Angular displacement is usuall+8/q(3 ekyxp cexun3 hy express in units of

  Angular velocity is expressed in uni)l/ v a;p q:mklt8q-3tn,hip5q3 uq fzts of

  Angular acceleration is exprlm 4r(v 6jpzs6essed in units of

  A boy and a girl are riding onl:s0dia0kjg+ n sdas 45b x32p a merry-go-round which is turning at a constant rate. T :bl3s2jgk5n400+asspxdaidhe boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merrf,5 txae1+dp0p2nq2i/v ome* tu q7dny-go-round which is turning at a constant rate. The boy is near the outer edp*q+nit dm, qexf0/22 oap7e1tdv5 nuge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry 869y hv2c8) skjaqgdl-go-round which is turning at a constant rate. The boy is near the outer edgkvqh cs 8 dy)l86jga92e, 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 constat x k+pzk3e0miz-78c fnt rate. The boy is near the outer edge, while the girl is closer to the centek8 c3z-0 +ptfkz7e ximr. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merryq8*aahhldf7/y (rj;s hp8 np (-go-round which is turning at a constant rate. The boy is near the outer ehd87f8 p;h/j( *asn aqhyrl(pdge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which mb w;nr48 j7 mtqmw(.qof the following is an accurate st8(nr mwqmm7jw.t ;4q batement?

  Rolling without slipping depewpd+78tuwh ;v nds on

  Two equal forces are applied to a door. The first force is applied 8o3lro0) v ynr k2eae1yjj)-oat the midpoint of the door; the secr 1ja j2 ley-o0)e3y kn)vroo8ond force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door atz qkbyis2l2/l. h6gn j/c86f k the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the kj86l /b ilkn. z/ 26ysgcq2hfplane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular gwh+d:m 0vv*h(.p ggy/wsls* 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 second gplw 0sgvgh*m(/w * dv .:ysh+is

  What is the quantity used to measure azqy 2ffw. ((iu51os bxxn/3o sn object's resistance to changes in rotation(5 u231wfso(x sb qfoiy/x.nz?

  Consider two uniform solid spheres where bothk ;x,+vzzy8q:tmm6 v(chrww ( have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia mvzzt( vrx, w q8mchk(;6+wy:to that of the smaller moment of inertia is

  Two uniform solid spheres have the sambyq * x.gpioh7:xe+w)e mass, but one has twice the radius of the other. The ra : g.7ieb+y)*phwxoqx tio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform sols ku;zdh 3gtf88kq 9z.id spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of td kuh.s t8q39 fgz;8zkhe smaller moment of inertia is

  A uniform solid sphere rm,ge 2vyfo k*zt)uh g/d-b89 has mass M and radius R. If these are increased to 2M and 3R, what happens tk /dv -,8ruzfb* 9hg2yteo)gmo the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an objectj(mi(q j s3a8*e 5coi*uro+ja , that object will

  The moment of inertia of a solid cylinder about its axis is given bbp3);c u d77tws imcy,z d(6sey $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kj i)y4 bsct,bz5f2b :xg and a radius of 30 cm. What is the ratio of the rotati)xyb5fsbt j 2,iz4:c bonal 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 rolls without slipping down an inc3rig kq88j(l y6,w1j:a)f kdii9oqqk i0 wa5zlined plane starting from rest. The linear velocity of the sphere at the bottom of the inci)68 ,0ki139 8wya qq k(j:firg doawjkz5iq lline depends on

  Suppose a solid sphere of mass M and radiusu)6 tc4oa; .xosa 7rfm R rolls without slipping down an inclin.r 4fx)saoto ac;6m7ued plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particleset+xn)u h1 qyv q5,ml:s2 wibkk7g*;u changes when a net external force acts on the sy;7ht+ sq:2 q*,v1lu ke )gibnxykm5 uwstem." This statement is

  In what circumstances can the angular velocityczyaxz :njy ): 6.dp2l of system of particles change without any change in the syst2y jz:6 za)pcdx yn.:lem's angular momentum?

  The Earth orbits the Sun in an elliptical orba1eh z:j6c ,sig;qp,b it. Ignore any friction which may be present. What happens over time to the Earth's angular momentuh6egz1s qp,ac,: b;jim about the Sun?

  The Earth moves about the Sun in a;qrwjb)z 695hhfh; vg n elliptical orbit. As the Earth moves close to the j6h5;fz h9b h;w)gqvrSun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fastr)lni) 82md: q(:h bdaxls 0nz spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum ab:qnd la2hx()n8)r i zlb:mds0out the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by vw7ghz6v.qt-w a:/ytykc1c/ pulling in his outstretched arms close to his body. What hztvw 6a:wg/ 7 y1 ht-kycqc./vappens to his rotational kinetic energy about the axis of rotation?

  An ice skater performsg ew/m tl/9z5z a pirouette (a fast spin) by pulling in his outstretched arms close to his bogwt/9e z/5m zldy. What happens to his moment of inertia about the axis of rotation?

State the law of conservat2,-x3.2pjy z tmnqjioion of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly-x-ns nc (qsr7 circular orbit about the Sun with arsnxq c-- 7n(s radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thec +rzs88hw f:hoha:*o tip of the second hand sweep through in 3 minu*:8 s: h+fh zoh8ocawrtes and 45 seconds?

  How many rad/s is 25 revolutioat dr39m,k *9 byyv6xvhl b(7cns per minute equivalent to?

  A bicycle wheel rotates uniformly throughl0o l2iuqw r5gfj +a2 r2hw410i3p ylr 2.0 revolutions in 4.0 s. What is the frequencllri+0 f4j 2052yr2 uwilwoh 3 gpr1qay of the wheel's rotation?

  A pulsar (a rotating neutron star) ea3p 8d ab fwk+bc,i52xmits pulses at a frequency of 0.40 kHz. The period oab5pbc8i fx 2adk+,w3f its rotation is

  A phonograph record rjkcsad n.k,-nl4,7xh6r h ;wnotates at 45 rpm. Through what angle does it turn in 0.20 s?hn;n cn-. r xkh4sd,lkw6 7a,j

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the o) dt8 w*j+gf6 /utqjfiuter rim m wtjqi/ff t6 dug+*8)jove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thef wu(wz/-jt u* average angular speed of t(/w* fzt- ujuwhe wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions inbv-g+* wr2rjv 4.0 s. What is the linear speed of a point 0.10 m fro*rv r2+gjvbw-m the center of the wheel?

  A cable car at a ski resort carries skiersm*r)0sfsf v8 x a distance 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 pulle0) f8msfv *sxry rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 xc 63mj/vqb(prad/s. What is the linear speed ofmpq/x c3(jbv 6 a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the motor4/k6* x*g 2.;y qpftphivyjz p rotates at the rate of 20 rev/s, whatj ; i 4yy6*th2qfpkpp.v*x/ zg is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.01j:pr h*v amxy9g*ht5 rad/s. What ph1m*y 5trhagv*x: j9is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of aqhe*tf+l5p4 2zv( sprv yb2/, *v zodi bicycle wheel of di*2f zv,5 soy/(l zebqppt4 rvid 2+h*vameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a cinvq; uwi,,q3d72 ak horcular, rotating space station (r = 1000 m) rotate to produce an arto2,v7 nu aid ;,kq3hwqificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 06 v cc1fuic0z50 m with a speed of 20 m/s. The maximum centripetal force (prc6vz0cc10uf iovided 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 bap+epgt5vl3 9 2p7:/rgs:wpu)s cr,mv8b fwof radius 50 m with a speed of 20 m/s. The maximum centripetalessg ,m)u a/+p3wrbbtf g5vl r:c7v29 wp:p8p 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 thgn ysmtxs m*3*n 9-q7de end of a 0.750-m string, is whirled around in a smooth level nnd gs x-3*7syqt9mm *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 7.6* tgg3vdmgbs 87 gcui9/;djf5 kg and radius 9.0 cm rolls without slipping 10 m down a lane aib7 6*;3ggdutgs9 vmgf/8jdct 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 wit iv2h br pcl*ww,z(6;th 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 acn(v;ju,s lxr. celeration 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 automobiln3ms6tu g.vm) u*tk 0ge tire rotate after starting from rest0 s)*6t.ug3vtmu gmkn and accelerating 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 accelera8dkjp4rh: 1k; u)ndtc tion 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 constaz7 skx )sfx g0zgsn5:*nt angular acceleration kz:z)sxgf0s 7gn5s x* 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 radu5mumfth - 387l/rh hk/s while turning through 2.0 -uflh3u/7t 8 rm kmh5hrevolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniforml2d4qa8j d6.za9kq98u/wws b5z-ej mg ixy :o ey from 8.40 m/s to rest over a disuqzs6 i9mzedj a9 qeo-g.j8 wyd45x2ab8/ wk:tance 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 una r*kcxzgq 2c+),vcftz fz6 9;o(qn:siformly from 8.40 m/s to rest over a distance of 115 m. What is the angularx2 rc(ftzqgs )*:cqcz,azknf6 + ;o9v acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40ix0 hf034jbkz m/s to rest over a distance of 115 m. How long does it take f0b 04ikj 3fxzhor the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational s/bkr9w w+ )v:zqys-5avtbe j*peed of 3600 rev/min. When switched off, ij/we z 5qk+9awsvt)by -*r v:bt 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 90 Nm. If d .wxxc k(*v9la 30 cm long wrench is used, what is the magnitude of the force required when the force is peckxwxl* . d9v(rpendicular to the wrench?

  The bolts on a car wheel require tightening to a tvt*86qc zz 5jborque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applievcz58z tbj*q6d at $53^{\circ}$ to the wrench?

  A wheel with moment of iner x2p wq4*.b7tqyv)7;oxdnv5k xyo 5gltia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: 1w8yjmhwx 5n*mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the mo5yw*h1j xwmn8ment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought tykd nmijss4xz ,fxppv )5 33tkdt4, 9+j/- dmihe center O. A rope wrap-n43 )fmpyx tsp d/4 djtidkimx+3 z,,skj59 vped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionlessdsa efa 60m4z0sm-n+nm(h :xo axis thought the center O. A rope wrapped around the out+z4a o6:(nehs0dam- x0fsm mner radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 initially held inavxd0p *0 hefh5od/q1 the horizontal position, and then released as the free end is allowed to fall. What is the angule*0 0hh vqd/1 o5pfaxdar acceleration as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wed03nb/ 1tiumx iis:- heel to be a ring 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 1usximt0i/ en: d-3b ifor 4.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on am,llp2x ppt/- mi t;cv(h.xh: rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whmt ;-2pt l(hicxp.xm ,:p/hvlat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a+j5hhztm4mej u , )lfw3tle(9 rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration oeemmzll 5 t( u4)jh+9,wfj3ht f the mass?

  A rotating flywheel can be used to store energy. Ifxcwe *fpd+ ,* v8zcd6c 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 inerth3pqvl . jktg1 +,pya)4m1qchia 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 anp9 demc 05n7vgd radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottom o9 ev n7d5pgcm0f the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls - p .w:peyn4)xs)*2l txfvf qxwith a speed of 10 m/s. How high up an inclined plane can it clwtxl) nsf-v y)pxq x p.*42ef:imb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.mggw-s 7wni05nm76 go4e 1 ybn20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a venm0no-m g1wswi7n geb 6g45y7rtical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15dkqouru(p1+ jy8.mz1 cm rolls without slipping down a 35e incline thkqj1+o y zup.m(dr 18uat 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 momentum changesn-tpw:mge0io6mq yvw(x/+ +nah -bl1 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; ey5onxxn4ii,,. g (wl3dp0,dffvdb 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 h :ufiah60 :bgvas a moment of inertia hv:gf0a:b6u iof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?