Angular displacement is usually express in uni)op 0xi3pt6 wjts of

  Angular velocity is expressed in unit)v qjttuu+(h:s of

  Angular acceleration is expressed ind1( +vkhoe 2zb units of

  A boy and a girl are riding on a merr5lfd 6ypaen3 mr0,kl0y-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has thpln, km60ldyfe30 ar 5e greater angular displacement?

  A boy and a girl are riding on a merry-go-round whichuldg0:p-13j wme)t 4eh dm3fd is turning at a constant rate. The boy is near the outer ed3g1 0u d-d twf:l4dhpe m3ej)mge, 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 wk3dg0ow mc5 9x*n+f8aktbj77 f/ yhufhich is turning at a constant rate. The boy is near the outer edge, and the girl jfbm*w7g/ka0+ kfdxofh9cu7t 38y n 5 is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding ts fh1/v7: z3hi,zhrsa merry-go-round which is turning at a constant rate. The boy is near the outer edge, while hr:zhi1htv /3zfss, 7 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 is turniiw ieax7y y8s0 :6c1hqng at a constant rate. Thy1 sce7i 6 8x:iahq0ywe boy 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 rotating. Which of the following is an c5d/g w-e)ais *ig.+eqa;ki h3v8 k m9of1vraaccurate statement/rs.8 iew13oaei a)af;9h vk*+kg dcq -5mgvi?

  Rolling without slipping depends oajj; n25p4abpm k,yq 0/ 9merdn

  Two equal forces are applied to a door. The first force is applied a2 nqb 9tf6pfd6t the midpoint of the door; the secon6pfnfbd q 9t62d 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 doorknob. The fbm 7rzt.nf fc w8lqdr3;7)/ nuirst force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which for3 ftrl qr7m/zc7nd.f)8nbw;u ce exerts the greater torque?

  Two forces are applied to a d6os aybq*/(nzoorknob, perpendicular to the door. The first force is twice as large as the secaqbo/sny (z* 6ond force. The ratio of the torque of the first to the torque of the second is

  What is the quantity use9q2vvp ,g9pgtd to measure an object's resistance to changes in rotation? v9vp,2ggq 9tp

  Consider two uniform solid spheres where both have the samw k594r*zx3r gyk9w jre diameter, but one has twice the mass of k z9ry4rg5kjr9w3* wxthe other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the bsmn8k/5 ; jivzy)s gi ddk7:3same mass, but one has twice the radius of the other. The 53)/jvsygdb8 ik z: d7 kmni;sratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where on74wr6 qf4jj tsv w 1go*ic7hz-qpq7t+e has twice the mass and twice the diap 71hjoq7-wfjqcw* g is 4q6t+z74trvmeter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has masosdz9uy ij 2x;yc7sza. nk2:3h(8l pgs M and radius R. If these are increased to 2M and 3R, what happensyn 7yg8ilh s(ca jsx zp:.dz29 o;23ku to the sphere's moment of inertia about a central axis?

  If a constant net torqtx r ;lea jb)xdz()qlh:-.o6 que is applied to an object, that object will

  The moment of inertia ofofhq/fow(:;ojbv90 n9:gzfm a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, ;0oo:m (jf n 9fq9hbwg/ ofzv:the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of z( lgah(x1b,o8m0ul 5xnc* ap 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 translational kinetic energy of the zag mch(8n*05(ox, lp1x bualbike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and razgj (yj2 xv+5f fs/l 1rr66oobdius R rolls without slipping down an inclined plane starting slfro2x+jb5/ 1 (6z6ryvfgoj 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 rolls o;ui -r;mco tc9j1 )dxwithout slipping down an inclined plane st9jod; m)- co cxit;1urarting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net ex5 8dg+ravd -gvternal force acts on the sad5rv d-+vg8gystem." This statement is

  In what circumstances can the angular velocity of sys:b/vxh21 w aym( biprd +yizp 95yq.y(tem of particles change without any change i q19zyh5 adim w2p(/y.rx(b:+ pyvbyin the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whi63+a6jf ppzm7jk(qq vch may be present. What happens over jmf7kqp+66 a(qj 3 vzptime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As tz, r- kzya.j.fadudc +x2yz;1he Earth moves close to the Sun, then which of the following best describex2f j,.ydkaz cd.1 yu ;zr+za-s the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched:/ek u5tbr.kw arms close to his body. What happens to his angular momentum about the axis of rotatio/e bw.:5ukkt rn?

  An ice skater performs a pir8dzz yv2qmw h.7k9pr )ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens hqk)w 7m.yzvp 28zdr 9to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ib9e y+ 6wsa0rhn his outstretched armsay 9b+hwr0es6 close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momef.x;ug d-jqb 72tec7e6 3zakz ntum.

  What arc length does the6x1jmslcdbv,gy:sr1 xsfw 4d,s*h0 - Earth travel in a three month period in its nearly circular orbit abo16 b10l:sjs wdsx,gs,d4m* hxry- cfvut 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 1 *5tq a0glryi,/(svyu6o: nmlwsd0 bdoes the tip of the *s/0vs60l, y wq5t(iuml:o ba1g ryndsecond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions xc *6vau0eo/;c+bkc3du x7jvper minute equivalent to?

  A bicycle wheel rotates uniformly through 2.7rl*yb gf5i4 ow- mqs:0 revolutions in 4.0 s. What is the frequency of the wheelr:gs*mwlb57-oqiy f 4 's rotation?

  A pulsar (a rotating neutron nqb6li5u2 q9rstar) emits pulses at a frequency of 0.40 kHz. The period our9 2nqilb6q 5f its rotation is

  A phonograph record rotates at 45 rpm. Through wha8l*s1s.c je8ktxunm* t angle does it turn in 0.20 s?esm*xs ljt1*uck8n 8.

  A wheel of diameter 26 cm turns at d:0m()h hc v8w1zfbvd1500 rpm. How far will a point on the outer rim move v:1v0dhbz8c(f ) wd hmin 2.1 s?

  A bicycle wheel rotates uniforqrg.f m5-wm f.mly through 2.0 revolutions in 4.0 s. What is the average angular speed ofrf m5.gw mqf.- the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in69bo60*r x 1ndaiyybe;6da * gvla r*i 4.0 s. What is the linear speed of a point 0.i b;6 lod6*0ya* ivx g9*61nyrreadba10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance 9w0 fd4jybj3h 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 make the trip in 12 minutes?w fdj0439hbj y

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rcup7f;4 jm9arad/s. What is t9 cr;fajum4 p7he linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. t hb0 q35l*wx tx/.-v8q; hkrhkxblj/ If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord? ; lh0 */hrkvxh.8-l/q3tkb5wbxqjx t

  A wheel of radius 1.0 m is rotatingm m0ulo 0zdi:8 with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a poid0mol0:im8zu nt on the wheel's rim?

  What is the centripetal acceleration of a0xk/amj4 b/fj: pct b7 point on the perimeter of a bicycle wheel ox:b /c kf7pabj /0j4mtf diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circulnj v1f) go70tzar, rotating space station (r = 1000 mtvj fgn7)1zo0 ) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m suy+p c-pme*vj6r6 8za6pa - jwith a speed of 20 m/s. The maximum centripetal force (provided by s6 p+*8-aue jspavm pj6 rcz6-ytatic 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 aatyna0a bkd.x62brb dv+)6 9speed of 20 m/s. The maximum centripetal force (provided by static abbdn.a9r62a+v dykx6)bt a 0friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end 3lgg,w6 .zh(cjh xbgtzc *sy vv:-++ pof a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximu- w pch b*g,yzs:hxjg+6l. g vctv3+(zm linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kjlsaih2 d5:7z xv 07u,ue1fq yg and radius 9.0 cm rolls without slipping 10 m down a zls7f5 h jy:u2exqi 1d0,vua7lane 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 angular acceleration of w my2m5t3pne ubyk(h -.q a*b:$4.5 rad/s^2$. 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 p-40rqv :p;1i/mcxr;5zj ah yvcc vr: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 rota9w+7it-) fp2 a -dqu*sgn jo dtcc(9zpte after starting from uoadcci-+7( twq- gz*j9) dfs2t9p pnrest and 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 accelerationhmv*v ktf y( 8(oj19ls 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 azx):/h w eesnx) dt)2nngular acceleratio zsnxe)2hx:d/nw )t)en 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 6.0 ,hp huiv oxmiv4d.5+*u(qp.irad/s while turning through 2.0 revolutions. What is the (4p +p m,.uvdxqi*h5h i io.vuaverage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to :95 dnmawrw) srest over a distance o9wwd5ra n :)msf 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 ue w0x t)p.w 3plu77qfdown uniformly from 8.40 m/s to rest over a distancuw p3 f7q)t7u.px0 ewle of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniforqumd3* s 6v5d+lyh-ad mly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to l5+v*dq-mu syd dah36the stop?

  A centrifuge in a medicxz 4gm) 41o8aama:qi4 vz +uuzme66 nral laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelaxz au )m8ne +v:oq64uzi 1ra4mmg4 z6eration 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 of 90 Nm. Ijz hd, 0vrr (zqpjm1z/((-gjff a 30 cm long wrench is used, what is the magnitude of the force required - zjfjjzvd ,1gmhzp(r 0/(r(q when the force is perpendicular to the wrench?

  The bolts on a car wheel requireft3 )8 (cj*eqrhn v3ze tightening to a torque of 90 Nm. If a 30 cm long wrench is use3)hf r(cnq tjz3ev8e*d, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti kcf/qpf 99eu xk z3i2ca,4b0emh;se(a $3.00 \; kgm^{2}$ 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 they1 pzsfdlu* / xs6a4v0 origin, mass 2m is at x = a, and, mass 3m is at x = 2a. Wx 04vd6aulfs1* /ypzshat is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictk :t*cl(cjs 7fionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a f kt(*lc7:cjsforce 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?

  A solid cylinder of mx-rdopejdm j dd3wd:o x 9ee8++n1n2 2ass 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 another section of radius R2 = 0.50 m eo3+:dxjee ond12r+dw-n dpxd92m8 j 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 hinged at one end j 0t4em 5ovbb rm3*pryq)uho+r326xy. The rod is initially held in the horizontal position, and thenrjp4om3y3tmrer o 2 06+bq)bvx*h5yu 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 one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Neglect y7s55oq+ u 3yzogg-mithe mass of the axle and sprocket. If a force of 20 N is applied tangentially to a s-zy3usg+iy5 5qog m o7procket 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 pu;wm k/w 82h0bf. edxd5qe(omslley of mass 7.07 kg and radius 66.0 cm. What is the angular accelerf hs8x(5ww2.b ommdq e;e k0d/ation of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pullu6t weke)o4g wy 3j61 hijfj47ey of mass 7.07 kg and radius 66.0 cm. What is the acceleration of ejuk6i7t o)hwy f6w3g44jj 1 ethe mass?

  A rotating flywheel can be used to store energy. If it is required t -63bl e9qlo-qs p b6o1qkycl0o 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 inertih-(ng p1a crn v-.z)0ncmfk(pa 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 and rolls3 )+v*hsii9r -cbxonc without slipping down a 1.0-m high inccx-+i vr3is 9nco) bh*lined 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 i v)x gfcuip7+6hu5,wrolls with a speed of 10 m/s. How high hcwvu+)xgifpu6i 57 ,up an inclined 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 and al2dyzlk.v:wv6gw) 1yv lowed to roll down an inclinyvvwk)z:w 16dyv g.l2ed 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 s y 2)6jo c-sdh5hi h;;e2xy+;dxq cqiglipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inerticyhihodx2c+;5g )x6; seqy-;2j ihqda 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 mo4s7dr4bh zt *j *r;wcxmentum 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 omu5:u*yjdcdsad4 5 h(f 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 at 5.00 rad/s with arms extended has23l) ttye0 xiy a moment of inertia o tly)3e xty2i0f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?