Angular displacement is usua jrerfkcwq6h ks66:erqrgv6u (9h-.y8: t9pzlly express in units of

  Angular velocity is expressed in un3:f+vpsa sv2.rg8 tioits of

  Angular acceleration is expressed ink) s0.wv:jnmm6ao7o (o onqg0 units of

  A boy and a girl are riding on a merry-go-round which is xn2ihlfw.y *:turning at a constant rate. The boy is near the outer edge, and the i *y.xnhw:fl2 girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on. nnhm 8gie 5e6c.dw(o a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closeom.n 8edn h(6cwge.5 ir to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round whichij: 1r4r(p38 msrs skg is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the ce :3jk(r8sr 4i1pssrmgnter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a co:fn,it;ah; aovefn2n3 b1 fr7bp)+jj nstant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the great; nj h+,ve:io1f2aj7 natbp )bn;3rff er centripetal acceleration?

  A boy and a girl are riding a merry-go-l k ,,tqjs)el)round which is turning at a constant rate. The boy is near thtk),el ,ls)qj e outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. *d12f : oke;td2 ;koxia wo6iu Which of the following is an accurate statement?df:1oko2 ui xeat; k wio2*;6d

  Rolling without slipping dep(lw:49+tsjn1sp:s j n s .ewsqends on

  Two equal forces are applied to a door. The first force is applied at the midp u3f8qn v, 37uc6nvdoxoint of the dv ,do363vn nfu8qxuc 7oor; the second 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 at the doikjax89x9.z.78b g e p/xxevk orknob. The first force is applied perpendicular to the door; tpxvie8kabk.ezx.j 8 x9/ x 7g9he 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. The first forc-y ort;ow1q 1be is twice as large as the second force. The ratio oybwto 1-;1rq of the torque of the first to the torque of the second is

  What is the quantity used to meajrry gujd6q*snug1 :xe2t9rz 9z86o ( sure an object's resistance to changes in rotatis(2 jx:o9 zz 1r 68u69dgrnejqgu tyr*on?

  Consider two uniform solid spheres where both have the same diamete. r2gmg;: m2aackt/vy r, but one has twice the mass of the other. The ratio of the larger moment of inertia to that og.t mr :yk/2aavgc m2;f the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius of60 gwevvu7qtb z1vb )2 the other. The ratio of the larger sphere's moment of inertia to that of the 67ezg u1vvb b0t vqw)2smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice w -:zls4ox poa bo21*mthe diameter of the othpmz2:* oal x4bwo s1o-er. The ratio 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.j7lu ii 57zd:t If these are increased to 2M and 3R, what happens to the sphere's moment of inertia i7ltui: 5 j7dzabout a central axis?

  If a constant net torque is appn tjws,a8 c))slied to an object, that object will

  The moment of inertia of a solid cylinder abogae3ja ao;w5 1ut its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational;g jw5e1a3oa a kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whichxi2e/qks wpugxy2qqx qo59( 8 0d23 pm 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 p5k 0q x8mqxpdg3uwqo ys/iq2 x2(29etranslational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere // d4(kd -erez, uxadflf0jb/t2ap0 jof mass M and radius R rolls without slipping down an inclined plane std/0(t /x0arbj2dku, zfjal 4/ee-d fparting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rold t)fzvz)k0; gls without slipping down an inclined plane starting from rest. The angular velocity of the ))dkg0 z;tvz fsphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles cha8e7q+r bhp geo8 wed4 7xm/-panges when a net external force acts on the system." This statemen+h b/repepqe8ow7a7 -dmg48xt is

  In what circumstancexfr: )z0so 78x/:y cbqde,tass can the angular velocity of system of particles change without any change in the system's angular :s80e/bxtoc:dqzx) y f ,s7ra momentum?

  The Earth orbits the Sun in an elliptical orbit. Ine x y2vnutayu+++)v+gnore any friction which may be present. What happens over time to the Earthuxay+t+uvn +e)yvn2 +'s angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eartt8y.6d sl +o3ik vac+ch moves close c 6.+8oyalc3d kvi+ stto the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouett ewi8h ma p 0g)bn.pd ,n/0j.k1eov5vce (a fast spin) by pulling in his outstretched arms close tvp.0w . 8d /phgineom1nj5kveb, 0ac )o his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouett-;dg:f hir 7kte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about ;:hkg tdr7 -fithe axis of rotation?

  An ice skater performs a pirouettev5/64diw qoxv+ i edfld/+;lv (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment vi d+ f/6dllv4xw;edvqi/+ o5of inertia about the axis of rotation?

State the law of conservati:p r7;p5 iki,c zndekehi)q )2on of angular momentum.

  What arc length does the Earth travel in a three month period in its nearly c :k o 2tvw5mv4n9ed0muircular orbit about the Sun wit wm: m9kvu42do0t5 venh a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance dcq, gn :dcd-w:8snxu7oes the tip of the seccqxnw8 dgs,dn -u ::7cond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivm 8 ppt.p/v2vjf k:( sgc8nh/wua 8g)calent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is th-bq4u9 9t7 0tcm0iv ke(o0w uzr;ked pe frequency of the wheel's kcv 9 4 uzu owtq(700-kpde timeb0;9rrotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 8:lvvu(br.lvl7qi y;ae a2 -d0.40 kHz. The period of its rv 8l7u irb ld ev:-(2;ylqa.avotation is

  A phonograph record rotates at 45 rpm. Through what angle donk:0gf x - u)ostg6/jyy -mz,ues it turn in 0.20 j st-/0-f )nugmxzgu 6k :yoy,s?

  A wheel of diameter 26 cm turns at 1500 rpm. How farrm8(i; jan0q0 meiv2t will a point on the outer rim move i0(je ntvm;mq 28ia0ir n 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revf 6quf/wcz6 r0olutions in 4.0 s. What is the average angular speedf/qwu6 0z 6frc of the wheel?

  A bicycle wheel rotates uniformly through 2.0z-l*xbnbbt: 7 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from th *b:btz7-x nlbe center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable m97z-z8jqye3crulic ()1a no ( 9gqciwhich 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 ca (37i zra1c oml(e-uq 8cz)jngqc9iy9r to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.5 o isl7: f fp239-a8jzyqdnqd0 rad/s. What is the linear speed 9zdqlfo i3p n8y27 :qd 5as-jfof a point on the wheel's rim?

  The cutting cord on a gas-powered weed cut4fddvr, f4g;h62k k y 7zmwdg9ter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear ;49k4zfgkvgf,dwrhd 7 m2y 6dspeed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of ve z3i 7ypv6cc6v/4n:pcodmu1 ,l8qu 2.0 rad/s. What is the centripetal accev,pn/:y6o qpdv1vc84e uzcmci6u 73lleration of a point on the wheel's rim?

  What is the centripethliyb 2+a+ -fxal acceleration of a point on the perimeter of a bicycle wheel a +y x2l-ifb+hof diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circq(vn03 zlv2jx2h eyy1 ular, rotating space station (r = 1000 m) rotate to produce an artificial gravity olz2 e nv1(j3yvy2q0hx f $9.80 \; m/s^2$?

  A car is negotiating a flat ci6d f,v17ugahe 2+xa ezrcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static fricea +6ufg7 2v,hxd1 azetion) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curvd z bhkh(,t20 4su+xmwe of radius 50 m with a speed of 20 m/s. The(wtkzuh,m ds +4bxh20 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, attache2km qt9hz/lahv;(xjns+ ;s3 pd to the end of a 0.750-m string, is whirled around in a smooth lev;xh2 /+mkjzqan3; tvsls h(p9 el 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 break?

  A bowling ball of mass 7.5 kg and rafjn5mjb ra7vms41:*e dius 9.0 cm rolls without slipping 10 m down a lane at 4en rvfb*maj5:j4 1 s7m.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 a,6gmy+ k wu/x380sllwfbna8j:mqw w.ngular 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 wit+xpqyibq 4;6obo5m2uh a constant 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 after s(;/qx *zz xzdkxo)ry)tarting from rest and ac*z() xzd orx;/)yqx kzcelerating 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 ang5o 9zdm0)gvh1cgs+ v wbg:2m kular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deckf4:uv3ky0urx/2c96v kg b wj elerates with a constant angular acceleraxuv9kg 4jkw/f6y2ub:k0c r3 v tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest afrw;ya 3sl 7*ind reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is i ylasfw73r;* the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mufi 56 ox hbdty9jl.76/s to rest over a distance of 115 m. What isbdhxy5f6 .u76jti9o l the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over bc+*yc s n(8nq0w,ncha dis(+n*cw ccqy b0n8n s,htance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uni2l 0k9n. oycz4,jlh ubformly from 8.40 m/s to rest over a distl lujz2kh y0n9.c4ob ,ance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 360k34xzdd8mbt 7hit* s 20 rev/min. When switched off, it rotates 50.0 times at a coktt3idm2 h84zs dxb7* nstant 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 whee)8njrv2/s bjul require tightening to a torque of 90 Nm. If a 30 cm long wrenvr82n/ju s)j bch 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 30 6(s yba/3ewjjha0j v-cm long wrench is used, what is the magnitude of the force r h/ je3ybva -jj0as(6wequired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inn/ -/r2ibw 1zsiq 7vzbertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule xiloom f5vuk9yb v+6u/xk9:. is modeled as follows: mass m is at the origin, mass 2m is at x = vo+l xf/u.iymx vb95ou96 k:ka, 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 frictionles)lq(0 sv(fnf6u e6lyes 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?une 60v)y(s lffql e6(

  A solid cylinder of mass 10 kg is pivoted aaatzwp) 5u w1zd;tghdjzz-x; +x4.(i bout 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 another 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) w (t1 ah- u4+wdadi.z;xjzz5ptgz;x from rest?

  A 4.00-m long rod is hinged at one end. The ro k 4yfy;iax. 5-h :7df0nfkylgd is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is release yf;fil0k h.xyf:5 n4-d7gk yad? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be *p3mdpr09a fbo9 zi7c 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 applied tangentially to a sproc 0br7*m3 da9izp9 ocpfket 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 pulley o:vpb0vf(n)/f dirw ,qf mass 7.07 kg and radius 66.0 /nwqr fp),(i:0f b vdvcm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrar q4bcz qb4n;6pped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the rqqbz46 b;c4n mass?

  A rotating flywheel can be us/3*+vki r8qfo)p c yy*6dkcppr my 3w7ed 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 of33/8gzdq pkx*ig lrn+z9 5ayq inertia 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 rafmj ;8 8pi 7nit:ejn,xdius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it refnne:i8x8jip7 jm t;, aches the bottom of the inclined plane?

  A solid sphere of mass 1.0 aglt95x ) m*t: fac2wbkg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it clim 9w *a)ca:flt g5t2bxmb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowgsta2: ;:-q dtqpyyj.:lj0 ck ed to roll down an inclined plane. How fast is it movingt kc02.q;s:-yyl j:aqgptd :j after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cyeq4z q/j b6d.m rolls without slipping down a 35e incline that is 7.0 m long. Assume itb.edqj6/4yq z 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 cf5q6r5nzzum2 u m8xl1 hanges 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 inerm od 0w05(y-f+pruct mtia 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 extendeduho pdr jpzb1(a.*xu g* 03;a7;kutiz has a moment of inerti* k0ug ;ip3dap orb(u. z;xhza*tj71ua 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?