Angular displacement is usu:c jk49u 9eua.eh( uq 4w9jlzxally express in units of

  Angular velocity is expressed in usz;sq6rlo ad29p51a d 2z f;xtnits of

  Angular acceleration is expresse54l n-egk bi6u cgtx.agq5c38 d in units of

  A boy and a girl are riding on a merry-go-round which is turnin1gxf0 pcodbl9 /a oy8:g at a constant rate. The boy is near the outer edge, and the girl is closer tybloo 01d:9ax8cf/pg o the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant ymrg .*y02nsy rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greaterymgyny0*2 s .r angular speed?

  A boy and a girl are riding on a merry-go-round -+-(wlb 9j; x29 ibcgch;pbnq i15qago(e qcrwhich is turning at a constant rate. The boy is near the outer edge, and the girljq ;cr1i5 g(c aoqbb;9+hc(gn-xlp-iq9be2w is closer to the center. Who has the greater linear speed?

  A boy and a girl are ridingdq 8r5r7bj1x,y j-ngn a merry-go-round which is turning at a constant rate. The boy is near the rg8jb -,7dxnnr5yq j1 outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are t ,;u4/wasu6e d0c-bthxjuj59 zll5y riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to t te6 wuj a/x; u54509uyltl-d j,hbcszhe center. Who has the greater tangential acceleration?

  Consider a rigid body that is rota u*d mo eu)m4mmmzv)05ting. Which of the following is an accurate statm)z me4oum5d)v0 mm*u ement?

  Rolling without slipping depends on1f6 tb,lc3pztv cg 10x

  Two equal forces are applied to a do:f)2hna re.iz+lsao4 ( 0uaveor. The first force is applied at the midpoint of the door; the second force ifus 2)zrl+v(.eaahi0ane:o4 s applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied.zbih3( *x amo*z7 f(k,buim e to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the pl7oh *,3aimbz*x k( zuf(.beimane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first fz, 3cl:3 ind, inqa4 .oi0nqztorce is twice as large 3n4q c.ai3nq:dz n,zt0il o,ias 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 object's resisak5f8s .1ympgtance to changes in rotatio18. k5m fpyasgn?

  Consider two uniform solid spheres where both have the same diark ufr j rc9i6yq;.i)uv0 gk hn2p3/l(meter, but one has twice the mass of the other. The ratio of the larger moment of 2y/jp g.k;)fv9u6q(r0i kchri rnul 3inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice x m 7gjkj-o+f q;l7t.px 13xkathe radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere ij.7kpgtqo1;al+fxj37m k- xxs

  Consider two uniform solid spheres where one has twice the mass abqu0/ql en,+,dlg- wz4ey :yqnd twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inerqe, ed4znuw+yyg,bl/ q-:q l0tia is

  A uniform solid sphere has mass M and radius R. If these are increased to w+spf4 k(qlh.s( kd1p 2M and 3R, what happens to the sphere'shfd(s+ p4wkkq(.l 1ps moment of inertia about a central axis?

  If a constant net torque is applied to an object, vt 9u 36lo8p6cxwgdu6that object will

  The moment of inertia of a solid cylinda78b 8+s 0y-mjaqcg+lii+cf,ho.r np er 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 wheel of which has 5-14r eoeaot4 4u w,vex izh.ma mass of 10 kg and a radius of 30 cm. Wha -aerw5,44 .euxzoiho4e1t v mt 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 massax4k , jyg v9n wumtss09h29+s M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the b 0js9vagyx k2w4+9n,h t 9usmsottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withoufno 4b;r;t6d -fm;w41* gk mjl+f;b pjzh7 wmst slipping down an inclined plane starting from r 6bo;mf;7lpg-s1h4 fr+ kb ftjm*jm z;dwnw;4est. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net exter1; 4wrvyubx dt3/f9y rr0p km-nal force acts on the system." This staw t- uy0xrv93p;41yb /r rmkdftement is

  In what circumstance61ep:ymwi2r w ku2i g0s can the angular velocity of system of particles change without any change in the system's awuy62p wek 01:gii r2mngular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whicwev n-z3g0 3enh may be present. vnzw ne-30g 3e What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in aty)3q9w6tk( ck zjx 3yn elliptical orbit. As the Earth moves close to the Sun, then w )kq6y9zc(3kx3tyw jthich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hispqb0/xf,1hxg 9d tu p/ outstretched arms close to his body. What happens to his angular momentum about the axis of rotation?xgt/ xp0fh, p9d1qu/b

  An ice skater performs a pirouette (a fast spin) by pulling in his voumag+ c,.5kl3qy o; outstretched arms close to his body. What hap, yo3k;uac oq+l.vm5 gpens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fas f0vzir; m:((d6x:*cjz qeluqy3qy 1ct spin) by pulling in his outstretched arms close to his body. What happens z(l(;:z0:je1cy dv qxqmq 6rcu3fy*ito his moment of inertia about the axis of rotation?

State the law of conservationarn 6 1qx8j/ty of angular momentum.

  What arc length does the Earth travel in a th5-z.db exmc)x;s3 fw xree month period in its nearly circular orbit about thee swx)c.5x b 3dz;xm-f 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 dis8; j1wrbn6w 2( 2baksyxlbf2wtance does the tip of the second hand sweep through in 3 minutes and lx;b s 1 njbka22ry2fwbw8 w6(45 seconds?

  How many rad/s is 25 revolutions per mhim(9 +ung gbh)zjk7: inute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatwajy f68lv;* aoo7h/ z is the fre o7*6h8 w a/j;yolazfvquency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequenc1bzxv7;gj z5,wm b/x4ftavb3 y of 0.40 kHz. The period of t az7 x jm;g 5/xzf,bb4vbwv13its rotation is

  A phonograph record rotateszqa 3b+)h p ;k0rtb:rh at 45 rpm. Through what angle does it turn in 0.20 s brqhzh03)pt k:;+ba r?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the oute les7b6dt0)* a oap;o4oofemyrt(5f1 r rim moveraof0b 7 t6d5pe)*(oelo ayso;t4m1f in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.jcy1*-7/ bt emr) ;w)nakxbqo What is the average anobqk-w*nya /xc ;)t17e r)m bjgular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutx5di sk++jpt s6v6cbtls8 n74 ions in 4.0 s. What is the linear speed of a point 0.10 m froi5 47tnslvdk+tj8sb c ps66x +m the center of the wheel?

  A cable car at a ski reso/wgti;4uj0 gq rt carries 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 for the cable car to make the trip in 12i;u4jw qg t/0g minutes?

  A wheel of radius 1.0 m is rotating le+ vm r13nlc5vbdil asw. +so(+,bz1)adwz,with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the whee),3w+ dba. +ml nlzwso5l+ 1cvvi ed1r (sbaz,l's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the mots y4de x4utf3+or rotates at the rate of 20 rev/s, what is the approximate linear speed of thuesyxf 4t +d43e end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speedms-do q(jp* 1k of 2.0 rad/s. What is the centripetal acceleration of a point on the w1-(kdqm*j ops heel's rim?

  What is the centripetal acnf8mn v h,d , (crtst65n8er6zceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mov(8t,zhnnt r ne5 6,6vsf8crdming 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotatin f5kb,: y( fmc5b mn.uqpwj97vg space station (r = 1000 m) rotate to produce an n m.57pjb(b9vkwy: qcm5f ,uf artificial gravity of $9.80 \; m/s^2$?

  A car is negotiatingl(pu;dia. *xc .m dovt;r*o+p a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centr.;t(dmpdxo.u lv; arpc*i *+ oipetal 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 with a:qwmje r,7l4 3qbxh h9 speed of 20 m/s. Themlq9:r3j b ,hx7 4qhew maximum 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 1sdk)npfn z9kwyi0 2, the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum 1 wsndp90nzyk)2, ifktension 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 without slipping 10 m24bm8qps(.iw uf0o hs down a lane at.m(b h0uq2spi8sf4 o w 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 constandpq,v4; y/k.)urkqc q t 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 angularjhwlfd;n g) .+ 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 after starting i-ooz z8uk)l /from rest and acceler ikzz8/)o-u olating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleratio zohz vto: n*sje:08(tz)yhj+ n of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20ifhon ajm,9)w- o- ap6 rad/s decelerates with a constant angular acceleration pah9,i -mofaj)n6-o wof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularzpgi o/va;hr4/srr1* speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accelerati*;/p a ihzs1r4r/orvgon of the wheel?

  A wheel of diameter of 68.0 cm slows down uniforl2e6pk) -se 3vneqr-p pagq) (mly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the-as- ( )qk)p2pen g e3relvqp6 wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rqg5 ut(1-z jm- gnbv38cyujkq3 hy,:kest over a distance of 115 m. What is the angular acc (q nh y5kkj-m3y83 uj,g-cuvqzt g:1beleration?

  A wheel of diameter of 68.0 lsmehyz+x+ l6/e6 /m)y n9d ctcm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to thedlxch+n6yles m em9y+tz/) /6 stop?

  A centrifuge in a medical la.g)e0ko jxtuaq vn6;ig2f .q+boratory rotates at a rotational speed of 3600 rev/mi.u)fx2a6gtj. q vn;+eoq g0ki n. 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 Nm6zy r ylkw9-j m:uxu);. If a 30 cm long wrench is used, wjx )zlyyu:k -69wrum; hat is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm lo(,6 cdg wm w8:iy*zywc,(msvc ng wrench is used, what is the magnitude ofm:,c(gwcscw*,(v mzdi w6 yy8 the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner9qnlmq dx w0;22.crbatia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as foqvgfs z306vjhtr a+0el(.s , xllows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is aeq ,30(vf6tzs svrj+.lgh 0x the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought zm5*(cy3czytthe center O. A rope wrapped aro*my5(ct3yc z zund 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 ;8g8,huncyi kthought the cente8 hngyuki8,;c r 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 hinged at . s(vma:0cm m;z.fskjone end. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall.mcfk:z;ass 0v .m.mj ( 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 xljjhxhym4723;mv.u1.5 kg. Neglect the mass of the jxm32y7h hm4 uv.ljx; 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 hangsx hjoz726x o4a on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular ac2 oxo6xj7az4hceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrauuq8/c. y2a) og3ya ktpped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the y2c 8uk3 au g/yqt)a.omass?

  A rotating flywheel can be used to store energy(ovzldx j8y.+gabl(xug(x:, . 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 inw asuo5.j*: gu/fmca+ertia 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 withqyhvu 8olj.lyc 5)0/fout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches fv.8c )yylj0/huo5lq the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10jjdly-.wj ,+ c m/s. How high up an inclined plane cajj+, cdw- yl.jn it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed c3ldz1v dxc ,z .wi42nv- )sjzto roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0z3.s-4idcvdn lx,2wz z 1)jc v m?

A solid sphere of mass 1.5 kg and bcqiog9* 20sy7kv d qz16p gv,radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. Ths0,do2yik vbv96z7qp1 *ggqce 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 3t; ffm.:ab 1d 6:whieqhub+k8h pb 2dchanges 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 mov7+0 ggwl -oh3y.mwhiment 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 extended-nija6-hox5 +yky o 1e has a moment of inertia okhoy-i1 -xjao56ne+ y 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?