Angular displacement is )s bx:kiz- o:qusually express in units of

  Angular velocity is expressedknj6(v01 ms 92)h c ku*nromka6xlui 3 in units of

  Angular acceleration is expressed in 0t7ls vds2iw, w, j-x1uore,m units of

  A boy and a girl are riding on a merry-go-roun)x jucys19 ovew 6:r/;ooi 2srd 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 ai 1rxo soyj)2evwu9 o/6src;:ngular displacement?

  A boy and a girl are ridi2)/ d6mjktbjv7 xd p9a)t fuu/ng on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closjap f7vu b)xu6 )tdjt2/k9d/mer 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 a vh82di1it*z constant rate. The boy is near the outer edge, and the2 ivdhat1*8 zi 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 constant ratem nk5x(s4* vjh. The boy is near the outer eh45snjmk ( *vxdge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant rate9k m8a7x8y jnjh/o5 q;qgpd1ll8qm2s. The boy is near the outer edge, while the girl is closer t8mg7xm 92n s lako qdpq58y;/jj8qlh1o the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following k0l f,yslbf,f1:v+zebr7. xo is an accurate statxvl:fo1l, kf7,+er .yfbz 0b sement?

  Rolling without slipv dbm6cmfa0, m ga-x25ping depends on

  Two equal forces are applied to a door. The first fo h3w5hn)fm2p13vef9 p ;mkeryrce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the grea h 15yv;wfemerpk h329n 3p)mfter torque?

  Two equal forces are applied to a door at the doorknob. The first force i)z,w rbziwl7 3nhh5:sm 9q8ahs applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exer,bhwn 73i h8sra 5zlmh:qzw)9 ts the greater torque?

  Two forces are applied to a doorknob, perpendicula u-6acjixa0c5tha,( orh 5xr/ 95bfw zr to the door. The first force is twice as large as the second force. The ratio of the torque of the first0jb5a i5hr r5 xc,xz-h(o afwua 6t9/c to the torque of the second is

  What is the quantity uiur1 5nso u4s8sed to measure an object's resistance to changes in rotation?5nu 1os4s8r iu

  Consider two uniform solid spheres where bo:t0na nkz;zm* -k0awsth have the same diameter, but one has-ak wn;0azk*:mt n0zs twice the mass 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 the same mass, but one hawsbzp;z e2)1:l/+18cvpsv f s*tqxwis twice the radius of the other. The ratio of the larger sphere's moment of inertia to thatx1w8w1vf)ss zts/v:;bi*+ pcleq z2p of the smaller sphere is

  Consider two uniform solid spheres where one has 7y- er*v;9 aztpp -nkid8 4hhdtwice the mass and twice the diameter of tzp nda9-dvhe-rk 4;t8 *py7hihe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these jfonm0)qau(hjbdt-/ 7(x0ps are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axjsm( jq7( o-nbx /0) hutdf0pais?

  If a constant net torque is applied to an b9k5:dgztq )b object, that object will

  The moment of inertia of a solid cylinder about its axis is given az4 k slsnc+43by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy cnkszl a44 s+3is

  Consider a motorcycle of mass 150 kg, one wheel 8wfqb,,dp3tm9iep z6 of which has a mass of 10 kg and a39 zdeipwm6t8fq, b p, radius 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 R8 x:gpkm4burn6i ;m9p. z:aj,rhpq,b rolls without slipping down an inclined plane starting from rest. The lpm zib8rp,knj;. :mx:, q69rh p uab4ginear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down 8ps;ft h3u(/ a wk)*nqci zpu3an inclined plane starting from rest. The auqi(tw k* 3p8s f p;a)zhncu3/ngular 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 externalorzaf 5cy6vo38 8.vkw a ojb1; force acts ono8wcy1 f8oaz5j.k6ov3av b ; r the system." This statement is

  In what circumstances can the angular velocity of *h4ip,p* yu8 (jzca wosystem of particles change without any chanw*y p4ji 8ahopuz,*(cge in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whzxmumk te3is( 4n+ 4:iich may be pre4 isnmzme:k4( ti+ux3sent. 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 * o)z m+(op2 vwwu/qp0n1lfs vEarth moves close to the Sun, then which of the fwnz*0 )u( p v/2l1pos+vwmfoq ollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pullingef,k3 sz(;tp3f-ld s1ux l r7q in his outstretched arms close to his body. What happentfz3flsrk xpl7;, qe1u-3ds ( s to his angular momentum about the axis of rotation?

  An ice skater performscqy6sqrmm19/g1zo *w .a ep2(2jgs vyo1 xs/n a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic n9 jomyy1s2.e g qc(1gz s1m/2pw/rsqa*6ox venergy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) byqk phh4xfxym o j.0;88 pulling in his outstretched arms close to his body. What happens to his moment of inertia about fm4kh o y0xhpxj q.8;8the axis of rotation?

State the law of conservation of angular mi+ yxkl.d*:itomentum.

  What arc length does theufnt(.0mwk4hl + y2ta k 9y/dw Earth travel in a three month period in its nearly circular orbit about9nl.ttmkhfy k u /4yw2a0+( wd 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 distance does thebw +;kn cq4vlw-efg:m 1s mq*6 tip of the second hand sweb1q4*mmcs ekgnfqv w:- w+;6l ep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equiv/tzf ut n/q:k/alent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.68 nr f(gbs;zl What is the frequency of the wheelg (bfr z8n6sl;'s rotation?

  A pulsar (a rotating neutron star) 0g ;.9 qss gdpr8t9lvmemits pulses at a frequency of 0.40 kHz. The period of its rov 8m p9;l.tgqd9ssr0gtation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in k;v 3oat+b ok/0.20 s?t;/ kka3vo+ob

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on4lwbmq:i 2 a ngfsx3-. r,7ndx the outer rim move in 2.xqg .nf2 w-7sa:d, imbx4n3rl1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions inqe/0fuk fzqym *r8i.+ 4.0 s. What is the quf 0mf+iy*eqrk./8zaverage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 7f:kjkk jrr 4 o- *j6(xnw2t8jmtj-eu What is the linear speed of a -f2krm8 nktj*jutk - j6ojj:rx4(e7w point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries dw d-)o8-s :.i thkwmfskiers a distance of 6.8 km. The cable which moves the car is driven by a pulley idhwk .d8:ofs --w )tmwith 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 wi)5 r4t cznel9n7f pio zv/l7 jrj*wzvrs)j++)th a constant angular speed of 2.0 rad/s. What is the lp5 i) sz j7+ / oljvzvf9)zejl74*nrnrrwct+)inear 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 the moto: 0n;. hg6vfs07mdhe *xzk jdzt)- lpar rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord7;ak sj*0t0 gf.:mx nhp hz -)6zlddve?

  A wheel of radius 1.085(dc.k6nzvz0,uu fuqh 5ma b m is rotating with a constant angular speed of 2.0 rad/s. What is the cen n ukvca8bfu6 .hzz5d m0uq(5,tripetal acceleration of a point on the wheel's rim?

  What is the centripetatihz(me.:s/ c*m;lq zl acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cmm;t sel/i:h(mz. *zcq when the bike is moving 8.00 m/s?

  How many revolutions per minute (him02e p3jp,usie 2q:0vm e 9qrpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificia32 qjhe 9m0 :ieipquvpm,0es2l gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed pl1k90 y l),vt/ghorp of 20 m/s. The maximum centripetal force (p9ltplygo1v/0)k r, phrovided 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 ofn19l0zmnj lmsr c qve/*j; 6w; 20 m/s. The maximum centripetal force (provided by static friction) 1rws*/q cn lm;;jvm9 jnle06z 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 stq8( hnu(gyoz i/*nyr*ring, is whirled around in a smozu( q*hy(/8*grn noyi oth level table. If the maximum tension 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 a); c r6nv8mm44d nyppcm rolls without slipping 10 m down a lane at 4.3 m/s.; pn4vmry8c 4d6p )nma
(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 constoj/1h(lyg t5xant 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 8 nhrp5otq h,5xt on9,with a constant 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 doesm. jlt,vi9f 7o a 0.300-m radius automobile tire rotate after starting from rest and acceleratfo,vm 7.ijlt9ing 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 acceln:am a tm1.;mferation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleratxexut913 (rut4u; +bd s3rzcp es with a constant angular accelerati pbr9tuu4 3rs cuxde1z(3tx;+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 6.0 rad/s while turn0n /;j vu.:h.yisza fiing through 2.0 revoluvyfsn u;h / i0:j..aiztions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly fro7jcz qq -cupar-bdf: /1 vpr6/m 8.40 m/s to rest over a disr u6 z7b-1/f :qrdc-cppq/ajvtance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uj ,w9 4rshn+ lpd 3m tcfjx9/s,l/ai8mniformly from 8.40 m/s to rest over a distance of 115 m. Wh9cwlnmtj,8rxd,i p /+l9/a jsfs m4 3hat is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down upgh1e9 cr v;,uug9 .icniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for thep;ievrgh ,uc9u 9.gc1 wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotatiookiib0vxa8 tl9,p 9n4 nal speed of 3600 rev/min. When switched off, it rotates 5i9bo nla,ip8xv k49t 00.0 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 abs mp7s(88 hwm torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requmh8spbs mw 8(7ired when the force is perpendicular to the wrench?

  The bolts on a car wheel require kf1jh c9p:ys dg3 b0/v qqq)a+tightening to a torque of 90 Nm. If a 30 cm long wrench is used, whajqp )+gd kqc1qa / :svy390bfht is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ity)s87v ox1 mgnertia $3.00 \; kgm^{2}$ 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, mass 2mr.if;alq87e :r f2zn v is at x = a, and, mass 3mzlrfq7 rn;a 8:.fiev2 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 thought thra;i:3 kx e;pee 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 = e:k3ai; e;rpx6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pm9r) :ae ggn9w*5e bzlivoted 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 5.0 seconds, if it starts fromg9 *m9blaez ew5 nrg:) rest?

  A 4.00-m long rod is hinged at one end. The rod isx12r stk vl/+4abncf + 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 releasedaxstr+vclkf12b+ /4n ? (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 mrcuwm51 lyp59 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 f9yl wu5p1r 5cmor 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 frictionles5-iqpxo1eju,+2 hej xs disk pulley of mass 7.07 kg and radius 66.0 cm. ueeqxo -1 x5jp2,hi+jWhat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictiepgp u4795g5ons1cs d onless disk pulley of mass 7.07 kg and radiesnsu5ocggp 75d p941us 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to st/n-zawwcu s. 6;e krhix.xl*:ore 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 inertia 2ed5-3u r yh3uoh:a d1delcx/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 radiusnwucfn7/x7 h. 0.010 m starts from rest and rolls without slipping down a 1.0hn7x nuw7 ./cf-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 m rolls with a s:4rf 0wj, 2yzgop.f9tlr5i ogpeed of 10 m/s. How high w g.5ijfy:z 9g4opf rrtl20o ,up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is releas;,vyez. zz-xw pype5 vp5b(q8ed from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?zz ev55yw.v (p;-pbpe 8,xy qz

A solid sphere of mass 1.5 kg andgdwd6 tl-*-qhjl 2 7 ac0m;jma radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moawa *-7gmjd6 -ldhq2j l0;ctmment 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 changes2m6nj+y l;b uw 1kel+y 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 o4m,x/h kr loeaw-uuw (-6k(bgf 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 withjn-ccptyuscpj 04p 4;7cj 22q arms extended has a moment of inertia occ04j2 7q j pc2;jtuypps4nc -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?