Angular displacement is usually ex6mg1t9 o 6jtil)md r +*na5ujqafp.,g78vatipress in units of

  Angular velocity is expressed i5.sdd * of dbzfhrv15 (t*rpm)n units of

  Angular acceleration is expressed in unit8yzxq/v lq ro)l-:xzew-tt : ;s of

  A boy and a girl are ridinoo62swmw8- +wdlb 9 ztg 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 cendsl6wb-o+ w82 zo9mt wter. Who has the greater angular displacement?

  A boy and a girl are rid5o5b z0 tugnj* mllyg*v-k w)v0g2: rning on a merry-go-round which is turning at a constant rate. The boy is near thtnm zb0 0-2: l)yj vwnl*rvg go5*g5uke outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are rijtcy i2 -e 49qx1gb*ieding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is close i9ecqiy-2t*exb j14g r to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which 6eab 3 3t7rovais turning at a constant rate. T3orb v73 aeat6he boy 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 riding a merry-byu5tca hgz1;e)r( *igo-round 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 tangential acce51)gti(ze;uhcya r *bleration?

  Consider a rigid body that is ro(3turjd sq ;k 5gec+7ftating. Which of the following is an accurate stat73(ge5qjf ruck;tsd +ement?

  Rolling without slippixn aun0 xkr74ihnj,. :ng depends on

  Two equal forces are applied to a door. The first force is applied at the j9)v4qgh((uri sozn ju7 .ra v *wmu1-midpoint of the door; the second force is applied at the doorknob. Both forces are applied perp)i jrr vu.(squhznmw41a-uo(* j9g v 7endicular to the door. Which force exerts the greater torque?

  Two equal forces are appliedxs qh ks2:+cvg2wbf9 7zle k-; to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torquev22sbg;f-h7w 9e +k:sklzqxc?

  Two forces are applied to a doorknob, perpenjb / w)*bdm atnni :ar2627txqdicular 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 the b)rjit nx t* :6mw2/a7 2qanbdsecond is

  What is the quantity used to measure 4su6 xk9nr1njz 97kyt an object's resistance to changes in rotatio91sjy kkntur9x7 n 64zn?

  Consider two uniform solid spheres where both have thf) a5ql f:0krde same diameter, but one has twice the maslfr:) 0fq akd5s of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have tp athi(0xelf qvk40x5g1+j l,he same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment o fa vlk,(qg0i0pt1xx +4e h5jlf inertia to that of the smaller sphere is

  Consider two uniform solid spheres wh*xznh*hbo(h mm )t*k 8ere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that hhb*ot**8h)xz n(mm kof the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increaslx qo72fa/9gn ed to 2M and 3R, what happens to the sphere's man x 7q9olfg2/oment of inertia about a central axis?

  If a constant net torque is applied tcc2j+l3sixe)ko ;lj7o an object, that object will

  The moment of inertia of wc:-pz n0*-.pm gvixe42 qdg8, qbygoa solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its t-i e g8x vq4c*m,w.qo ygp b-g2:z0pndranslational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a man6f3(iv zl2h*3 uoizgss of 10 kg and a hf63 ii2l(zvg*z o3nuradius 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 the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rosy ikatpu4s 73f;*)aulls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dep3*p)y7fsi4 uuska t ;aends on

  Suppose a solid sphere of mass M and rau 689l z ah/apqi;zrcv:ft8 i*dius R rolls without slipping down an inclined plane starting from rest. atp8la8 fz u 6i:vrziq9;h*c/ The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a syst-ah. hy0wyz8m em of particles changes when a net external force acts on the system." Thiszhy0wm. -ay8h statement is

  In what circumstances can the angular velocity of)dnr x sxt1x)w 9u80pt system of particles change without any change ipn0 tx91wxtd)rx ) 8usn the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignoresnw 3-y(+ypgn* csc4k any friction which may be present. What happens over time to the Earth's angular momentum about th gy cp *skws(n4-+3ynce Sun?

  The Earth moves about the Sun in an ellw ,/hqh :pbrp*i0w zk2zlz)r9iptical orbit. As the Earth moves close to the Sun, then which of the following best desb:hr9zr )p/*,hiwk lq2z0wz pcribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirou f/zpwh*a7jurnv: n 4:ette (a fast spin) by pulling in his outstretched arms close to his body. What happens ta7/ fuw 4hj:*npn: zvro his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hifbz/ v3 ,isxbbf3 1df 1tno0m9s outstretched arms close to his body. What happens to his rotational kinetic energy / f3zimo b3f 9sdbf x0t1,v1bnabout the axis of rotation?

  An ice skater perforl 1(kv i3,41*b hrb(zjhvjogoms a pirouette (a fast spin) by pulling in his outstretched arms clo4jo 3 1(bkv* grh vh(bj,ilz1ose to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum.,w3ika / s7sb rz3l9ln

  What arc length does the Earth travel in a three month period in tgzbk 39cuf 24f7hu)fits nearly circular orbit 34k )gfztbfhf9c7 u2u about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a ju -nic5cui *2clock has a length of 0.30 m. What distance does the tip ofuc 5ij2u-*nci the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions pet9cdcu+ *j qmu.)f1 qoaet0: 17airqar minute equivalent to?

  A bicycle wheel rotates uniformld4li 4j+yrg+e y through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotaeg4d yj4i+ +lrtion?

  A pulsar (a rotating neutron star) emits pulsoc*w u(pxtws34- pyx; es at a frequency of 0.40 kHz. The period of its upp4(ts ;3c* yw-wox xrotation is

  A phonograph record rotates at 45 rpm. Throughjc;e*sf4c-s;yeg2 zg what angle does it turn in 0.20 ss4c gfce e*gj2- ;y;zs?

  A wheel of diameter 26 cm turns at 1500 rpm.cifuf71-.ga v;i) j8oievp -q How far will a point on the outer rim move in o ga)1j7ce--q8 ufiif i v;.vp2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revet 1k4*.kx5gjxj.iora2w8e i olutions in 4.0 s. What is the 2ke e.. i w xjrtxk81io*4g5ajaverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolu,s oflhd,b(jeyssza 2wre7l:67f/ ,m8v 0u fptions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wheel0 7wzsys,6e am,,pfl8js( / vdrueb7 :lhoff2?

  A cable car at a ski resort carries skiers a distance of 6 h*3ebem.ygdwezt) 3..8 km. The cable which mo3z). h d*weytebe .3gmves 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 12 minutes?

  A wheel of radius 1.06lm 17vwc( en8b.grfn4bx1jhi5o : wd m is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on e7jmb6 dnhfxoin r18.lvcgww :15b4 ( the wheel's rim?

  The cutting cord on a ga*eb n72avgm+ v,3jeg o 0t:smms-powered weed cutter is 0.16 m in length. If the motor rotates anmegmb+to g ,:vm2 7ev 3asj*0t 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 is rotating with a con,pj.g h /*/w mb-v6j .6jirxomynrtv6stant angular speed of 2.0 rad/s. What is the centripetal achj-, vxt jpj6gn/.iw/ v*r6ryo m. 6mbceleration of a point on the wheel's rim?

  What is the centripetal acceleration of 3jt e9f)w:zh wb-(gxsrog 9m3a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movingegt (whwr9-b x o9 zfgm3)3:js 8.00 m/s?

  How many revolutions per min usj22o-n1nkmr2u ht;ute (rpm) must a circular, rotating space station (r = 10j2uor khs ;nn1t-mu2200 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/8uc5 5qywmdjpkc h8- p;c- 1;nvbkq m/s. The maximum centripetal force (provided by static friction) -quck 8;- cbk/cypd;jh m8 55w1qnmvp is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat cycn zp,:a3vb 8ngn,c ;ircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) ispn8,cz,na;g :3y vcbn $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end ;di,3tscnd3mkv k/ /fof 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 spmkfc d/k vt;i3,d/ ns3eed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kgvz 13 )l:uflv0c c85 vl9yzcco and radius 9.0 cm rolls without slipping 10 m down acy 5c 0ll8v9 lf:zucv3v)o1cz 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 with a constantp r3ruo dqq59snm/ rsk;.clx s0 -1:dt 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 constantv-6 2ktbksk+ff0 q0jk 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 0.3u9y,g27ixrvma.* pobc3ojy6 00-m radius automobile tire rotate after starting from rest and accelerating at a constant angular acceleraturi. ooxc9 ygp 62,*y37abvmj ion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, atf- ;pngw 1)mb+ a7dgdnd 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 with7 n9yblh+v 6xr a constant angular accelerati9n 6vrx+lyh7b on of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6v:h,t: ruy+2kdic 9xv.0 rad/s while turning through 2.0 revolutions. What is the avhdtx cuk2:ryi +:9,vverage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8+f (xzbc5u r7s.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wb 5fxcsu(7zr+heel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows dow*/ygov )jzq5 cjm1l l-n uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleration*qz /jl1 lm)ycg-5jvo ?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mfdh*fay r3yw ;we;f4 1th;x j,/s to rest over a distance of 1w*e,x; ft;r 4hf; fa1hwd3jyy 15 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical lbe do -uo8bzaiy* u4f, +vwpc9, 4vd+jaboratory rotates at a rotational speed of 3600 rev/min. When switched oedvc,ub+ *zv4uo 8jbaw9o,diy+4f p -ff, 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 907v5w7q-ljnar . *dhqv Nm. If a 30 cm long wrench is used, what is tha 5*vl-j7wr v 7q.ndhqe magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening ev) e x/c3e8)qx(x+,p o0ezrpkvr dx7 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 a p,rp)dqxr e0(xcv kxxv) +ee8oez7/3pplied at $53^{\circ}$ to the wrench?

  A wheel with moment of iivuci/f8 y hhgv.g+k 1:d2bu*nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as fo gg(bwzg7;0 g9im*-iqc;gyf c llows: 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 abou7 (;9f i;zwgy-g0cgbimcgg * qt the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis q 6n8i0v0lh x6of/i 8khgx/jnthought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. 8j f/ln8gnq6v0/h xh0k6ioi x 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 isowv 2 h25/ e08iorxq 5f1kdqft pivoted about a frictionless axis thought the center O. A rope 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.hie2kvtr/2fo55x0 qd18q w of 0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in thejg z2 b8.qj6hlx1d8si horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is released? (Tblz h8s.6x jgi12qdj8he 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 m0jlu7x; wd;gq ass 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 7g;xw;0ldjqu wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of max*4s 2 v xuy3wa0pal eyxr80(yss 7.07 kgy42(0ax0ry yela xsx3 p8uwv* and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of gjbl1 8uo- csuf (m)iuz 0x55kmass 7.07 kg and radius 66.0 c(fuxubj558lo u1) mi 0zs-gkc m. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to6m+r dqxxow,. 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 of41,xhm 4 .u*h ohzr vyc+9mvhx $5.00 \; kgm^{2}$ 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 r fu3bk9aq :k av;7psk1adius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the s uk3a p k9aq1;7kbfv: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 of 15 wegt;js6 +f/h ixok00 m/s. How high up an inclined plane can it climb before cominj+sh5 o60k gtiex; wf/g to rest?

  A hoop of radius 0.50 m and a mass of 0. plx3 i/ym50au20 kg is released from rest and allowed to roll down an inclined plane. How fast is it movi xiy 3l5um/0pang after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slippin f7gtgjx4py,;6 2sy8vrvb ua1 g down a 35e incline that is 7.0 m long. Assume it sta816rg f ;s yvp4a ubvtgx2y7,jrted from rest. 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 ch:jm 8 /+plwxananges 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 moment0 jul p6i),axq9n,juw 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 has a mome7s vlufm,3e.niu78 ybnt of inertiai 8uvbn7u,7y el3. msf 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?