Angular displacement is usually express in units oe imll h2 zr4+7w*+chvf

  Angular velocity is expressed in unit)4 d fk8yqmzo, ezpg(qbj-z/8 s of

  Angular acceleration is exprevv02c09 qlnw6 ri +tscssed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constak v 48eg1tjua9.orbumzqp;0:7 r 0u kmnt rate. The boy is near the outer edge, and the girl is closer to the center. Who has the grea kmak;9u174m u0 pquzvj.bteo :0 rg8rter angular displacement?

  A boy and a girl arecr)c3jwo+;(qqg lwnhme( c5( riding 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 has the greater angulaclw 5)j; nc h c+m(eqqwrg(o(3r speed?

  A boy and a girl are riding on a merry-go-round which ib o.nggggexo7z f- 5;4s turning at a constant rate. The boy is near the outer edge, and the girl is close4;gbzo o 5exnf g7.gg-r to the center. Who has the greater linear speed?

  A boy and a girl are ridjxwx96;ie9 ;muo.z08 flo ia ping a merry-go-round which is turning at a constant rate. The boypilim ouoj z60f 89x ew;a.9;x 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 rgs/j l lt9i )-op,mk- 5qi1gqhiding a merry-go-round which is turning at a constant rate. The boy i ,9/--pg)milhk ijqqlogt5s1s 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 of the following is an accura y52frohcn :-c-5wr cgte sta 2or-gc5c:yw n5crfh-tement?

  Rolling without slippin p*gudgoqa g)+,9fxh,g depends on

  Two equal forces are applied to a door. The first force is apai0mg 21e.lxpf7zor 1f 1 7uwpplied at the midpoint of the dool ffpro.wx0z i77m2p1g1e1u ar; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are kx2g:pov .ue)9zx(vui2 pob 3 applied to a door at the doorknob. The first force is applied perpendiculapk(xv.xgu2z 3bo:)2oe vpiu9 r 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 applied to a doorknob, perpendicular to the door. The first forql5 vxya4hxb -pe4l+ige 2: x-ce is twice a xqbl : ve phe-y+45x-gi24lxas large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an objem(a :*p9ag :igynj p7lct's resistance to changes in rotatiy(mp gjn : 7ilp*:g9aaon?

  Consider two uniform solid spheres where both have the say/q,z*;oj5qzrz4 u vtme diameter, but one has twice the mass of the other. The ratio of the larger moment of inertiatzqz,v;r z4*5jy / uqo to that of the smaller moment of inertia is

  Two uniform solid sp a f**oggrpo48k39h (tqb(qdnheres have the same mass, but one has twice the radius of the(b94a* *8 nphrqqf g k3oodt(g other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniformoyztw 4c6)g( o solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment ofcw zog4t o)y6( inertia is

  A uniform solid sphere has mass M and radyqbk 9 )gjzc0um6e3 j:ius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a c mujgcz :j e36yq9k0b)entral axis?

  If a constant net torque is applieryj.7g +h joi(d to an object, that object will

  The moment of inertia of a solid cylinder adbequr8p9whzp1 bi) t( -:9wpbout its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the raw1ru:ebb d 9i9wt p8qpz)hp( -tio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one whcx k48y9t ej6ceel of which has a mass of 10 kg and a radius of 30 cm. cxytj6e498 ckWhat is 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 an i w uvi1lm1y,gcuy8-e2 nclined plane starting from rest. The linear velocity of the sphere at2wmycylei-g uv ,u181 the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R uzr m) uh6wl8g6v(q/prolls without slipping down an inclined plane starting u 6)qpv8mglz h wru/(6from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of pj1; z0n6zd - tp vgfy +lobii5gra0q+(4+ujswarticles changes when a net external force acts on the system." This statemenadg nv qw;p(0+4 rjyl+ituj16z0z-o+ s5bfg it is

  In what circumstances can t evys:0:m exe4he angular velocity of system of particles change without any c0 vys:em :xe4ehange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictio 7nidb jke*q/.av*q 7 ay/1rpun which may be present. What ha e /aub **7aj vprqyqik1.dn/7ppens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Enl-u2 hy/ 1g*l+ v59yo jyraakarth moves close to the Sun, then whichu2 +kyyon yl5l-jrg /h*va 91a of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by ph8/zhmdfj. mo h.y4z, ulling in his outstretched arms close to his body. What happens to his angular momentum about the ajhodhh .,8z. f4m yzm/xis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcha, w,vdpc 2n3ded arms close to his body. What happend nd3c 2,w,vaps to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in q*sgsd2q2wwhj, 5ry *his outstretched arms close to his body. What happens to his moment ogss52h*qyj 2 * rw,wdqf inertia about the axis of rotation?

State the law of conservation of an .,d/xe le84cizjsuv 0o8ek5tgular momentum.

  What arc length does the Earth travel in a three monta*dy+wgd (xe m 6 a hdr4rxf j4u6p37o)kki42xh period in its nearly circular orbit about the Sun with a radius o +krgx6 k4fwrj43(6 )*d px4 dd eaoxiya7muh2f $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dwg ,ccu)r*5;m0 ffataistance does the tip of the second hand sweep through inruf*,) w amtf0c; gc5a 3 minutes and 45 seconds?

  How many rad/s is 25 revbxd e ngp4z8q1 u.h-8zolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 refv oahg+;9gcv6c zg n3 6tp3x/volutions in 4.0 s. What is the frequenczafg6 +; t393 x/nvo cgh6pgvcy of the wheel's rotation?

  A pulsar (a rotating neu 0b2p moh ygfsds(gi02rar2y, hz ,;z,tron star) emits pulses at a frequency of 0.40 kHz. The per0 h2 y0f2ys ,g;2ahgz ridsz (r,bop,miod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle dod ay,3 0rcvvv9p bp-2ues it turn in 0.20 s?bv9 a2c r -,uydp3vp0v

  A wheel of diameter 26 cm tu;jttdas-lx(: +d:cm frns at 1500 rpm. How far will a point on the outer r(-tlj d:+x :;cdsftam im move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.8s9hf 5m8oj aat f*b:s0 s. What is the a sjm5: 9ffoaa*b 8sth8verage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revfan3vu twe /07bs-e5 eolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of5/t e0v73w-nesuea bf the wheel?

  A cable car at a ski resort carries sk -iwovo(, bibhn4v+;aiers 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 ho4w+bob;, v ai i-nv(the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating wij8v 0c;hu5a lphw+t2wth a constant angular speed of 2.0 rad/s. Whac v05lha htu+pw8j;w2t is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powerll0ag cwihh,8 txle5u- c/h64 ed weed cutter is 0.16 m in length. If the motor rotathlih 6ac 0h4w8-/g5cl u,lex tes at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m v7w 6xhro -ljh3-ye6g6vo*js is rotating with a constant angular speed of 2.0 rad/s. What is theh jvo6y3 h v-so67r6*xjgl w-e centripetal acceleration of a point on the wheel's rim?

  What is the centripetav8)e7kkrgr 1uzhb 8* ik a1qr,l acceleration of a point on the perimeter of a bicycle wheel of diameterqzur h)bg88rvk*e 1i7kr ka1, 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulay eg4gp/03 wcar, rotating space station (r = 1000 m) rotate to produce an artif0/ 4agcgey p3wicial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circulkpy1djhp/ -p+xi8, ypar curve of radius 50 m with a speed of 20 m/s p/jxh y81+,ypppk -di. The maximum centripetal 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 flat circular curve of radius 50 m witb (7hc2m ygz+vh a speed of 20 m/s. The maximum centripetal force (provided by static frib7h2+(yv g mczction) 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 strinvjejt 3xgj0s/ a9 .r ;osr1y1zg, is whirled around in a smooth level tablg.x sy 3jvoja/1;stj0r r 1ez9e. If the maximum tension that the string can withstand is 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 wf-6-unx.bldp fv6s0 ywfu* r-q q2 sv2ithout slipping 10 m down a lrpv- q- 2f*0x.66vuu-qfwyn s bds2f 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 witv( 6jy1rs :tffh a 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 accf)0j-r+bxpg 7. y swss-f.5 c(nox zcmeleration 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 after st+g2a(u z rig m(jud-o7arting from rest and accelerating at a constant angular acceleration oj7 diga -2mzuu(+(gor f $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest2 l.fvq0nbn+b , and has an angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating atm9j: n7b9 cjyscx 9jx mv3e//;h w,nth 20 rad/s decelerates with a constant angular acceleration of mt9s j7v3 c,n/h b;c/j :9hemjwnx xy9$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular shu7/; v v53v vclf* z7zmc f+jar9-tlrpeed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acceleratio5mvvtc7r-v*hvar z7l3;9 f l j uc/fz+n of the wheel?

  A wheel of diameter of 68.0 cm slows down unif*iiklq33r lql i8a-x3k u )qu.ormly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rot- .k3q qrlulx i*338ilaqkui) ates in coming to rest?

  A wheel of diameter of 68.0 cmg*ov /kg3dd7j slows down uniformly from 8.40 m/s to rest over a d7j 3* g/gvdkdoistance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm8p2wbnii hxt m1;d4ny t 5a)s3 slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel taw45im s)int1x;8 hy 2dt3n bpo come to the stop?

  A centrifuge in a medical laboratory rotates at a royb0wmf il3*1 k )shr9zf0ed:qtational speed of 3600 rev/min. When switched off, it rota i )0sd*bzrw1q0khmy3 l: 9ffetes 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 qvgnb :q81ce 8require 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 perpendicular to the wrn egc b:qq881vench?

  The bolts on a car wheel require tightening to a to-;s vprddja.)rque of 90 Nm. If a 30 cm long wrench is used, wdr ds.;v-) jpahat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerto4y6tz (r:niy5m gq8 u+g:nkpia $3.00 \; kgm^{2}$ 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 origin, mase.nzb2/id -qks 2m is at x = a, and, mad/qibnk . ez2-ss 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is p 9fvcvj up5(a4ivoted about a frictionless axis thought the center O. A rope wrapped aroundc(4a5u9pjfv v the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a8i)gc 05pxurki z xlecr,5:(1 isl5sd frictionless axis thought the center O. A r8,pll) (5:sz05r1gc ikrxx5u d c siieope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. 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. Th g z0dhe881nymsv6l kvsnu+ju)jm ;/2e 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 rodshnn ;yz28s6 gjuk) mdm +8vv1eu j/0l about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cc, i q8u8xxhg6t(h/gcm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is qgthxxu(8c,8 6/ ihg capplied 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 pe 4mwg5 w1y,u i4ac5pfulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pu4muf54capw1 y5w, ig elley?

  A 1.53-kg mass hangs on 3l 8 w -/ l1dyvfhcctt.hglt9+a rope wrapped around a frictionless disk pulley of mass 7.079c-lg f ./t38hd+ t tyc1vlwhl kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy.vv pr/x v/ww5b8r*n)i 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 iner)jcha:)bmj7rd qn,1dz 1v q: atia 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 0sh)( sadve2prvx toq- )d*o68.010 m starts from rest and rolls without slipping down a 1.0-m tes oh2r* apvx)sd8 do) -(qv6high 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 8u vm745o49 s ng3 xuj2fgxt r.zpjq4tof 10 m/s. How high up 4 ovtrqg4gu49jj.57tmpxf x83usz 2nan inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is rele5 /w-fx(:b 9cq6mgt ,fxln itoased from rest and allowed to roll down an inclined plane. How fast is/,5x gf im c:l-towxt6b9(n fq it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm,ip m9ei8 i)xv rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a spheexi pm)v9ii8,re 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 changes by,uuita 55 l+xt $20 \; kgm^{2}/s$ 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 o u bi2len4n ls(sn3c;6f $5.0 \; kgm^{2}$ 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 atz,jn.in 3 u0aj 5.00 rad/s with arms extended has a moment of inertia ofj,n 3ianj0z.u
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?