Angular displacement is usually exp hmk8ck 5 ;z1xyxm3c w y2l64d,4ojaabress in units of

  Angular velocity is expressed in units of9 d0t/x4lmhkh*1(c ejrj7us x

  Angular acceleration is expressed in units oz5 n mzx8cfd,z)y4;nw4 ng w1b;u mp8bf

  A boy and a girl are rpcp3 1e vp-xj(iding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Whopjxv1c3- pep( has the greater angular displacement?

  A boy and a girl are riding on a merry-go-rounyek5 6w.km3 hmb)di7od which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has themb) 6 3ek.oywid7k hm5 greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a o06mc z 8thb9uhw)g* zconstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater*)hbmc g w0zout96hz8 linear speed?

  A boy and a girl are riding a merry-go-round which)lx0ta 1z2xt h is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acx12 hl)t0xz atceleration?

  A boy and a girl are riding a me; e:qqeu 4kum3rry-go-round which is turning at a constant rate. The boy is near the outer e34 u:eqqu;km edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of thv+y ljz s+c;x,e following is an accurate statejx+ +;z ,sylvcment?

  Rolling without slipping dependsb +1*egefl9l n:j2p rl lnp09b on

  Two equal forces are applied to a door. The first force is applied at w c+sik5k6j n4the midpoint of the door; the sec 5+cji6skwn k4ond force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are app4c r98h-f(zc jlx:ysllied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of hc:x( 9rjzl4-sycl f8the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicularc ovfd. t/x+-k:vq .er *q2vfere+ ys6 to the door. The first force is6-yqde2f:+ k/ o c vfe.*vr xtvqser.+ twice as large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantityigf 8r*2ti;xr used to measure an object's resistance to changes in rotation?r it gf*2;8rix

  Consider two uniform solid spheres where both have the same diameter, but onep8m+kl sg+a /j has twice the mass of the other. The ratio of the larger molkas p/j8+mg+ment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres havr1f93;y c0yv.j a7b-dp qk qfie the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment -;qqr.7y1f9d yi0 bvkafc3jpof inertia to that of the smaller sphere is

  Consider two uniform solid spheres fj //s+8 fsmjuwhere one has twice the mass and twice the diameter of the other. The ratio of the larger moment o uj+mj8s /f/sff inertia to that of the smaller moment of inertia is

  A uniform solid sphere haspnl zh cyetcpws-fv/6:)60 6k mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment ofw pts f)6/vec-6ny60pckzlh: inertia about a central axis?

  If a constant net torque5 6vz;t;(b-brrwr 7are wuip, is applied to an object, that object will

  The moment of inertia of a solid cx*xt* lx,dk- dm5rq6 hylinder 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 mass of 10h 0( q2,dk/yedjwd *ks kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheel02k/ hwysd* (,dqk djes to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass Mkm-s/l7 hz w0y and radius R rolls without slipping down an inclined plane starting from rest. T7lz-ksw/y 0h mhe linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of 2fg 29gznand 8mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the dnz82ng92fg asphere at the bottom of the incline depends on

  "The total angular momentum of a. jya3 0j/u08as gawqc system of particles changes when a net external force acts on the systemj a00 /yj g38u.acaqws." This statement is

  In what circumstances can the angular yy/+. zwgzgkz03 dpe;velocity of system of particles change withoukgpzg;3/wz y z dy+0e.t any change in the system's angular momentum?

  The Earth orbits the Sub: m. y:x dx-mbj7q8won in an elliptical orbit. Ignore any friction which may bmdjb7.m: yq-8w xx b:oe present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. i:2)oq-x:p. ouv :xst4cosdtAs the Earth moves close to the Sun, then which of the following:u4.t - q)tsvxdo2 ox poc:i:s best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fafv 8u.l t2cbygpv-8j: u q3afr7 )z-hbst spin) by pulling in his outstretched arms close to his body. What happens to his au aqj gf-ht p)r uvb.7838y 2vlcbfz:-ngular momentum about the axis of rotation?

  An ice skater performs a pirouette (a bm,slyf46m5ju5/ wk z 5wr: x3xzr wx2fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic ene xrfwl5y23:b/ukzrx j 5wsmmw,x4z 56rgy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched s ziu899+/aaisbdl 5(lza(xr arms close to his ba a5(xi (aizdus+ 8bl9/z9ls rody. What happens to his moment of inertia about the axis of rotation?

State the law of conservatirlnpj; ;bc -.8.xbf;(q bdvmuv*sg, ion of angular momentum.

  What arc length does the Earth travel in a three month period in its w*e(j 9u(u1z,3obm,x j xgfyhnearly circular orbit about* o ,hj3m fe1x(g9,xujbu z(wy 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 thj4k g,vqj- aq h/oe5j,4ruod svk0,z 2e tip of the second hand swek0,5o/ea-vjqg2j vs 4oqud4k z ,hj,rep through in 3 minutes and 45 seconds?

  How many rad/s is 25 rev+4d zzlxci wj t,2v(:golutions per minute equivalent to?

  A bicycle wheel rotates uniformlydb/t5 i oejn09b)qc4p through 2.0 revolutions in 4.0 s. What is the frequency of the dtbi9o bc5/0q4)nejpwheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency o k5yl(aod3+ wbf 0.40 kHz. The period of its roto a+5 3kdwbyl(ation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.22 dr+y)p 9ovtz0 s?pozdt9r y+v )2

  A wheel of diameter 26 cm turns at 1500 rpm. How f+g 6+1tstr5upufzg/ u(hda5 rar will a point on the outer rim move t 5g zru f(++sh5g/r1u6utdap in 2.1 s?

  A bicycle wheel rotates ui hxen y..guf; j24,oeniformly through 2.0 revolutions in 4.0 s. What is the average angular j n.xe o,2.;fhuyg ie4speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is yp* gb.g vj(:*w(wfo jt3q)jp the linear speed of a w tvw *j.y pjbg )qg(*(j3:fpopoint 0.10 m from the center of the wheel?

  A cable car at a ski resort carries sk 7pt m/uj5 yxp-)stm p-:ghg7biers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Aghpxp-tgbj t m5m-u/7 :p)y7sssuming 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 mb:v-vr+ee9(ii p *ohh is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a p*+9:hpoh-birvee v(i oint on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.1z d..v;q*i sva6 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the esa.vzi. v*;dqnd of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular spe2im 87iyvz g+ uzav-jbc ou9l6+((u teed of 2.0 rad/s. What is the centr7a-buljgvit26o8u9y(i mv + zc+ (uz eipetal acceleration of a point on the wheel's rim?

  What is the centripetal acc0h;vc9 w hqihbwz8;0neleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/ ;c0089zinbwq ;hvhwhs?

  How many revolutions per minute (rpm) must a circular, h*otxfx j .)0rq :cjvk fws82-rotating space station (r = 1000 m) rotate to produce an artif0 skjqo*8rt)- :xhfcf j2xvw. icial gravity of $9.80 \; m/s^2$?

  A car is negotiating a fl(69/rp r.b fm hx8fyfeat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal pf9bf6r./yr8h f( exmforce (provided 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 cumn8 j,4 (bxfqvdsm/fb+33u drrve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static frictionn ,s8 mmf 3 v(ud4jbbxrf3+d/q) 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 strin3dhsj,k:eyz 1 17fpej g, is whirled around in a smooth level table. If the maximum tension that the string h311f,7ed z :epksjyj 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.y ta ihcf4p h.e.*y-v30 cm rolls without slipping 10 m down a lane at 4.3h cft4 .y hiapy3ve.*- 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 angulj0 ; zcz/slahfx7;zw15 zo1s var 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 acceleral9k gj no+jnkxd:ars;/, 7 tt:tion 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 autom s8*yviev.md-u-)sefs+rzhas j.a ) (obile tire rotate after starting from rest and a).yhr .-szds-ve m ( 8 fivs+seuaj)*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 ( gscp7)( jflcangular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/sks7j8txa v 2.7 uqoga3 decelerates with a constant angular accelerat ux .avjqa378k2sgto7ion 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.p 6od (a9m5qtm0 rad/s while turning through 2.0 revolutions. What is6amp9t (d 5mqo the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 muw7:c2vw ) dkcm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutiodvk2 :uc) wm7wns the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from :)v ah w4p ;blk9hph,e8.40 m/s to rest over a distance of 115 m. What is the angular acb94v;kahhhp,)l w p:eceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 f y9nt0 w2z3d2g*qfjom/s to rest over a distance of 115 m. How long does it take for the wheel fo3d2 *q 9zwntgfyj0 2to come to the stop?

  A centrifuge in a medical lab v:a+ r-q,16axbtu *kp,tvxmx9dtsw 8oratory rotates at a rotational speed of 3600 rev/min. W-xv69 :t ,dqsap8xtr*u m, kvbtxaw+1hen 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 torq/2 r*db(hzp,ancdd 4t j5g a6jav:m 5que of 90 Nm. If a 30 cm longjat4pdhbdn*m g,(ja :z d6c5q avr52/ wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 3hb7oxygquv9,)g (t i8 0 cm long wrenuqh o)g7(x8g, 9 itbvych is used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia *l,gff uq,p.t 3:cerb$3.00 \; kgm^{2}$ 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 r ugr.vr dcdx,8xp7vq9a,6 s+v* gim0m is at the origin, mass 2m is at 9.,ru8vxx sm7 g0 + r ,rgd6qcipavvd*x = a, and, mass 3m 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 i3n) .ij s1whcg47,j3a rtpdw axis thought the centerjr)i4ahst pn 73g iw3wdc,1. j O. A 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a y sjjz,r,r j38frictionless axis thought the center O. A rope wrappedjyj ,3 jr,r8zs 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 oxoc- h 2dns6s)ne end. The rod is initially held in the horizontal position, and then releas)c2h6s os -ndxed 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 wheq90qu ;lc lp n+ 2z8cs fq7u2.nb,ofssel 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 appli02usq;zc2 b.9,nlnl uqqs7fo8 fp cs+ ed tangentially to a sprocket of radius 4.0 cm for 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 frictionless disk p jq) 5nk0et7vlulley of mass 7.07 kg and radius 66.0 cm. t)5 vjq enl70k What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley 9dwvtr 0u3 5soof mass 7.07 kdu s95 vr3w0otg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. n -,, b (,q az 8kkgnb5vanptx+4zv9ypIf 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 ik b cklm/o lo)..,tih-(rxb:tnertia 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 i;- nrmk :8bmqand radius 0.010 m starts from rest and rolls witho rq:m;mn 8-kibut slipping 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 rolls with 35c+9 njr0nt 6crs/i2bkjbnia speed of 10 m/s. How high up an inclined plane can it climb before n93incjbkrb5/j 026tn cisr +coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and all+j1*w86xp3s0 uo ib;uqhumtrowed to roll down an inclined0 u 38wut6 us;rqjio1m+bxhp * plane. How 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 down awik;ox 1xl x2l5*7b v :cxqef: 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is giv: *;qbf wlxivlec2xxk x5o7 :1en 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 ve(ta3 c6lhlox1 wr50 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 of iih*nn4) r*ops nertia 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 has a momenyt e-h; bep: +gt,tctpm0yk,xh,05v st of inertia ofkyht,: e p,mb0+0tvtc-; ,te y5p hgxs
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?