Angular displacement is vlv 0m8r /ph6)x93h;ffy(canu l dxf,usually express in units of

  Angular velocity is ewy63r of s,l*u cxhur,c.dq ;e 2lf)*oxpressed in units of

  Angular acceleration is expgio+ i kpwe8.6ressed in units of

  A boy and a girl are riding on a merry-go-roun uiqpjl8z-x 5rrr 16 k.ys7a8fd 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 angular displacemenr78ya8k .1urj i f-r5pqzs6lxt?

  A boy and a girl are riding on a merry-go-round which is turnif); udl-jf0e bsdj2 ftqs y2y; /6az4qng at a constant rate. 6qly0-t4sf z j2jue;ya/f;2fqb d)sd The boy is near the outer edge, 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 at a consqpa7+ ts8( /3hln fxfdtant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear s37fp+f/qdn8 la(thxspeed?

  A boy and a girl are riding a merry-g;2kwweawn, k4o-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 centripetal accn; 4k ewk,2waweleration?

  A boy and a girl are riding a merry-go-round whi)cjmcy;( kh-twp0i+ uch 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 ccm- (p;+)0j khi ywtuacceleration?

  Consider a rigid body that r/vrqcrio 50 0izv.:x is rotating. Which of the following is an accurate statement?5vz0x/ . rrvoriqci0:

  Rolling without slipping defkv:yblge2t /lxqe)xl;/d1k 3 :b a8 mpends on

  Two equal forces are4o/;p+ yhm+rl9yb pcu applied to a door. The first force is applied at the midpoint of the door; the second force is applied at t+p+/ byr9clpyh mu o;4he doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at tiilk:/8fes8 -1gbq euhe doorknob. The first force is appliedie/b ki8 u:s1g8qe lf- perpendicular 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. T*4skps7gya)/ftt s( : ) d am+rwx)bwlhe first force is twice ast)ay/( x+p)l)w4 dss*f7r :gm t kabws 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 object's resistance to changes i.2tr j au;xt9xn rotatio.rjx;2atxt u 9n?

  Consider two uniform 51unont18,vo ) fril tsolid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that ofuf)1ntoil1ot n v 8r5, the smaller moment of inertia is

  Two uniform solid spheres have the same mass(hgi*zoif127vy.1 sja yl0 yx, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia(svxf yi gaz*j.ly 2yh7i1 0o1 to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mah46- aua6)w ols kp65r)xxnpd ss and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of i sunopk65phax6rl- )wx6)d 4anertia is

  A uniform solid sphere has mass M and radius R. wi;jaf s 3;l gy 9i/g3akq8l+d If these are increased to 2M and 3R, what happens to the sphere's moment of ine9 qdi/kj3g;w8 ;ay g+liaf3sl rtia about a central axis?

  If a constant net torque is applied to an object, thaxl7nu*t 7(bhat object will

  The moment of inertia of a solid cylinder about its axis is given by 0.5 MR2.aod g4p 8-1lbv If this cylinder rolls without slipping, the ra8oa gv dp-bl14tio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which dyispipz9dc/o0ia .):o 1 r;ehas a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinec)0p9 oyiid;s1 o.ri/pa:d zetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M c1d0scqjtrrr7qjn.j 7uq)0 8 and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends oq7r d ctc.q)q781rj n0jsjr 0un

  Suppose a solid sphere of mass M and radius R rolls without nymx,9(wqqem wx 5g (l7 3v:m i)jecd.slipping down an inclined plane starting from rest. The angular velocity x35,w(mimy. vel(9g n cwjq):x 7qmd eof the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a nel upals.,8zh 9t external force acts on the ph9z,u. a8 lslsystem." This statement is

  In what circumstances can the angular velocity of system of pa2 34xf1+ sb9o ocaogfypdkhw : 2o5uo1rticles change without any change in f1o2 h51asx3 2wof:og4byop 9oc dk+uthe system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which may l:nnc myf9zf (86h. smbe present. What happens over time to the Earth's angular momentum about lnhyf8(mfzcm s9 :n6.the Sun?

  The Earth moves about the Sun in an elliptical8exd:g7y6yf;,f 4x ci;rg juw orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed owgy4e gd:6;,yi jxrc ;87ffxuf the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulllty;h:s5.l7jy8 gb6hb fzea 3ing in his outstretched arms close to his body. What happens to his angular momentum about th y8ls3j7z .aby 65g;hb t:fhlee axis of rotation?

  An ice skater performs a pirouetthvhnaz/1)qexqt wss7g2 7h 2. e (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kihx1/2hn .zg)7e t 27vqa hsqswnetic energy about the axis of rotation?

  An ice skater performs a pirouette4bf9cnng08 28 pzb 3a qkvdf7i (a fast spin) by pulling in his outstretched arms close to his b pbc9 8d2fa kbnig78z0f n3v4qody. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentuksr :0sku21k km.

  What arc length does the Earth travel jzy1byb.,pky9lgtx . 95g0 t gx2 (wcmin a three month period in its nearly circular orbit about the Sun with a radiusb0gxc ,(l 9xtwym.ygg2z.pj t5b1 9ky of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distp z t8+ch3s:5pql8rc /tb9jqfance does the tip of the seco9zshlf 8 prpc35q+jbqt/ct8 :nd hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalentl.b y:jm/o:lut4 (zgn to?

  A bicycle wheel rotates uniformly through 2gag;,o9y v)ub .0 revolutions in 4.0 s. What is the frequency of the wha ;ogub,9 gvy)eel's rotation?

  A pulsar (a rotating neutronudn 6 ahqn:. qj*u-zc5 star) emits pulses at a frequency of 0.40 kHz. The period of its rotatio .56-qdcjzau:*nun qh n is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.203hru+ r kzzdp35:*rpg s g+rrr33 u:dp5kzpz* h?

  A wheel of diameter 26 c7 h;3;:d7m4xodh5k xzsnta un*-tj ep m turns at 1500 rpm. How far will a point on the outer rim move in 2.1 s xha;n7:zpm;ht -eu5sj x dkt73*o nd4?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 6y1z2yzqyvv1e 6f 2us What is the average angular spe2v6zv6 ys1q zyy2e1f ued of the wheel?

  A bicycle wheel rotates uniformly through 2.0 re;gp0i2-b bc rivolutions in 4.0 s. What is the linear speed of a point 0.10 m from th gb02ip r-cib;e center of the wheel?

  A cable car at a ski resort carries skiers a dib b2(kp+ost 7ystance 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 makko7+s(ybp2 tbe the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 jd 5qfv ,u*fhmtgo;x j(m;;1f;hvpz2w)vc x2rad/s. What is the linear speejgtf,; 2jvq5zv2;x ohu*fw;cfx h(m;d m )1v pd of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. 6wm6n7hjrluy 4 g)ie*) uve9o If the motor rotates at t 6jhyg6eu*rwl 4 nui7m)v)9oehe 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 constant angular spmw6)gyko6(k ks ykt0 4eed of 2.0 rad/s. What is the centripetal accelekowy)4mk6 ( 6sytkgk0ration of a point on the wheel's rim?

  What is the centripetal hud)j3t 4v9rq(ifr ;macceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bi udfr4 i9mjvt;)r hq(3ke is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotacq4 4(v.z1.(i3oet nsla6lug ez h 0kxting space station (r = 1000 m) rotate to produce an artifi1 3k(4uh4s06zai lo .cx(l .zqegtevncial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50f.08 d,g h)zbm usp(q stjd2ba h9ix8- m with a speed of 20 m/s. The maximum centripetal force (pr h 2sxajh0g9 8ft,isdb.bq(8 udp)- zmovided 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 4:b5 lv- dnr 6;-,2rjhnzt qwql;xqhfwith a speed of 20 m/s. The maximum centripetal force (provided by static f4;26qd-wll qq t z h b5rnvxhjnr-:,;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 whoh9nk zhw*i0.q cjek/v3l1-hirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed ca/1neh0 9-hkj3 l.vz hiqkwco* n the mass have if the string is not to break?

  A bowling ball of mass 7.5yd(1qrep,.ap- qudn w-7t4sf kg and radius 9.0 cm rolls without slipping 10 m down a dwr1ye4 d(pnpf7t.- quqa,s-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 constant / rx5 6vc*t,oo.tk8 fkz+ymlyangular 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 c8n 48u eo zen3hhv ,0/3od ml20wadidwonstant 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 0.300-m radius automobile tire rotate ao h*+)su(xnpg4 c 7shlfter starting from rest and accelerating at a co7o nssh 4g(+chlp)x *unstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at resuyu86o eb h0w1t, and 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 with a constant angular accelera8d3 m5:w:rwrd jjv-1q:r 2z3hg hi;yb)ny behtionw3dbg 2hd r h:-8h y rmvb5;yez:1jij )qr3:nw of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an 8:n bnokf9tw-r9/ so nangular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average af9snow -br9:n/o tn8kngular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 (te()5 mu2nswbie cr2m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in comu( 5iencs2 bmr)w 2e(ting to rest?

  A wheel of diameter of 68.0 cm slows dda-7ty .88 zzy kzp2r l.c,bmyown uniformly from 8.40 m/s to rest over a distancr d82.zyy- b c8a.lk7mpzy zt,e of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down un u3*: jpjmsv)hiformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to the stop:jmu p*v3)hs j?

  A centrifuge in a medical laboratory rotate ff * pox96q,xwmivqkp2ov04,s at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0o qi * 2,kxo,p4 f69qxvv0wpmf 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 sol82lcvx pzm 6798 xitightening 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 tx9x88m6vl2 szp cilo7he wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm lof70:utn /vizjlk h p(8ng wrench is used, what is the magnitude of the force required w : vlpu/ 07nfik(tzj8hhen the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertialyh-uhr* 6bmeu(b:cs+ z2l - j $3.00 \; kgm^{2}$ 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, massonteb 6m5/m8+ufl4 x aj/s5wk 2m is at x = a, and, mass 6btm/ ol+5kf4x 5aus jen8w/m3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoug;vxr.e3voa1 grd w*/ huuk);oht the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. 3u*ar1/;vxd)gowh kuv eor .;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 86y+.fccmg1 tlvl+i taxis thought the center O. A rope wrapped around the m+y8vlf cc 1.6ltig+ touter 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 umx88lqg7/z j +i2dnld h)yi+45dx dvis initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration asv ud7d/m5d 2 gy8 +qd48lz)hnxlji+ix 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 e8q ibod7i::zytmk.:n 7 9 horpk- e2bmass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N is applied tangentially to a sprocket q:8khi 9zk:p b7dymot:r2be-7.ieno 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 frictiom6wjn 2l wnm/;l8gc.wnless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular accele/ 62m.wllw m 8njcn;wgration of the pulley?

  A 1.53-kg mass hangs on a rope wraph ,vvry (sk.aq89k d(hped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is,v r9v.( qkd8hsah(yk the acceleration of the mass?

  A rotating flywheel can be used to store enebh./n m2x0 irurgy. 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 gxz5p64q+onzji4y3 +zdo *xs rtia 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 radi3e)lv ak):rhj us 0.010 m starts from rest and rolls without s vlj )ka:er3h)lipping 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 1.0 kg and radius 0.010 ma4hrxm1+3:cl ap f2jb rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rest?4mbr 1f3pa +c2:jlahx

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from 4 kj kgit *u1qeqin x9:*y/lu2rest and allowed to roll down an inclined plane. How fast is it moving aft nk2y iex4 kt /l*q9g:1uiju*qer dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 3gbk-:+ p,mx x bx+bt9c5e incline thm, x :tkpxg9bc+bb+x-at is 7.0 m long. 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 pta r8tr9ij4i (l8 ue)momentum changes 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 inertysl:nmac1bj bb-. tlo.bpxm.ct/ 4ho* b5, q:ia 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 atk jjk9 lj34jwe)/nkv 1 5.00 rad/s with arms extended has a moment of inertia o j1nk)kjj3 ewj9k vl4/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?