Angular displacement is kogx+dtawchn2: ) p+;usually express in units of

  Angular velocity is expressed 2vd . -hg hb4pcutdp-.iu,e+bin units of

  Angular acceleration is bb2z1 jmdy r2rj..x0fexpressed in units of

  A boy and a girl are riding on a merry-go-round which is turningooyfb- 2uez)15 jiu: eh f6t*b at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the*1tboife2:euhbz j65 ) - yuof greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning aikz* .jl ;5nixqs):ktt a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular spni l ikx*5jst;)z q:k.eed?

  A boy and a girl are riding on a merry-go-round which is turning /bbg3 ,v5 ij nyq3pb5 d dg9c1y)hjxp2at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear spd)/5b3iqypg2dy vn5g b hj,1b9 cpxj3eed?

  A boy and a girl are riding a merry-go-rb/4 :b:v 4a 2fvjib(ovnepap js(t1(n ound which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who hsf j4 bv/1 :(nj42panaibp(etv(: vbo as the greater centripetal acceleration?

  A boy and a girl are riding a merry-go:v .f(ol;,vfr grm e4j-round which is turning at a constant rate. The f: f .4rvler(;govj ,mboy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatiwt +ex:uzq0.zcjzc8- ng. Which of the following is an accurate statcxz q +e:utw.8-jc0zzement?

  Rolling without slipping depend0g oir/mrrz77 s on

  Two equal forces are applied to a door. The first force is applied at the midpozo/xh56.uat aint of the door; the second force is applied at t.x5a6htoaz u /he doorknob. Both forces 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 force is u ei*o5dnix+.spah yy89za6 :applied perpendicular to the*.z ox58+ phad sany 6ii:y9ue door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. :kl/zp8mkne i1os ad(s3m70o The first force is twice as large as the second force. akl :1do k ss07( meozn3mip8/ 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 u64,x/t .qoyly.72 vzz/4m ;norbyn6xu kuuo changes in rotatiomr / u6n y47l.xzqn2oy;tk ox6u u/z 4.buovy,n?

  Consider two uniform solid spheres where both have the same diameter, but onapm 8n.z+;gl4itv /+pi7m vphe has 7il ;4/ v8m++pp hvinmt gza.ptwice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the ;6zn ibz8 7 ctvy/n.fx+(h;kmh;ovrrradius of the other. The ratio of the larger sphere's moment of inertia to;t;vk nn7o6fz+mibc rx z8.rh/hv;y( that of the smaller sphere is

  Consider two uniform solid spheres where o tk/f;u0le: mf* od2pdne has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of ildkme:2/fu;*t p dof 0nertia is

  A uniform solid sphere has mass M ando:d*n,2 g1jx7o tte9moha hr0 radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia abot 90dx2nja grt1h:m* e7ooh,out a central axis?

  If a constant net torque o5f6u b*x;w*kxiky *pvwgtw;vi/. 9l is applied to an object, that object will

  The moment of inertia of a solid cylinder about its a bj1) c)s f:*rj;takdjxis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic e)d: r)s*ajkjj1 b t;cfnergy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one whe2;6j42z gqoa bg4l:mpd v0ok kel 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 th k60og4kdb l :amv4po;j gq22ze 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 sliphouk 60wos / 8bze4 u he)z9wx77arf0 fzg,xy2ping down an inclined plane starting from rest. T0k4sb fu7r9z08oe h2ouxh)6 f eaw/zg,yz7xwhe linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls rzpd6vr+wza (3 *i+1.lx dbukwithout slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inclin ra(6pbwvkz.1*3d+ izl+ rdux e depends on

  "The total angular momentum of a system of part / bukvg: g0 z2h*rypyor-new /oon968icles changes when a net external force acts on the system." This 0-/ rbhug/zvo w: y6renyo9 p*go2kn8statement is

  In what circumstances can the angular velocity of system of part k)rp2 ea*ekx5icles change without any change in the system's*ak xk5re2) ep angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which mayj( 3mshci n27w be present. What happens over time to the Earth's angular mome3hi wsjcn 2m7(ntum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth m8e+zfgb;hjci( twnj2w (5 e/woves close to the Sun, then which of the f2jiwncw ez8h;b j(fte(g5+/w ollowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling :zgq0wo xwopd9 ,e92e in his outstretched arms close to his body. What happeezw wqd 02,x9oo9p: gens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ;i)bohc b qe:pjp6pn3j.) y*y in his outstretched arms obj):pppe*njyyq). c6 b;3 hiclose to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outs)ts:svyiv m/n .0 rh8qlfe*- ntretched arms close to his body. What happens to his moment of inmrh:n/f .eqy-0* vs8 il snt)vertia about the axis of rotation?

State the law of conserva1y elh5s2im )ction of angular momentum.

  What arc length does the Earth travel in a t:z;18 ;wor 4ylpakdue hree month period in its nearly circulayo4azp;ldwke 1; :8ur r orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 (g nup)gq 6*rp7yc iomg-a;:am. What distance does the tip of the second hand sweep through in 3 minutes and 4 c*:;p) pya girm7anoqgg-u(65 seconds?

  How many rad/s is 25 revolutionsq)x ;o 2wz .jn,bgqib8 per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutiosuw mk2wqczz. 8m9+n8 ns in 4.0 s. What is the fk88zuwq mm czn.2+sw9 requency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulsesmr7) tc 4fkzy9 j(trrsm6)m 4w at a frequency of 0.40 kHz. The period of its rotation7 ytkt9mzjr64 rm( s rwf)m)c4 is

  A phonograph record rotates at 45 rpm. Througeaf iwehn 44y,c* 1dbjs(h, 0jik+vo2 h what angle does it turn in 0.20 vhk,( ,j*nos4jf4iy 1aceh 0e+di 2w bs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the oy1fi b60 zu*8l: dggiwuter rim move in 8g*y06dwb1g :ifuzli2.1 s?

  A bicycle wheel rotates uniformly throu8, :zong+r9t xadx(ytgh 2.0 revolutions in 4.0 s. What is the averng9:tx,(xd a8 roty+zage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions ,kixs *g)q p6nin 4.0 s. What is the linear speed of a point 0.10 m from the center ofs,nk) pqxg i*6 the wheel?

  A cable car at a ski reyl i7s1 nzto1:sort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m1y s7i t:nolz1. 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 n c4u:gjz+c jnz1;3olconstant angular speed of 2.0 rad/s. What is the linear speed of a point on the wc1lzou4nn :;3j gzj+ cheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16ibsj)xc)-mn+ b67zlj e(rf4p m in length. If the motor rotates at the rate of 20 rev/s, what is the app4e ji+ x)lnz- c7b jf6rb)ms(proximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rolx+ewi k67zwxjx1- y5tating with a constant angular speed of 2.0 rad/s. What is the centripetayx5x -liw7wj1k z+e x6l acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a poj. +fiaeql0l p(3qf l ibt(+e..qh)xlint on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is f(ft ej i(03+.+apbli) xqhl..e llqqmoving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statiqhp e(xigi,+xxh5;ggj, rea x(ti m/ ;v,3y4yon (r = 1000 m) rotate to produce an artificialjiym rtixy 4(; ggxeq(xph/i,+a;x5,h vg3e, gravity of $9.80 \; m/s^2$?

  A car is negotiating a we;lv c4w l rk4h6mw8xr9/t;iflat circular curve of radius 50 m with a speed of 20 m/s. The maxix4 vwi9etcw4;hmw;rrl /68 k lmum centripetal force (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 circuk7x35v c5wpb.av vdi (lar curve of radius 50 m with a speed of 20 m/s. The maximup3 55vx 7civ.bwvakd(m 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 the end of a 0.ix/em1ira pzr 43vlx ,q334oj750-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 bxa3jrzei ix,1vomq 3pl/r43 4reak?

  A bowling ball of mass 7.5 k+ h0d2 9ztygsjg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m0+ h2jg y9ztds/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 angular acceleratiigcuey2;phm101cb z4on 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 accelero ytxqks2rbo 01 w6. 1pjm4u9kation 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 rota c k9qy(3a +ui 4b+hmqbkm)5mgte after starting from rest and accelerating at a consthqbc(u 9b 5yg43)+mqmkim +k aant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has (hd+:hwx ng* ian angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerateupqovvwl1n z )h 2l1:gtv* /7as with a constant angular acceleration of 1ah1 gqv2t:pozvlvn/lw 7*u)$-5.0 \; rad/s^2$. 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 wpvj xd0kkf)):riim78;e tx 7p hile turning through 2.0 revolutions. What is the average anfpxv7;0)ketxj d :8)mii 7rkpgular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest 7g1s3a 6ior2zx)(w gkce+ uieover a 7o )ggcz ix+a2sr3u1w6eik(e distance 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 uniformly from 8.4kbwmo 07n/*ylp9 b9kb 0 m/s to rest over a distance of 115 m. What is the angular accelerationw o 0bkm9p97by*knl /b?

  A wheel of diameter of 68.0 cm slows down uniformly from 5cj-i7y8mnrj 8.40 m/s to rest over a di-r jn7ycij5m 8stance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatjl,g 64l2i9 mvu8dsk des at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a conliuv6l94g8j 2mdd ,ks stant 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 o x j,uv(3ax5qsf 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?q3xv us(5 jxa,

  The bolts on a car wheel require tightening to a torque ogula x 52;0.:iy- ehzst mkpv4f 90 Nm. If a 30 cm long wrench is used, what is the magnitud4v-5 yu2i ; :hk.m0 lstzpxeage of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ,bgf,9k eu74oceg x.kinertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as feyb8vah s,f7b)no .k7pra/k4 ollows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a rfa4. bk7ko/ n s,8bva)pyeh7. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionlimuzm mr-sh 8b u:4/(hx hw1o4ess axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (Seem simo xhz:44b8hu1uw hmr/(- Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of sab +)q 6y+fo x acwpxi32; 3su2k-vqnmass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around ankay xoxcv + +3fsnqib2swp6 u2) -;q3aother section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. 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 hyl-9 c5))b tsa5 onqyainged at one end. The rod is initially held in the horizontal position, and then releaseos9y bnca )l)55-tqyad 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 oei5tz d h*uehjlw20a0*qm7)uf 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 smljuqeze )hwhu75tiad*2*00 peed does the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fr)l70l;,y2pq mc vkvrv ictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is,k vclr 7lq;v mv2y)p0 the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pull 3i5,ikph9k )gr;kia jey of mass 7.07 kg ani,5) kij;kaiprkg 3 9hd radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If g p-1lyc)ui6 +o.zwmqit 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 ijey wb( o0hv+ixup 0qjw;us9s 1*)qx*nertia 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 radiun.up;l13o 1lw8mlhsf wbg9c * s 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclinel*h .3pno l9sl1wwmgbc ;1 8fud plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0s3s3 j1*hbuvk +(inx e kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclinx *n 3sshbk1+i (v3eujed plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest a5pkc l( txf .t8m)0fu.jgfs-qnd allowed to roll down an inclined plane. How fast if.px)0lfq t(tcg8fkm 5 sj.u-s it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls :o lkg.+ 3pca:)cef ptwithout slipping down a 35e incline gac.ec:p3)o kp ft:l+that 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 chl)m(u4pjas0 dw a*2ohanges 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 mome)/ sefvgn72gddta6 e* nt 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 rotatinxspog61n9z4, b gj 2tyq9- ka khu((lrg at 5.00 rad/s with arms extended has a moment of inertia oaj99 yh(ks1kp r6tg4 -2o, ql(xbnz ugf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?