Angular displacement+ehlo+ wz;7 dz is usually express in units of

  Angular velocity is expressed in unigsw(19 jyy+ 7wi nk*ists of

  Angular acceleration is expressed .,(rtjr/ar7 r;bsgvt5o:wj m:r y j 7ain units of

  A boy and a girl are riding.v 9ip. bhjim: on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the j im h.ib9.v:pgirl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a 2o8k l03cpvj jmerry-go-round 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 greate2 jj8lop3c kv0r angular speed?

  A boy and a girl are riding on a merry-ax7rjre da(83 s :xfv4go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center4e(8sd3a jx7vx:rafr . Who has the greater linear speed?

  A boy and a girl are ridis7,+e f.v4s fbh t p)ey23eytkng a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is4esef3fhk,y+b .72y )petvst closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning yb8/rntcv;x7 at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greatern /tc;x7vy8br tangential acceleration?

  Consider a rigid body that is rotating. ncv;i68cb+ wx Which of the following is an accurate statemeci 8x 6wvcb;+nnt?

  Rolling without slipping depends o7s ; iqpdmwi.hwv,c-/ n

  Two equal forces are aixk(bxeu* an 2/t +mr-y/tls1 pplied to a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both - +1/(tmxbk2 yi/lnau t*xresforces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first fo7x.q/h7i xus/psq* l urce is applied perpendicular to the door; the second force is applied at 30e to the pla*p/. hl sxqsxq77/uuine of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The firb nn,b59ndf9 qst force is tw 9,nnbq5fb9d nice as 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 ug +nd hn1ju7 l9.ss6*gr(qiyin rotation* dh sgisgqnly+7r6u9 n1 .(ju?

  Consider two uniform solid spheres where both have the same diameter,it7 jmi 25bsteca; -/m but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller;ibeic tmts a-j5/m 27 moment of inertia is

  Two uniform solid spheres have the same masr 11y *kbobvjs:1.ypss, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller spherevskryyp1o:.js*bb 1 1 is

  Consider two uniform solid spheres where one haxo8e m2c14dvdnmb /wb+ * btj3s twice the mass and twice the diameter of the othwo+ *e/b3c8bmbd 1vt2n4mdx jer. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid spher 79uh:ibqa8rr e has mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abou79qu:i rr bah8t a central axis?

  If a constant net torque is applied to an object, isyhd;;l:y+ythat object will

  The moment of inertia of a solid cylinder about its axis is give27weoyiqq 61 3 /glryfn by $\frac{1}{2} MR^2$. 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, on-vyuh6ax2 ( j;ji;hsa e wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic ha;a yih-sx2ju( 6;vjenergy 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 rnje kv wqd5o;3.eap 38adius R rolls without slipping down an inclined plana3 8o.wqd pnk;3ve e5je starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere o2:ximh0m2yb5 -u httof mass M and radius R rolls without slipping down an inclined planh0 t :-tobh22i5ymum xe 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 particles change ey:xr,zd+3ngw;jugi s(a+6 j s when a net external force acts on the system." Th+( ea gdiu 6;3zg:snxy,j+rjwis statement is

  In what circumstances ca ozlo1qm: i l9(,*w3git vjd)an the angular velocity of system of particles change without any change in the l v(qoj1 i9*a:lz g)t3moi,dwsystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictionl (u xmfyz7: yyu(b;y; 7bnjeb*8r0py which may be pr*m(;yxyfu7ry7lzbn p:je u8 b;b0y y( esent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipnx4zdu4 kswo5) om/;otical orbit. As the Earth moves close to the Sun, then which of the following best desc;o5d )xumz4w/4o noskribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulldz0m(n2t62bet3sx e s v)e8 lding in his outstretched arms close to his body. What h 3 dsv(txne 0)e8zlb2 st6mde2appens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outyiyle zh4u2 11jw4 8umz y7v: i5zatd2stretched arms ci8 17y ylw2y hi2u 1tvj4zemz:54adu zlose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a falmvzoqg25puqb.;+ 2 p/rzf h/ st spin) by pulling in his outstretched arms close to his body. What happens to his momentfz zqpv/2.lprmgoq;+ hu5/2b of inertia about the axis of rotation?

State the law of conservation of angt26 g.k;7 2vem9fn(uhw n tzlvular momentum.

  What arc length does the Earth travel iopxv kno)g t7-6l fe+cy17,jln a three month period in its nearly circular orbit about the Sun with a radie- )y,f7 7xnp1o+lgk6 cotjlv us of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does az)7tur ady,1the tip of rt azy17d)ua, the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per h99(hg fmsth8k om:3 yarz.z (h7ah0b-q 8kgkminute equivalent to?

  A bicycle wheel rotates uoql+rv;r/ ;3xji(nz lniformly through 2.0 revolutions in 4.0 s. What is the frequency ofrl3qj;( l vrxnzo+i /; the wheel's rotation?

  A pulsar (a rotating neutron s8d+riwb;9q9tu4 n4 6 v rwoz)p*sv;ti7jzs qdtar) emits pulses at a frequency of 0.40 kHz. The period+dispz 4 9bt; rzvso74vj dwqn;8u)i6wt* 9qr of its rotation is

  A phonograph record rotates ato ,c wmkilym;v7-og (ds .fk*, 45 rpm. Through what angle does it turn in 0.20 .oyosw, cgm *di k m(;fklv-7,s?

  A wheel of diameter 26 cm turns -v/rxevz4 wdu0 b;5*c dyle7 hat 1500 rpm. How far will a point on the outer rim move in bd uc/rvz7ex4 v50;-ylw edh* 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions inlgc+l:; *p dcn czmi98 4.0 s. What is the average angulaz 9*cl:p+nccl ;im8 gdr speed of the wheel?

  A bicycle wheel rotates uniformly thio wtiq10cn v(048mhdrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of th0q4 n0i8vi( w1ctdo hme wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Thy nqy1f(nfvul9+ h.a6s) 0hi ge cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley yhngis6 auh +1fy( q9)ln.vf 0rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with ( :r +j:e9t:0yxjzlpbfcqx(x a constant angular speed of 2.0 rad/s. What tpe90( +qxrjy czf(x:::j b xlis the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered qg8y l-qkfud/yb:/; aweed cutter is 0.16 m in length. If the motor rotates at the rate y/g-:/ab;ufklyq d8q 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 angulc n.me t,;rn:pqns 1.yar speed of 2.0 rad/s. What is the centripetal accelqn .cp,stm r 1nn;:e.yeration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on 9x73h tblq8ndthe perimeter of a bicycle wheel of dbx 38ltnh7 qd9iameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minutsat( i0yrl8b0 e (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity of( rit0sa8 0byl $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a sp;q tydtmq3cz )2h:pe+eed of 20 m/s. The maximum centripetal force (p+tqypcd3mtq h:e 2 z;)rovided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a fla*vso f3a6fmv kw7m x*+t circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by st*v6kmfxv w*+f oas3m7atic 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 0.7-w urmlh6.a/e crxt3i8 k46su7 jgg5k50-m string, is whirled around in a smooth 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 brehxr/6-gwt7 u.58 r3 cm64akgeksluijak?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 m do* kakbvk(9dd c1tmi,bew/- :mwnm,b1(-tidk ak9/*wcvkde m: b a 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 aobt):yee9)82h fzt cl2 n1kkungular 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 cogexevwc :*m92nstant 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 a12ti 4;q::ywiiqe wheu fl8.qfter starting from rest and accelerating at a constant aitly8q f wii.:2; w 1ee4hqq:ungular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration v*.fwje -zty7+4mp+bnts s;jof $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 2sapq( 4h3qz cc lz3iz1gg2x190 rad/s decelerates with a constant angular acceleration z1z 3gcx(4 ihpa19qq z2 lcg3sof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reache fcbn.zp9/gy 1jzsmn;s ;c-6js an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular accel; ;/g6yns.j n9 p jcfbscz1-mzeration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly frfh7ty33lco 8kom 8.40 m/s to rest over a distance of 115 m. What is the total number of oyl3cth 8f 3k7revolutions the wheel rotates in coming to rest?

  A wheel of diameter of )ol8 zqb6p4kmfe zra-if.v)( 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angulara)pof4m- zi86lrzfkbe ). v(q acceleration?

  A wheel of diameter of 68.0 cm slows downrl6nt6m2 l-dso8e a i l5i(kr: uniformly from 8.40 m/s to rest over a distaan r :i(l 6iolskrle 2md8t-56nce of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at abgpgh-:p b(h9 rotational speed of 3600 rev/min. bbg g:p9 hp-h( When switched 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 tightening to a tora4wf0 njc ei,1que 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 jfe1c,ia 40wn the wrench?

  The bolts on a car wheel require tightenidu xxq fo;a9;0rya .)lng to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude0 l.;);d xr9xfa yqoau of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inert +hwu,f98:ac vm 7ziptia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follow;z0mgfkvqc pwf(15+rs: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momentzp 15r (+0kqw vgffmc; of inertia about the origin?

  A solid cylinder of mass 10 kg is pivotypa4qb-(x ovvy (xg8- ed about a frictionless axis thought the center O. A rope 8-gy(ovxy qv4 (b ax-pwrapped 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 10rrj) 7c3dmy wkrb/d *w. *(nny kg is pivoted about a frictionless axis thought the center O. Amww j*)/yr7r dn k(3.b*ndyrc rope wrapped 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) 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 i.n;o3wd98ytllm p1c l 7 1hbuonitially held in the horizontal position, andwu1 b.l81 tph9ldo 3y;cm7l on then released as the free end is allowed to fall. What is the angular acceleration as 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 mass 1.5 kg. Neglei 753e ya;qorvct 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 i3 ove;ary5q7 it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless i30ulr0ip1tt )gedyvc m-)a3disk pulley of mass 7.07 kg and radius 66vg-)u 1yac rttml3ii0e3d)p 0 .0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk gs/ y,9-con;i2qu w knpulley of mass 7.07 kg and rugs2ok cqiwn9n /, -;yadius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to 3u h)p)ot m d9e4n0dc kwpyf31store $1.00 \times 10^{6} \; J$ 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 bhwvps5hl,4rnmb1 + 1inertia 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 3(6 b ibqjp4egz,zkb-and radius 0.010 m starts from rest and rolls without slippj-b zb k zq64(,ip3ebging 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 m rock(3o1a-prx6 l z,qwolls with a speed of 10 m/s. How high (r3 lwkpq1 coo-z,6axup 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 release +nvprs;j c)(sd from rest and allowed to roll down an inclined plane. How fast is it moving after dropping r+(sn)cspjv ; a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and ra l-2x(lroiq+2; )kjesh-m ipldius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is oi-q p-l j m2(lx +2s;ehlrik)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 mbd, 2indcmjbb+s) ;i7 omentum 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 u r(k/e,4 gidzgn2(xb; yatn: 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 extypu.i,,zcpuu 3 ;(fz yended has a moment of inertia ofy( cu .u,zyp;,zfp3iu
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?