f5o/tab ration of the mass?

  A rotating flywheel can be useda1mv br, c5p:,gegp4 vd/m wp( 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 ofkkwxl :l7 d(fnn-w esq.s/p ;+ $5.00 \; kgm^{2}$ 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 wi i2isr20rqea-hjc q*0thout slrriq -j2hecqi*2 0sa0 ipping 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)xt9j 04h353 hom ohwzb:bb*e.lejm l.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it clim9bhm5jo el3).emhw:lbh4 txo *3jb 0zb before coming to rest?

  A hoop of radius 0.50 mu*uvv- 8g s7ck and a mass of 0.20 kg is released from rest and allowed to roll dow8s*u k7 -uvvcgn 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 d09,s4ttymfm yf9k*jfz p(: t lown a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sp* fsyt 09f(fk,mltm z4y9: tjphere 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 changt3c)w1g y gj0qz,f l)2m lkw33 rjn7ypes 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 ofyf) g5 :r)vs+nk7qmjgli 3b h6 $5.0 \; kgm^{2}$ 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 5.0hrphq9 5sq2p 7oh2h y*0 rad/s with arms extended has a moment of inertia of op2p2 *h9hq7r qhyh5s
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?