Angular displacement is usually expres z jpe+89yy2giyq 12xukfwfb 2fbt6+3s in units of

  Angular velocity is expressed in uniczro4 gw0s:1k ts of

  Angular acceleration75br 9/nz 8d7)9q(c2igqprjdgjli gk is expressed in units of

  A boy and a girl are riding on a merry-go-round which is tnb;acjq3- )u a-7p+hb dxg db 7n/ylk1urning at a constant rate. The boy is near the outer edge, and the xy1p+cd/nb u 3an-;ba hk- gqj7)d7blgirl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at10iox+vwz /*xrt iwv + a constant rate. The boyozxw/0i *+v 1tixw+r v 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 consg aiw(( i0;kwjtant rate. The boy is near the outer edge, and the girl is closer to the center. ;i( kjwwi0(agWho has the greater linear speed?

  A boy and a girl are riding a merry-go-pm n )-c ,epjj7 x7u;weq7atharcz+38round which is turning at a constant rate. The boy is near the outer edge,; )w,c +p3m 7hux qraejcea7j8p-7ntz 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 6o*oua /bebb7 is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Wh ao6beb uob7*/o has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an actf. *d*am0bg zcurate statemeb ga.dfz0t*m *nt?

  Rolling without slippidmc p0ep1( d/ung depends on

  Two equal forces are applied toolnfrg,2n n44:t u1o f a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicugrn 2o luto, 4n:f14fnlar to the door. Which force exerts the greater torque?

  Two equal forces are applied to a d5zes e:, rnjo:oor at the doorknob. The first force is applied perpendicular to the door; the second force i:,seoenjz: 5 rs applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a h;kuv7 ti 2c p. /qewmd .8gxy8*q3zicdoorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torq8u /pyzv3hw..eq 7xd 8cmk g;t*iicq2ue of the first to the torque of the second is

  What is the quantity used to measurb(hr/6fc uq 54s hymc7e an object's resistance to changes in rotati4 7cqb6u5rsh /fhy(mc on?

  Consider two uniform solid spheres where b4 8 +1 jzm:snpklv0tdc- zt6aloth have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smalsz ltz8c46k :adn1-v0+ plmjtler moment of inertia is

  Two uniform solid spheme).ejfs.(mi k*6n vxn qs64-e9d cm jy+ga;eres have the same mass, but one has twice the radius of the othj 4 j .ee-sa* 9m6nnd (eg;cfe+q)yiv6m.mkxser. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twvwd4 bt; czx4f(,91 ;cvteltvice the mass and twice the diameter of the other. The ravzwct,9c ldt4btxvv 4;;f1(e tio 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. Ifise(.b* rf- xf these are increased to 2M and 3R, what happens to the sphere's moment of ineie.xr(sb f f*-rtia about a central axis?

  If a constant net torque is applied to an object, that +j9bhyyr:q1qf .li5 +ehk(h eobject will

  The moment of inertia of a solid cylinder about its axis isz;cbud/vp(vdrf(z4e6 w l 8.d given 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 motorcyclevni;2c lygr +4 of mass 150 kg, one wheel of which 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 tran 4yg+vic2r;lnslational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R b)+9z)5pz)o wkzpywbrolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom obp5)o)w+z)ky p9bz zwf the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping do3vo/; dutxl *hb 7q,j/hcwzb7 1ig vt,wn an inclined plane starting from re77//,g dc;qt l w v3j,uhhob1xvizbt *st. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a sy/cg hpim (l5(j* cmj:o ox/xv+stem of particles changes when a net external force acts on the system." This sv/hjxljc 5pc i(goxm/:o *(+mtatement is

  In what circumstances cazp+63rmk sfl-o 2z,gyn the angular velocity of system of particles change without any change ikfs,mg36 zoz2 +yl- prn the system's angular momentum?

  The Earth orbits the Su3h :gwciji4 d.n in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentumwi4c h: j.i3gd about the Sun?

  The Earth moves about the Sun in an elliptical orbbpx+cs nxyc4ax:4;.sm1 t+ hzit. As the Earth moves close to the Sun, then which cy:s1.xcsp4+z;m xtxn4 b a+hof the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piroueum3rhoux9qp((d8 j) c0nx mo6tte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentu u oo d8c(ju)0r 6x3m9qmhx(npm about the axis of rotation?

  An ice skater performs a pirouette (a fast spg gt mo*b0gdj86: l(qjin) by pulling in his outstretched arms close to his body. What happens to his rotatg8q g: m60j(b*ojltgdional kinetic energy about the axis of rotation?

  An ice skater performs a piroue dwus h53 y/q:o czs8lo26s)jjn+j85q0iacbntte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotati5jh /6lwc+bu j 0 q8yn:sia oq5jn8zs3s2co)don?

State the law of conservation oihln -* 72fak ecyn4z(-pco3af angular momentum.

  What arc length does the Earth travel in a three month period in its nearlybu(yj,i9r) t t circular orbit about the Sun with a radius ofitr(, )9tuj yb $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thx) 5qnl r.jo8he tip of the second hand sweep through in 3 minutesn5.)jqr hxo8l and 45 seconds?

  How many rad/s is 25 revolutions per minute equivad xg7v 6(:hshclent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4r62:zgg i(q0v3jlc lz .0 s. What is the frequency of the wheel's rotation?igzq3lj2g cr :vlz0 6(

  A pulsar (a rotating neutron star) emits pulses at a frequency2 xyekd.-+lliz40zbc of 0.40 kHz. The period of its ro x4i lbl0zdy-2+ck.z etation is

  A phonograph record rotates at 45 rpm. s/jua lfzi)(he-v k/ bp z ,d.b7h.gg;Through what angle does it turn in 0.20 s?hp fv,k(.l/bhsig /7. ; e)gdzbaj-zu

  A wheel of diameter 26 cm turns at 1.;9 4v izfsq6cmk8qskj p g0c0uk+ pk.500 rpm. How far will a point on the outer riskzcjfq4 u+v6 0;9. qk0gmksck8.p i pm move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What rr j6f4(w2s1 wm8:jckedgu v 8is the average angular sp fs 4kwj 1:(m68cdr urgje2wv8eed of the wheel?

  A bicycle wheel rotates unifo-xkdqhn-*(jvwdf2:.u dr )l ewc5 o: prmly through 2.0 revolutions in 4.0 s. What is the linear speed of a point:2dexpq:jv)ou-wdl r c(f n-h k*5.wd 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distanceqszb;mp/ uf7c r l8n-q93iw6q 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 qp8lsz b 7rc6q w /9u;3-fnimqmake the trip in 12 minutes?

  A wheel of radius 1.0 m hi7 :jfey4n:b ,z38ehpu ta b)is rotating with a constant angular speed of 2.0 rad/s. What is the linear spe:4hb z:38ht u niae fj,ye7pb)ed of a point on the wheel's rim?

  The cutting cord on a gas-powered xi3euer5 gw+ v gensr48,yf mwt..5g3weed cutter is 0.16 m in length. If the motor rotates at the rs.5 34xfg+w g,u.mwyvtereei3ng5 8rate 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 angzw(- d d lq+qtsbaz0)d4gt,wyj iazr(v56t+ ; ular speed of 2.0 rad/s. What is the centriplv(dz +dwtgi0,zz()dystb t4 ; aa5- wrq+ qj6etal acceleration of a point on the wheel's rim?

  What is the centripetal acceleraticni +vdhsc /)92 b4pmdon of a point on the perimeter of a bicycle wh h2scc+iv)p9 d/4dmnbeel of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per mios 84lvhp;cqj2* n )8tja zu3hnute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity s2hp tj4j3na uq l8*o8c;hv)zof $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 mj-;auu .fyd0f with a speed of 20 m/s. The maximum centripetal force (provided by static ff ujau -;0yfd.riction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a fle9f8qq.kwvpm51kpg dfx: l* :at circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by statiwf.p1qk 5x:8fk lpg *:qed v9mc friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attaa 8d+rwac;3 lbo/ w9lvched to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 rw 9lvb8 ;olaw/dc 3+aN, 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 4rg 8rbvchj(9without slipping 10 m down a lane at 4.3 rr9(4cvbgh8 j 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 coxj 8w i:id6-obnstant 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 accelerati7u6yu jo8u ce4i8v2 lcmy+w4affvl -5on 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 tib9 wwd0s :/o0nuq1cj ere rotate after starting from rest and accelerating at a constant angular acceleratd j:so9wuw0 c1qb/en0ion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acce 9pv e+n 3mfpv +e,f,v5gl1gqrx+1zg pleration 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 ang34hyi 5pptx .fular acceleration ofh5fpypx.it3 4 $-5.0 \; rad/s^2$. 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 whi9 buy g.jeylvm02d/ c/le turning through 2.0 revolutions. What is the aveu0y/ yvec gmj.9lb d2/rage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly lzoki (*h-yjnb.b1b ;uujx94b l w k:.from 8.40 m/s to rest over a distance of 115 m. What is the total number *bk-ouh: u.b;i9.4xj n1ll( bbyzjkwof revolutions the wheel rotates in coming to rest?

  A wheel of diameter odf,wbx 3gctw8 zm ,:ud5(v8fmf 68.0 cm slows down uniformly from 8.40 m/s to rest over a 8zx3dgw d5uwvf8m ,:f tbcm(,distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest 6 c pq9j fk1 vj(v1p;xvi0qw)oover a distance of 115 m. How long does it takpw61 xjv1v09iq(ojc f;q) vkpe for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at c28 4va gqu,2cmm+hxga rotational speed of 3600 rev/min. When switched off, it rotates 50,8u2cmmx+4qhagg v2 c.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 tt+ig q)60(m iv-g2ci14 b2nuw vyhpxqorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the formxv)1 b+0(piwu2v -ihqqity c2gg4n6 ce is perpendicular to the wrench?

  The bolts on a car wheel req oky51/ sbnsut yok w.2,8ts1ouire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is uy kn oy5,ko1.8/swttsb s2o1 the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertwh u+s f)2i9 :jpk vxo4lfa2z3ia $3.00 \; kgm^{2}$ 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, m ewibu+vi9w/r+3 q ef8ass 2m is at x = a, and, mass 3m is awbiq93+re/vwfu8e i+ t x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thougfmi3p;x1 5v yrht the center O. A rope wm;y r1pfvx35irapped 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 pr(vj(mte - 1u( p(zkkyivoted about a frictionless axis thought the center O. A rope wrapped around the outet1pj( ymk ((z-kvru(er 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 e/j9am/3e8vvy*x yf xrnd. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleratioyf8xv/9 r3yve/jxm a* n as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ringpw vl 29q,zs7wv9a 9ej 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 for 4.1 s, what linear speed does the wheel achieve, l7w v2,s9q w9jpae9vzassuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless ,tq 7z)qm8eqze7 yl3hn-xey ,disk pulley of mass 7.07 kg and radh ,q8)q e7,y 3-zylxtz7qen emius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped arousk:;n-fi1 2: 6zoxk r8jbgx qend a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the8e-os b 1jx :;nx6: fk2kgzirq mass?

  A rotating flywheel can be use-xugb5dmk 4n +.l 2ttp:4ihuhd to store 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 inertin;eww )iv1 ,odov4/sxa 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 res/ 9cquq4fr; :mk2gpent and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sph2 n;/eprfuk4c 9g qmq:ere when it reaches the bottom of the inclined plane?

  A solid sphere of mass :,att3 t+lqrki1 s2je 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coms jt13ekt2 li:,t ar+qing to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is release xp 01cyut(r99atklm1d from rest and allowed to roll down an inclined plane. Hop(9 09tty1k xamr1lucw fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping dowi v d+)jw.nu3vn a 35e incline that is 7.0 m lon)ud+j.vwin3 v g. 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 chano )cy-g 6au9s4-ay qgqges 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 mo6lzay1u 85wmv e-mka)ment 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 a.e 9x* uvvhgb*t 5.00 rad/s with arms extended has a moment of inerti ghvv.x*e9b*ua 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?