Angular displacement is usual.b;odl wlbxsx..+q6 aly express in units of

  Angular velocity is expressed in units + d mwpq5r3r/vof

  Angular acceleration is expressedgmm5a0b dzn4 t ja-*3x in units of

  A boy and a girl are riding on a merry-go-roun o:9qgbt5wy/w d which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater aww9q5bgyt :o /ngular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constantj,i;5 cdh *hwwwxv2 (j rate. The boy is near the outer edge, and the girl is closer to the ;ih(w, v 5wjxwhjc2* dcenter. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round wh3ivywzy20r : h1c /igaich is turning at a constant rate. The boy is nearryv 0 z2:iw acyhi3g1/ 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 turning at a constant rato+qcyrc0o.;c /zozr -r0-er ee. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centri+-cco/; z0rco yzoree- rq0 .rpetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a hh9w8 7+8m1s lb9rk0hw9d esfpp x)y yconstant rate. The boy is near the outer edge, while the girl is clo d wey9h 1r79xh lyfs0)9sph +m8p8wbkser to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurat2bh2d z:rs cn*e sta2n:czb * 2hsdrtement?

  Rolling without slipping depenj 9-ewlohw aa2. *:rhnds on

  Two equal forces are applie8 blh(p7bbn,h d to a door. The first force is applied at the midpoint of the dobphb8b(7,l hn or; 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 aen1* bl ;.g20nl4qizbp5u nt k door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greaterz tgnukbi* ne1 pn0.;q2b ll45 torque?

  Two forces are applied to a doorknob, perpendicue zwr1h1s 14iylar to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the secos11ihr4 1zywe nd is

  What is the quantity used to measur7lw2xbd tiw+;e an object's resistance to changes in rotation?7tw; +l2 ibdxw

  Consider two uniform solid spheres where both have the same dim,x6hack qs87w6 kh)u ameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that ofkqakh6)u,m sh6x cw7 8 the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radis: /)7// fbm :-s/ r(ybrchrxr u tlmpceat66vus of th rsv-:rcubtxl/rhp)(rt/fa/6 mm6c 7 :y eb/se other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where oneszd8a*y sz ,;;te cy2o has twice the mass and twice the diameter of the otheas 2e, y;dzs8cotz;y*r. 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. If these are increased to 2yh 4ucdils:))n 7 lv(lM and 3R, whatlv):7 y4 dhulcln si() happens to the sphere's moment of inertia about a central axis?

  If a constant net torque isyg qr-3dj1tobse (-z4k -;f xs applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is given by 0 h2 sce*waa1g..5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energyaasw2* gc1.eh is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass byuw-3gx.+od:e *vx o of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total.oxy*wduoxg :-3+evb translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slippingz5 6ib3j j*6 tk 0gu*ri *xpcmr.cj5;yzfi-os down an inclined plane starting from rest. The linear velocity of the spj m5ctp xcj b6yzirkf630 gzo-.5*iju;*r i*shere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rsxh9 x )y2xeh1u6x/w7h rws)zhk1*af olls without slipping down an inclinr*ax 6whkwzx1xy1hh/hx f 9se 7su))2ed plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular mor nq*q. s,iv2 ul-ut b7p+nh/ymentum of a system of particles changes when a net external force acts on the system." l,qrh bv2u.pq/t- n+7i *suny This statement is

  In what circumstances can the angular velocity of sfm kv9sb4 7lj9ystem of particles change withol ms979v 4fjbkut any change in the system's angular momentum?

  The Earth orbits the Sun izp; -yh;dqr/ o smy-; s7 iqsn6xk.s+q,cs (osn an elliptical orbit. Ignore any friction which may be present. What happens over time to; qs-.-6ndrhz +s i 7sc;sq ys,s mp(xq/ko;yo the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in4fwtz( w aqu./ an elliptical orbit. As the Earth moves close to the Sun, then which of the fozq a/ .uwt(w4fllowing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirqx ;o3dz0k4 sj4hf/rfouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular dzfrqx h;4/fk4o0sj3 momentum about the axis of rotation?

  An ice skater performs a pirouette (a2 +)hx hzu;rkt fast spin) by pulling in his outstretched arms close to his body. What happens to his r+)hrk ; 2hutxzotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his oud76.k)9 6t gbr:cxp qmal.3s hasyks3tstretched arms close to7m: 6ks9. r3sabdph3gl.q 6 kcsx) yta his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mome,f4i 2ka4inop ntum.

  What arc length does the Earth traveaznzw(o)q6bh1b 5t+)v*qfb u l in a three month period in its nearly circular orbi6b(abn b1 ouz*5wqqv+)z fht)t 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 m. What akx4ig 3 /7c/bj+ 1fnl3/ msqn;rs rcydistance does the tip of the second hand sweep thrqgljx 7i;3/s3bks /a +n 4f 1mync/crrough in 3 minutes and 45 seconds?

  How many rad/s is 25 revolut8x m +)-otohe q 7hkz9jwy(kd:ions per minute equivalent to?

  A bicycle wheel rotates unid5tc(od/-ibpp 9u.s yp 4lo-f formly through 2.0 revolutions in 4.0 s. What is the frequency of the whel obd/ipdu5.cs9 tof( 4pyp --el's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of bia3 ok3a40e0r yi 7pv8tem-a0.40 kHz. The period of its rotaare3 i 0 mo b8v0tiaapk7ey-34tion is

  A phonograph record rotates at 45 rpm. Through what angle does .qu.mi3d1 mis it turn in 0.20 di1ms. mqu3i. s?

  A wheel of diameter 26 cm turns at 1500 rpm. Hwehpw0( 5o,q how far will a point on the outer rim move in 2wo(w0hq5 hpe, .1 s?

  A bicycle wheel rotates uniformly through 2.0 rey(phsk4yd .: gvolutions in 4.0 s. What is the average:p(4hdsgy .k y angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is8jze buw: ,hbwm/ 4epkm:hs(, the linear speed of hkpe humzwjb4,,8m:wsb:e(/ a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distafu71e-y5nrbmq *qt x* nce 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 mn1re bmyxqu5tf* 7*- qake the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2dc. mp5 tpfyzww,i+3(.0 rad/s. What is the liy.zw+d (3 ,fw5pc tmipnear speed of a point on the wheel's rim?

  The cutting cord on a gash3(3jrq g1.msxb , j p51p+d5xfq s2mw8oi ngr-powered weed cutter is 0.16 m in length. If the motor rop+ j.p8sm sm2xr1d3wnqji rx53o1g,qbg 5(hf tates 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 m is rotating with a consta1qz4o/ol6e 7tkh hbdk *,fjms uv5,:yd(5fsent angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on thkso1t moe,6 fys :hvd5ju/* 5q4kb, z7de(hfle wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of rjp2,ry)acw1je f 8 ;ma bicycle wheel of diameter 70.0 cm when the ,1c2faj)m;wyrpre 8jbike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stationvj) f/6)yds4 qc)c2qj0wjmd vly w2z4 (r = 1000 m) rotate to prod vvczc yd/2jfq l6mwy 20w)4s)d 4)jqjuce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radiusn(ziu.y 3 41 sxamy6y5,vps ua 50 m with a speed of 20 m/s. The maximum psyzxua5i mu3 sa6 (.4vn1 ,yycentripetal 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 circular curve of radi d,-f29ayw q0m8vwd gxus 50 m with a speed of 20 m/s. The maximum centripetal force (provided by stativd8,a2xfyd m9 -0gw qwc 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 0.750-m 0hgv/ii::vl: *jyriy 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 strigvijy*0:r h:yi /l:ving is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipping 10 e 6n +vaba6d2vm down a lane 6aab 6vnved2+ 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 acp08,uxg3sr y2 3 t-urz6pr ukyceleration 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 c 2shkwsx/5 f.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 startingq1-wp: a7. 2mavkg5 fe -gmvxz from rest and accelerating at a con-2aqkx v7pm 5gaev zwg-. 1:fmstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angularv/h :c kp6-t.29uqumj azsr9,n tc;gs acceleration 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 angular tb15cf)c jzntn ev*,-rt 8wrx 2i. po+acceleration ornnc *cv -i8t+2 twr.51x ,ot ejzpbf)f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reac*y 5baezxzv.6 v3hnw qz(2rb;(f vf8xhes an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angular acce v r(f bf;hzb2qn.3z v8z5*xw axv6e(yleration of the wheel?

  A wheel of diameter of 68.0 cm stfs:vxwk 2u5 ox 8f(1ulows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rov (k2fxf 8x 51:sutuowtates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest u3gh7q u ago7*6kx /izover a distance of 115 m. What is the angular accuuok q gh g3iax7*/76zeleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to resm ,be-zyq5nds lm;l+:t over a distance of 115 m. How mq,-d:y llze+5bs ;nmlong does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/sk(z 8.ca5j8oa5i2 e6s rl*3h d wriimmin. When switched off, it rotates 50.s j582o k . 5ea3 6im(ir*rczd8wsihla0 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 torque x-hkxyf7.8l*w t j) wqof 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 wr8qw -*j xyfx7k l)wth.ench?

  The bolts on a car ww0vh 2g3wlo( iheel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the 2(iwgw0vho l3 magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertijn jn nn0-b+l5 ta:6+qufrw r*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 modg1.ipi u wyi*/eled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a.y.w /*gpiu1i i What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted ab-wav9nm ftwif*+ibv;w (,2dv-ftc.w out 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 ncw,ti+wm. wvabv2*ff( w-v;d- fti9of 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 mass 10 kg is pivoted abqol *q,dnign7pyki1 ::keo ,(7ga8kjout 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 arouj,q*o:8p ed7( kgl, ina1y:k7ko iqgnnd 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 from rest?

  A 4.00-m long rod is hinged at one end. bazfk3kiqm d ik;w;(/8wt 63 i The rod is initially held in the horizontal position, and then rebqik /kmiw336aft;k 8id(w; z leased 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 30qhph6 +ci uc2- 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 fochip6u c+-q 2hr 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 arouhj.ae n489 kpd3 fgd*ond a frictionless disk pulley of mass 7.07 kd9 8fog np.adj*4khe3g and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless die y, kr)+ 84tcs2gffcusk pulley of mass 7.07 kg and radius 66.0 cm. What is t c)yg,tr uef24f+ skc8he acceleration of the mass?

  A rotating flywheel can be used to stor ,4,c03e4 fgcdtz(ib b0cjj xexj :,ete 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 ine)mcmkpnmju w3z/z./ (rtia 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 sz7vy(x fche+e-uk98 8 8 rozmckqw-)otarts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of thf-e zy 88(o87uv 9ozqr)hcwkkxmc-+ee sphere when it reaches the bottom of the inclined plane?

  A solid sphere of maskw+z-+ ttpq( ss 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane cantw+z s+ p-tk(q it climb before coming to rest?

  A hoop of radius 0.50 ml4 l,*h; ekynv and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. Hlkey,n v 4*h;low 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 sl; .:cyali ,nnjipping down a 35e incline that is 7.0 m long. Assume it started ;yic: ,j.n lnafrom 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 chan2cr, ss8fw j1xges 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 ofn10tt)-7olpzq aydjh /eco 8v r.b.6r 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 fia. i7 qg:2br2bm*eurad/s with arms extended has a moment of inertia .e q2 fg72i abm:r*ubiof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?