Angular displacement is usual laagum.2*/pwj lp, 6ely express in units of

  Angular velocity is expressed in units8p /go+ 65 cwcrr3*kmnqa)lqf of

  Angular acceleration is exp2j ;,mbe ou-+swhpk.b 3r)jpfressed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a consu aak.e :uvk9t*i2 au0sy51o qbpu3 z8tant rate. The boy is near the outer edge, and theu u5kavyep *u: bus109a.8o t2k3azqi girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-rouni aidrh4+ jw(gu)) o7cd which is turning at a constant rate. The(+ohc 7 r )jda4iw)igu 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 turn)5honh)6:r qg gz wvc:ing at a constant rate. The bo))z whgnv::6rq ho 5cgy is near the outer edge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a mer8 e4s:,u7s7mv at6ufbc; x kl4rvm/axry-go-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 c emfm 8us,4tas4vvb cx :u7;6/a7rlxkentripetal acceleration?

  A boy and a girl are riding a merry-go-py r3v+91qgi yround 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 acceleration p9 qyryvi+13g?

  Consider a rigid body that is rotating. Which of the following is an accu e3f/j5()ltcplwf z7)qet 0d urate stat ) jtleufq)7z/wec5d 3fl0(p tement?

  Rolling without slippinz;n-r(g2-dk5;v uth 5jif sl wg depends on

  Two equal forces are applied to a door. The first force is applied at the midpfrg.(g1 3 yir 12gdrfwoint of the door; tg3ir1 gr gyf1wfr.d(2 he 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 applepl3w2g gj k u4iq9+rz9yhv(0ied 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 torque?kwy2ph eg3zi 94qju9v l(g+ r0

  Two forces are applied to w.j 5h(lh2 jlma doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to2.w(m5 hlhjj l the torque of the second is

  What is the quantity usd+xpdl3l*f9; t7ga k* gk7g uped to measure an object's resistance to changes in rotatio7 kppdk 9*7lg*dutag;f l+g3x n?

  Consider two uniform solid spheres where both have the sagg/lohs8l ;nyoq uzgj*t:h0 x/av0-+me diameter, but one has twice the mass of the other. The ratio of the larger momenvy - :hlos0gzqtg0n;8*j al/+xhou g/t of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radiusg a /o(.2sorw-(pok dq; fc db(r-1cav of the other. The ratio of the larger sphere's moment of inertia to that of the .ar(v(o-o-b/2; raqg(1kd pcs cwdof smaller sphere is

  Consider two uniform solipacg.rj7 pdz0 :4z)zz d spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger momprczd :0g.zj z)p7az 4ent of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M 04sjszoavrz g*7 *i7b x isk1-and radius R. If these are increased to 2M and 3R,j7 s1*r4kiob zzsi7g -s0vxa* what happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applihc;- y7 shkei6ed to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by.p6ss0l1hh9jx+yvhc: a 4kg y /s ,is7qsktk3 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotationali39h4s:yp+ 7x0,v6s1l h s kgjstkhqs./ cyak kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whicjsl;hf2fjho4o 6a6- xh has 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 translatio6jf4hx6ol2f sh -oj ;anal 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 in*uxz6ez09fk3 v -xy3v/w bkhjclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline dependxkz6 *w3xfe 3 vvyz-bj/hku09 s on

  Suppose a solid sphere of mass M and radius R rolls without slip hn:/mxp(rress7 hql;0y +kjv6e84faping down an inclined plane starting from rest. The ks vrj4xhm:+fr;6 /e(seplaqny0 7h 8angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system fj1/,95pnpx ,f 3tf.q(pw;awxfank mof particles changes when a net external force acts on thfw x p5;kf9.nt,/n j fmqafx(pp3,a1we system." This statement is

  In what circumstances can the angular velw75zbggdrj:g e;20 fo ocity of system of particles change without any change in the system'7wg 2z;5bd:fegrjo0gs angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any fric;-u hi7zndl: mtion which may udz:;i- hnm7 lbe present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Ezv d9j *h,o0st2m2uo l/is(q:v: nqquarth moves close to the Sud q*:,so0v92ql /vum o iz:t( u2sqhjnn, then which 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 jhcnxywuo02+eukp )72)l /xw his outstretched arms close to his body. What hap l)uynhwo+xw)c27kp0 2 ex/ju pens to his angular momentum about the axis of rotation?

  An ice skater performs t2,8 qoe 6po (.kjzguov eg;-ja pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happe.geev t uojo zoq 2gk(-;,j86pns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcm4v1nptk9:+.je qhd al* gzo/hed arms close to his body. What happens to his moment of ineltez j /ado*mn9 h+q pg.4:k1vrtia about the axis of rotation?

State the law of conservation of angularp0osk s+t2p 0q momentum.

  What arc length does t si;x6i 1zjb (wdz;m5jhe Earth travel in a three month period in its nearly circularsjz56dj i;;ix(bz 1wm orbit about the 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 df -w-h vk+eet0fi p+;distance does the tip of the second hand sweep through in 3 min-dwphe + f+ f;v-tei0kutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equiv 9f45eegal r5salent to?

  A bicycle wheel rotates uniformly through 2.0 r ,5tg n3qr s.27wu 0 l7flqn-3kupgzwhevolutions in 4.0 s. What is the frelnw3ql rt.swg- 5z pg7qhu2 k7n3 ,uf0quency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses .d 6dcd8h(6 v(is pkqrat a frequency of 0.40 kHz. The period of its qp6.dr 8hd(sc (6 vkidrotation is

  A phonograph record rotates at 45 rpm. Through what angle 15s6xyqs(zba 9 posf;does it turn in 0.20 s;1sp q zx fs9(6a5obys?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outeqr*eg6 62j iyvr r qi j*2e6grv6yim move in 2.1 s?

  A bicycle wheel rotatehx/zh kj-+ 8bgs uniformly through 2.0 revolutions in 4.0 s. What is the average angular s jxb-g 8/zh+hkpeed of the wheel?

  A bicycle wheel rota,ny zjfxy-be)o d h*85tes uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center oxz8- yd*je) ,f 5hobynf the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whinfn fl.i8w9qi,rx 3p,ch moves the car is driv n,r8 pi9.qf3l f,xwnien 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 uld, .oieoi .,rotating with a constant angular speed of 2.0 rad/s. .ild ioo,,.eu What is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If t /rclr(zr5006wf9j/;tgm omwv zgob 9he motor rotatb jzo lgr m twmr(/6f/95rc0 w9o0vg;zes 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 is rotating with a constant angular mw-+ sy+i:ksq speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel'is wyqsk ++:-ms rim?

  What is the centripetal accuow)rn0+fkl513w0ezidhz n /il*. pkeleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is m.z wl3n5d0 e u1i)0+f rzhi p*klwkno/oving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spaiqz ekh4i2g6ai un2)/ ce station (r = 1000 m) rotate to produce an artificial gravity of unk2i4i)i2a6z/e hq g $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a spea4kbbgh :m;: wed of 20 m/s. The maximum centri4gb;bm : ah:wkpetal 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 speed g aebg2d1.v9z 0vb s1fof 20 m/s. The maximum centripetal force (provided by static friction) ibb1 ev1f9.vsa z2 gdg0s $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end o1lj2 fc-acrl i1 x*c;cf a 0.750-m string, is whirled around in a smooth level table. If the maximum tension th*xal-jlccc;r c21 1fi at 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 m d x/w65lemb+y16;osetb on j 8xown a lane at 4.3 mw+6/nb8soe51;lj b t oxmeyx6/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 angular acceleration ofeh7j(ag z*n* pz g8(dng6g1mv $4.5 rad/s^2$. 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 angulav)v*p fjii2,o bsc a5;r 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 afterjv3 p 58c5 dhx0gjnr/z starting from rest and accelerating at a constant angular acceleration/ 5phxd j 3c58r0vnzjg of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angul2qzb5n9fc-e qar 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 witd4i:; pkna ,czh a constant angular acceleratio:p;4cazk ind, n 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 sp30fa wy3m ec0ceed of 6.0 rad/s while turning throug30yce0 mfa3 wch 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slow)jly3lfrtv i;5(nuu 2s down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?;n3illf (yut5 uj)r2v

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over at al ,b rsm-.7tbnbf(5 rh1(fsv n)*jy distance of 115 m. What bb jlbn. *t7)1 ,tfhnr ya(fv5ms(s-ris the angular acceleration?

  A wheel of diameter of 68.0 cm slbpgm 4u:m j+m7ows down uniformly from 8.40 m/s to rest over a distance of 115 m. H7gu +m:jp m4mbow long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates o5 ab,afp ,g7aat a rotational speed of 3600 rev/min. When switched off, it rotatef5 a,ga7p,oab s 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 nl9 6ucqcui*590 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force unc q9lu *6ic5is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nmuawdoa, 1xkf +,hg+ny6t l7(q7vo 9ly. If a 30 cm long wrench is used, what is the magnitude of the force required wh u77fn kw+y1aqh,tx 6dyloaol( 9g+v,en the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiu /s+h0i70os acb rsqr.fbb(0a $3.00 \; kgm^{2}$ 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 or c08c2yn zoa,ligin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about a c80ylzn2co, the origin?

  A solid cylinder of mass 10 kg is pivoted aboutk0-a b;u n9j -ym.yshj 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 downwjuy k-0 hbj myn;.9s-aard. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivol.w;-9 cnibdvbbn8)dd.e an0 ted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 w-lb db.cda9 i dn;.evnbn)08= 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 on9lvqlm b m+ y:8;c4br8/ej fp4r.sppwe end. The 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? (Th/;f+ lc4eprbs p4qrpjlv898mwyb m. :e 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 mbhh(8qx5lvo q9m.l f7ass 1.5 kg. Neglect the mass ob(qfx9vohl8.q m7 lh5f 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 slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictio- qgebn66gl32cbati 9nless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acl- ntigqa936bb 2g6ecceleration of the pulley?

  A 1.53-kg mass hangs on a7o(ppr69oygx(eawr d5*o g6 h rope wrapped around a frictionless disk pulley of mass 7.07 kg and rr5eawg(66xo*7d( p9h go p yoradius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store em at pta+j3.*vnergy. 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 ixdly ype0)i19 nertia 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 anlnuy2qgu w/bm,x ,q+(xg0x23n9cnuq d rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom of the inclinedq0nn2 +g9nu l3 q,b(,xwu u mqgy/xcx2 plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a spe:/t4t; umidzw z 5jt9 ,sun1fiag/h:ned of 10 m/s. How high up an inclined plane can it climb before coming mt,zsgin ; 1/wzjtf:u 9:da ih 54/tnuto rest?

  A hoop of radius 0.50 m andg5znw3-zn v 0 4xm)spv;s ig+p a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane.np3vzg z0mv +4s;p)isnxg5w - How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1btmqvrims9 ni5,ms88: mqi4 :.5 kg and radius 15 cm rolls without slipping down a 35e incl8mi 4, m:vrnsb8m9mq:tiiq5s ine that 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 momex2 ngymnh-yk v6tmrvjb(9hjri 5e0+wuk *)(0 ntum 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 momenw-5bdmy) s eh.t 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 moment o 9 aroh5fpcbtb*)-q xc81io- yf inertio)thx *-bcc5b-yo9 p18fqi ara 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?