Angular displacement is usuag+( dh-qyw8h 7caor(mlly express in units of

  Angular velocity is expressed mj8 m.h m3dk)qcoz439rt op 6kin units of

  Angular acceleration is)y f,we:.q9qns:y nk-b f5*bb am:dyt expressed in units of

  A boy and a girl are ridi9atdbym.f*apayk,d; . f(+iuda z c jo2+4 rp*ng on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer.kt pa +mbdu;z2*fc(ay.adirf4 a+pd*9yo ,j to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turnid(i+u6zd bt.(p /;o3x+vp. fvh jl naong at a constant rate. The boy is near the outer edge, and the girl is closer to the cenu ph3bl6f+(i+apjz;v ot.(dx n./o vdter. Who has the greater angular speed?

  A boy and a girl are ridingtiym0w1p3/ws,; w.ofw n p/n l on a merry-go-round which is turning at a constant rate. The boy is near the outer e1l,m//.nfn sowyi p0p3w tw;wdge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a cn)e+rqd4+pi0x 9 6-v xfsrginonstant rate. The boy is near the outer edge, while the girl is closer to theprf)9-eni q+v4s x6r0 n+dgix center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turnqt8diib3 g92xing at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential aqbig t8 i39dx2cceleration?

  Consider a rigid body that is rot xe( b3:c:6cqdsod0k 4fxgcz 3ating. Which of the following is an accurate statementqkcb x ogfzd:s043 c36:(ce xd?

  Rolling without slipping depend;(r (tzo:maz8x (rmfzs on

  Two equal forces are applied to a door. The first force is aprd8u5.xax yjj 3p-x.dgn: na3 plied at the midpoint of the door; the second force is applied at the doorknob. Bothd.dyxjx3 u 3rnpaa8 . -:xjg5n forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at t: s/e3t9xmfwdhe doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of th9me:3/fw dxst e door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, per838h7f zbr rj 4b7tyldpendicular to the door. The first force is twice as large as the se8jz4f7yd bl7 3hrtbr8cond force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an obc:ss8uq h.zg0( hem p*) d.junject's resistance to changes in rotation?z:u g .(dcjum*hqnpe h0s ).s8

  Consider two uniform solid spheres where both have the same diameter, but one- nmxt2n6/ slh has twice the mass of the other. The ratio of the larger moment of inertia to that of thet/lmn6h-x 2 ns smaller moment of inertia is

  Two uniform solid spheres have the same masowjx4g9 gpdj9, :4zn vs, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smalleoj dgj4w9 ,:94zpnvxgr sphere is

  Consider two uniform solid spheres where ohd gxpde13n j at/s.v/v(0)tjne has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smallvvjajs.p0h(te gxn/t/1d d3 )er moment of inertia is

  A uniform solid sphere has mass M and radius R. If these j0 +vpq/o dofx/( (w),a nv,lcikurm:are increased to 2M and 3R, what happens to the sphere's moment of inertia aboxj,0 /mk:n()v+ icqdp(o aur/,low fvut a central axis?

  If a constant net torque is applied to an object(qwu1n;3vn l w, that object will

  The moment of inertia of a solid cylinder aboutd-wrb h,k+r7u its axis is given by 0.5 MR2. If this cylinder roll 7+bkwrurh -,ds without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass ziz/89xw fbi/150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotationai /9zzwbif x/8l 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 * /i1 mlr25t62dhbya rah mfomxyq4*:R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at thmmym 46it5qb2ryo/f:ad h21r ** lxahe bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an inox -zn /utm. ;zt(q fs9*kggc1clined plane st-(omzzq*gts /g1k ;ct xn.f u9arting from rest. 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 at(0+it fq,c.0zvik mi net external force acts on the system." This statement 0ik z0fci ,ttim+v(q .is

  In what circumstances can the angular velocity o53t8jhivbip 3 f system of particles change without any change in the system'3 hpb5vi 8j3tis angular momentum?

  The Earth orbits the Sun in an elliptical orbit. j6n1y8iez)q h*.0tdxu8g ksfx sm5r: Ignore any friction which may be present. What happens over time to the Earth's angular momenturuzjn1ef m6xshq. 0x td5gik8sy *8:)m about the Sun?

  The Earth moves about the S5h2ge+ktekh/3g7 d42j x mpozun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes2he kgtdxe4p3h kjo2g7 z +m/5 the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched49, l vdmcjs4wnoc)a7 arms close to his body. What happens to his angular momentum about the axis of r4jl dv9w7s,occa )4 nmotation?

  An ice skater performs a pirouette (a 6 yii.jt 9lnu)vsb nvb. 5yy*)fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotatio ly. *)uvy)bi5j96 btnns vyi.n?

  An ice skater performs a pirouette (a fast spi 1tq0tgh5+ro dn) by pulling in his outstretched arms hqo gdt50r 1t+close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular moment 0e.6vez org9xtol+3o u *xpd,um.

  What arc length does the Earth travel in a three month perio61 vwn :cc5/szco lp f:.5fcikd in its nearly circular orbit about the Sun w nfc ./o5zs 16:lpf5wk:cccviith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What dijb ;-n*ot qz5istance does the tip of the second hand sweep through in 3 minutes and 45-;tz5*i qb jon seconds?

  How many rad/s is 25 revolutions per minute equiva* k5j ;g7hdu el8b0yiwlent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What i / pl 1i:wpl5xa30uupls the frequencyw1illxu p3 l50/ pup:a of the wheel's rotation?

  A pulsar (a rotating neutron stari efyp8,f7oib-o/ved ..gh .r) emits pulses at a frequency of 0.40 kHz. The period of its rotation ybgevh-8iod/fep7. o. . ,ifris

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.20 vg hcl3:1 qe3+t(nhzr2 hj1bos?t rohq2( b:33h+jgn 11lezcvh

  A wheel of diameter 26 cm turns amkp fy xk)t/is q5wv92 *av;3at 1500 rpm. How far will a point on the outer rim move in 2.1twpa/5)qvk xki2a y m9f; 3vs* s?

  A bicycle wheel rotates uniformly through 22j5dq e9 +xqct.0 revolutions in 4.0 s. What is the average angularct +95 qqe2djx speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolrs hfsy,qa65vp)4 4ahi6r 3bj utions in 4.0 s. What is the linear )avf hh3i ys4bj5s r p4r6q6,aspeed of 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 km. Thj )lxe9 k*im6/+x9yfq7ufjdv e cable which moves the car is vqm* f /97 6kijfyxlxduej+)9driven 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 1.0 m is rotating with a constant angul9cy(+ ea0z.s vlx vcb2ar speed of 2.0 rad/s. What is + bs .0ylexza(vcv92cthe linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered 7b 5cdfr3y;zx weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what if7ry3zx5cd;b s the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constaqt l/avk dajgm0 7 :4 kfvcdiu)-m6h)ety/75 unt angular speed of 2.0 rad/s. Whqd)//7yif4k tju7gmca k-vdvhm 0a6l:e) 5ut at is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the periazs z,k3b7v0 0h+hlqoyw:*n zmeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 lq7a:n3*sz zobh0 vzh+,0y w km/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (oxhy (.,ohek5r = 1000 m) rotate to .khxo 5hoey(,produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with bh ( t*nnmk6(.kmy0(otd2 bm ta speed of 20 m/s. The maximum centripetal force (provided by mbnk.o *0tt b(k(m y2(6mthn dstatic 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 wi9.30)r kq)bv;t 7gxgseamwis cii*j 9th a speed of 20 m/s. The maximuxrsk3ii)09.qwivjbm 9t*) 7 csgg;ea m 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 end of a 0.750-m string, is whirle1 rp(mn 3za4qh dug91wzxa7c(d around in a smooth level table. If the maximum tension that the string can withstand ip anxz 1mc(ardzgw (3q 479h1us 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 khkm,l t dv+pw0+s f/e ji3z3w1cr 52wwvv-ev1g and radius 9.0 cm rolls without slipping 10 m down a lanz3eiw+/f,kw10+ 1-v3wjt cw2dp hlvvemvs5re 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 mgc)7 toaig ty;.4lx0with 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 acceleration of /kd p-s 1rqgqs p2gr.e:63phr $4.5 rad/s^2$. 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 radiixpd4u7gq m4e:o/ an,us automobile tire rotate after starting from rest and accelerating at a constant angular acceleration o doxq/e7ig4u4 :,mnapf $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an an e/ xuloq db3xuy l0so)e yv5n5lg-/1/gular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 radh8( y1j: 4; zcgwry5ui:ju qmj/s decelerates with a constant angular accelerationyjcm 5(yj ;rwj1hgu :zq48:iu 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 6.0 radxlpm /n3*n:c(v:jpjbjz40vd pg, yl3 /s while turning through 2.0 revolutcp /gpjj,*jy ln3(x4 pzv ::vb3n 0mdlions. 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 rest over cdiro ,kfzm*pp q*v x,j/3y2(a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?rod j,pkx*zivcpm3/ q (2*y f,

  A wheel of diameter of 68.0 cm slows down unifoy8 0bo18zp4lor;t1 w eryc oz1rmly from 8.40 m/s to rest over a distance of 115 m. What is the angular accell yrry81pwbe o01 z8cozt1;4o eration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rec1j 0kt ey+u.mst over a distance of 11ck+ uye1j0 .mt5 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory ro3463o.zws5cs1r lfd4s e vxsotates at a rotational speed of 3600 rev/min. When sr53edxsvc6sf wso 3 o.4ls14 zwitched 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 g3zlf f-a0:20z p:blgqkk.)aq tfk g+tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when t.-gka qb k: z0t) +l:p ffzfag3kq02lghe force is perpendicular to the wrench?

  The bolts on a car wh3ehb0qz/hqbn9 i +gjo: kpft59zydqb 2k0 -z +eel require 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 applied at obib9:05hzzz+q9 t0fj 3kn h/ ebgqk -d+p2yq$53^{\circ}$ to the wrench?

  A wheel with moment of inertl 2r,xvd3)lpfi69fxu-cu y m98m;ng sia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule isjp m 7nllfsbv-jp-+ z:k9o +2k modeled 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 aboujs9ljo7-:+k+pzvm p2n b-lkf t the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictefl :g0swaj xq 6.ztl;ik,n6/( ji t :uel7x+uionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.t0fe zj. ,6 :t lij:w/eu 6kqxux7 gal(ni+s;l0 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 a frictionless axis tho0 h) -xwyi1idaught the center O. A rope wrapped adiiaywh -0)x1round 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. The rod is initiallyb(yr +d**v oqk held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it i*+ bodv*yk( qrs released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a rink z /,m5p9lhhdg 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 tangentially to a sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipzmpdklh h/95 ,ping?

  A 1.53-kg mass hangs on a rope wra f fffdbx 3i:4xs)*o2hpped around a frictionless disk pulley of mass 7.07 kg and xfdo4 x3*: hif f)s2bfradius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrappedftp46oz7zyp3qvc;88jt 1 *chm4 dpwp around a frictionless disk pulley of mass 7.07 kg anp6z*8htyp7t3 mwov4 cz 14c pj;qpd8f d radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can b;/8 d mdt*4yzw rc-pwntwnh4c ,24xrfe used 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 ine-j e4o: 0fskvxrtia 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 wjq zay7ayonx3ux6s(c(3 t3* vithout slipping down a 1.0-m high inclined plane. What is the speed3x73 3avn(y xq(uczjyt6oa*s of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 11hm9xuumv4ym te */6c*mpd2h .0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before comint6muv u*/mc1m hem *d9p2y hx4g to rest?

  A hoop of radius 0.50 m and a gfo0b;sfhx.; mass of 0.20 kg is released from rest and allowed too0.gbx ;f s;fh 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 slippijbbgwqhd 4 mwp5 e:+8r-se,1 kng down a 35e incline that is 7.0 m lo:q+ m8kdrb51 -shwgpw4ee, bj ng. Assume it started 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 changes by / kb 4w/,gjlyp$20 \; kgm^{2}/s$ 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 momentsr.yjvia6jzzyjw 87 syk ( 4f551w7jm 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 j e4i4g 8b*a 4e*mtmhuextended has a moment of inertia ofhmtb *4e ea muj8g4*4i
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?