Angular displacement is usuabunt7/:k c6izlly express in units of

  Angular velocity is ex-rwd-y8s4o,b d6x r3cmip8 4 ;yjdzecpressed in units of

  Angular acceleration is exprezl6 an rz6ya6*ssed in units of

  A boy and a girl are riding on a merry-.u ,,voho(cd wgo-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to ch,od(,u ovw .the center. Who has the greater angular displacement?

  A boy and a girl are ridin9s(rpnf;bx(m5 di us-a+)i txg on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer tot9 (b (aisrsi xu-5+fdn;)p mx the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at aggu00 t5tvu b+4zri n: constant rate. The boy is nearn4uv0 ri0tg :tuzg+5b 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 merry-go-round which is t(m 7t krgwx2z8urning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal accelerati2g8mrt z(7xk won?

  A boy and a girl are riding a merry-go-round which is turning at a constant.8i6qbivqcbpwj4.d 9 9/ tp kj rate. The boy i4.j9 q 68c/bdivkqp9 wjtb .pis near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate szpy)g(mf y*xke9n 8dyv:04 c a fj(nk4tatem *yxfjc za :0gpk4(dny 498y (nekv)fment?

  Rolling without slipping depends oi2oohe xm /:xk6vu+y4n

  Two equal forces are applied to a door. The first force is a zw4,dp,5fwx,bb 5u8b/tbpz ppplied at the midpoint of the door; the secdwbbfb x5z 4t8,/wu pp,5zb p,ond 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 atxadyqe36b .p2 the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e 2y6b.deqa3 xpto the plane of the door. Which force exerts the greater torque?

  Two forces are applied to pl-pab ,ix14q a doorknob, perpendicular to the door. The first force is twice as large as -p1axbq4ip , lthe 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 resis+3lcvnph- 9er tance to changes in rotationrpvcn9 +h3 el-?

  Consider two uniform solid spheres where e0ihim u1ig6: both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to thg0e iiuim:h61 at of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but onl ; p8t8xnay95skiuld jwfaj zq12):1e has twice the radius of the other. The ratio of the ltn :8dkyxj ;iwzllp512uq)j9aafs1 8arger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass antv7+z9agxg/oar13eju 6)hj c d twice the diameter of the other. The zec7 19agr3x+a/ j)v6u ogthj ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M * d .b(aj+jhyqf5i/ t6o d-bucand radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of ine+u(*.b6 /y5fdtdqhob - jj ciartia about a central axis?

  If a constant net torque is applied to an object, that objectrbio 42iyn /it0 i3fy3 will

  The moment of inertia of a solid cyd zr.em: - oo;5n,cdwllinder about its axis is 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 motorcycle of mass 150 kg, one wheel of which has a magg 9pxxvovz yqrn6 ,i.vl 0288ss of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels 2 90lx8g,86 nvvyzrv gpqoi.xto the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of massj5oozb z(y,: b M and radius R rolls without slipping down an inclined plane starting from rest. The linejo zy 5(,obbz:ar velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rollsekar1 .)ub z/i without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline dkb u1)./ iezraepends on

  "The total angular momentum of a system of particles changes when okoujg: c.wj4z xc)6 ;a net external force acts on the system. o4 gcc.6kxz:;)w jujo" This statement is

  In what circumstances can the angular velocity of system of ps6h:m0vtrm xhrw+ -kazw4;q7 articles change without any change in the system's wq ar46xv+: h h; 70kzmwr-stmangular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whic mucs ok4z*b -+wd;by25; zj2asdqc e-h may be present. What happens over sub2dqzzy jm2 + 45scao; w;*ekcb- -dtime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves cloee8c/ cadw8/ yq e7g,mse to the Sun, then which of the following best describes the orbiting speed of ec e q,8cdwmgy8/e/ a7the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc(l)ixmtncx+i 0 x6.p96 2+sdwopukin hed arms closmi0x kw 9ntxipdp+. (6s2li)xnuoc+6e to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a piroueerb1k.0+fvj j4oi, rwtte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his ro+ekb.r0f4j1o r jv,w itational kinetic energy about the axis of rotation?

  An ice skater performs a piwkg 7a7hz fp-/rouette (a fast spin) by pulling in his outstretched arms closg/k fa77pwz -he to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentucqy(zf*ti5p * m.

  What arc length does the Earth traveye j3ka(ggk z:x:+qh,l in a three month period in its nearly circular orbit about the Sun with a radius of y3agj,hzkk x qe:+:( g$1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does thewng.5 frv88t3 l9vn,fd hkc-a tip of the second hand swk dh3v rc59l nwt.gf88-f,naveep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minutefw 3(e9*ynqrd equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revol ;xo-pb6x--4 jneevpiutions in 4.0 s. What is the fr- bx-pjex-e 4 noi;vp6equency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencns*w4,d hjjy 6)bb5nh y of 0.40 kHz. The period of its r6 yhbb, 4jhs5nwjn d*)otation is

  A phonograph record rotates at 45 rpm. Through what qmo+wa,n ,xsdzc o 74qa9q8oq*8ftvh/:lcn5 angle does it turn in 0.20 zoo/lqn *4c9tqmqs 8 w7oa5 cdn+,vx h,af:8qs?

  A wheel of diameter 26 cm tur(. qrykg )robxkg 3:cy8 ef+w5ns at 1500 rpm. How far will a point on the outer rim ge)k3+xbg5fyrwqy k (r. o c8:move in 2.1 s?

  A bicycle wheel rotates uniformly throughx,qyn8d.znn-k;ssx /*k ijw5 2.0 revolutions in 4.0 s. What is the average angular speed oj nxi*sx/5k-n8 dn;w .z,qsykf the wheel?

  A bicycle wheel rotates uniformly through 2.r gtpwup5t) y9:+f/ej0 revolutions in 4.0 s. What is the line r)ujp e:+fg9ty5/wptar speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8:bdd3qzs tbz6fnt.:w7 e 78 od km. The cable which moves the car is d d.eotwd73zbb: 6:fz8 dqtns7riven 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 rotating with a 9(/+nwralo fh constant angular speed of 2.0 rad/s. What is the linefwl9arn/+oh (ar speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is w.pe2v-m; cx c0.16 m in length. If the motor rotate.wpv; 2 cxce-ms 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 6hq rnl kqe88ia r7vht.86, jum is rotating with a constant angular speed of 2.0 rad/s. What is the ceij8tla8ekq6v8q r. h hnu,67rntripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimf0kznaua35 :p eter of a bicycle wheel of diametez :5fp3u naka0r 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) mus mi3/aum5v ecq()3t k z2tlm)wt a circular, rotating space station (r = 1000 m) rotate to produce an artif3lui(z w 2vmetkm)5qc a/) tm3icial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/s2p qmnxap )a1u jm8osz*, :wj0. The maximum centripetal force (provided by sn:sp8p 0 m)* zqomx12aj,aujwtatic 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 of ur, 6clp6 mhf920 m/s. l6h 6pu,rc9 fmThe maximum centripetal 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 t*.sycko(q+ sa(*yanq he end of a 0.750-m string, is whirled around in a smooth level table. If the maxim(+. (qys csq ynaao*k*um 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 cm rolls without sle)x2k,3dc8fx 7)alxi a m,ms icq1 7hmipping 10 m down a lanm 21cd7m8le mahx) xk7c3f,,q)aisixe 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 5r59 f 5ge9ux v -,dd9tsjkazyangular 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 angu n;/nxwc :dxj/p:lud /a7qa c+lar 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 rotaju1bb+by l/3;:ps::tzd levwte after starting from rest a: d eb:ub :tl 1;+/psvjblwz3ynd 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 accelerats1ga+o0qk( y0g psx oz4.xq2cion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad.l*y9u9uc anbhx3fw2 /s decelerates with a constant angular acceleration u2*wlbn xcuf9ya 9.3h of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest andeun 5ibuw,:3i reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is thiunb u,5 e:3iwe average angular acceleration of the wheel?

  A wheel of diameter o(s/; lxzq0qa,lf-q q4frd m0wf 68.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the whea d;0l4q( -0mqqxqff/lzr ,wsel rotates in coming to rest?

  A wheel of diameter oft3o4y 2)lne r *pxktd; 68.0 cm slows down uniformly from 8.40 m/s to rest over alt43d*k po nx2tr) e;y distance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68./9smcg p m.ui-0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 9iumm-s/ gpc.m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speeypm+ipg1vb h/0 3jbc 1d of 3600 rev/min. When switched off, it rotates 50.0 times at a constant anjyb/p1gi p13cm+h v0bgular 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 requo0e j 3e kchtmoyju987a;+6 2vdfu(htire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requihumekt0odv2+ o7jjf6ey ut 3h;8ca 9(red when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. Intuan4: 8a l39iuzb,ef a 30 cm long wrench b3 9e,t aanz4:i u8lunis used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment *nqraq ok/:0 fof inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mod xg6*sh-bf gv*eled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertiagv f6h -bsg*x* about the origin?

  A solid cylinder of mass 10 kg is pivod/ae. k5t)+agdm-pln.o gh q- ted about a frictionless axis thought the center O. A rope wrappea /e5a- n tg+mkqo).gl.-dhp dd 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 in2k7 g6naob* os pivoted about a frictionless axis thought the center O. A rope wrao * 62ong7nkabpped 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 inws /yqlnn93y nv0 a*;yitially 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? (The moment of inertia of a rod about o0sqy wny9 /avyl;*3n nne end is ML2/3.)

  Consider a bicycle wheel to be a ringxf9np2f9:aact1 wi; z 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 x c9n fa9;apiftwz1:2.1 s, what linear speed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a ropey6 ue7/ld. ysv wrapped around a frictionless disk pulley of mass 7.076v uydye /l7.s kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wr d/..yeh (qkjfapped around a frictionless disk pulley of mass 7 .(je h/kdqfy..07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel cac;+yuh zea mfld4p*7 .n be used 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 ivz 3ll7ih o g92tnf01lnertia 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 a8 9 v5(yc.*llk qcqd mg+vsr(pnd rolls without slipping down a 1.0-m high inclined plane. What is the sq9 vccq y+l. 5s(lkdmvg (8rp*peed 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 roll3ar9jp,r eft8wl o,9os with a speed of 10 m/s. How high8,erof9 rlp3, oatjw 9 up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 1nnwv: ,9vedii tqc- d()fsq(0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a ver-wt1icqf,e)v n:s( dv( 9 dinqtical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipwllc5 58)neaos8w +ydping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is wln cywe8+ 5sd8 ol5)agiven 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 changes byw3xg )oect;(f j/5z 6*p/j2k m ibn 1a)cueuyp $20 \; kgm^{2}/s$ 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 momeno;ua8vze7 q /6/r l5za1jbc rwt 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 9+ /nd/cd2loz;hdtjp at 5.00 rad/s with arms extended has a moment of inerti jc9;+2l/toz dnd/phd a 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?