Angular displacement is usualsdg4.a0i5b0k4n judy zcqef3 990dl.*yganoly express in units of

  Angular velocity is e) *ykd l:lpvf.spy+-gy71 tsq :9copi xpressed in units of

  Angular accelerationb1-j6wj /z-gmj s dbr) is expressed in units of

  A boy and a girl are riding on a merry-gjpy 7f-0tyi(wo-round which is turning at a constant rate. The boy is near the outer edget0 iwjp-(7 fyy, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on6 f1oaf ) j4hq sk4o-utoej ;nek8p;q( a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is cl1) s otjaqepfofo- ;;(4e u8k4 6knjhqoser to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is 9x,yf-w p3j2y7qz;y phbom a6turning at a constant rate. The p2hxyp93q-7a ; m ,yb jyzofw6boy is near 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 coaw d0w/a +eruxeg*qwjr q3.*5 nstant rate. The boy is near the outer edge, while the girl is closer to the center. Who ha*/uqae ewrd.*jr q g5w+ 3xa0ws the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which ikrdbv4v.emt gz 5r 1/tei +l0+:8hopxs turning at a constant rate. The boy is near the lipb4x +o 0mz1v/. eer:58hvgr+t dtkouter 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 78jgp5h9pziqiox( 2 yis an accurate statpz29xyqi o(phgi85j 7ement?

  Rolling without slip0lcov+l ,;n(cw(dzkn ping depends on

  Two equal forces are applied to a door. The * nrfs ,7lz)n4d9bq+xszg e. jfirst force is applied at the midpoint of the b.fs )sn7jd,e z +x9rn *q4gzldoor; 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 3a7 + z2mmoq8eycbpc uv:iv;2applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is appliedv2+czvque;p:iay2 b7mcm8 o3 at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, pyyim09.pi +:t /ljweterpendicular to the door. The first forc/9 i l.m+0wy:t eiytjpe is 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 quantity used to measure an object's resistance to changes i4jsyj f c)t+r k:e6fl*s d*8ren rotation?lterjc 6yrs4f*sdef +k 8)j *:

  Consider two uniform7ui)obd+g mo 2 solid spheres where both have the same diameter, but one has twice the mass of the other. 7io)g2bm o+du The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same m;sg 84q a(8u5fidwrrg 2 q5pji nn)sw;ass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia tg siu (q8r ;s; 5w8pj5)i24gfnarqndwo that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twi0qby (/8x4u k+bhjyj yy2 exr9ce the diameter of the other. The ratio of the larger moment of injxye/b48x(uyq90hy2byr j+ kertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radiu5tix m njegx:j-n(x*,s R. If these are increased to 2M and 3R, what happens to the sphere's moment mgjx -*( neixx5jt, :nof inertia about a central axis?

  If a constant net torque iscr9nz7qwx fsdwc10;8*i(o oq:o mze: applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis p7+9;t)8 prjwwisce p is given by 0.5 MR2. If this cylinder rolls withoutps;)iwp 8 7tc9r+ ewpj 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 a,zg5e5(ic 6lgo lsmup-32i vhas 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 bike? Assume tzii 6a3eclmsupv25(g 5ol-g, he wheels are uniform disks.

  Suppose a solid sphere of mass M ak j+:bh,iqv cfx 4z1-0mro8ovuvgv. ,+mx yw .nd radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline de ..v1 v0v:bco,y oirfg whzmm,jq48+-vkx+ uxpends on

  Suppose a solid sphere of mass M and radius R rolls withoutcflg(.e3g5tt :ft0wai uu : t; slipping down an inclined plaf .tcf :;5lti gua0ett3( uwg:ne starting 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 cho08+3su p8 o*urmfl cnanges when a net external force acts on the system." This st s+ 8o 38lfo*upcnur0matement is

  In what circumstances can the angular velocity of system of particles chan:yvby;53 r.0a;xi8z u(zasqtc t,bgoge withou g5otars c,zaxiuv;y3 y(: 0.8;z bbtqt any change in the system's angular momentum?

  The Earth orbits the Sun in ft7p6:8 bvp nban elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angularp87vbfp:nb t6 momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth m 4b yg6yd 6kur+v9sit3oves close to the Sun, then which of the following best describys 3bd6 9r6ti4 +gukvyes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hisk- v/jf7eyln31qhds -w-+qc i outstretched arms close to his body. What happens to h -h1f -en/ywi+cqqsd k 3vl-j7is angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchxv8em0 w*gxh+ ed arms close to his body. What happens to his rotational kinetic energy about thgw mhxv8*e0 x+e axis of rotation?

  An ice skater performs a pirouette3bm d8 *gocu0ybt4v7 f (a fast spin) by pulling in his outstretched arms close to his bodym38 dovt * 0fguybcb74. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of ang8 xnk-:kss,zpular momentum.

  What arc length does the Earth travel in a three month periodju k6hw3/nb t0 in its nearly circular o w6th u/j3k0nbrbit 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 distance does tfco1kfb *.gn6d 5s,r pxq f**whe tip of the second hand sweep through in 3 minutes and 45 secf, dffbr.wxs** nc6 oqg5kp1*onds?

  How many rad/s is 25 revolution1 4u2 b6*rav,n nttepws per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutiosg x(d7y2dc(g a5,x8 qc hv.dyns in 4.0 s. What is the frequency of the wheel's rys(h 8v gqgd,cay5dd cxx7 .2(otation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40i;wx x vmt* gk:-uuw(8 kHz. The period of its rota-uv:x* (tmx; kuw8 wgition is

  A phonograph record rotawbp* 1kb+-cmz3 zw q ghz,vx+0tes at 45 rpm. Through what angle does it turn in 0.20 3 kxcp+ bgvm0+z -h,b1*qzzwws?

  A wheel of diameter 26 cm turns at 1 n0/s1 xxxq6cm,f1yus 500 rpm. How far will a point on the outer rim move in 2.1 sfs ,uq yx101csx/xnm6?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. - +tfnm ae48rp What is the average angular speed of the whe-en4rt8 fa+mpel?

  A bicycle wheel rotates uniformly through 2.0 3 swgt tcoe-g .9wxx./revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the centerwo-e .9/gsg.t3xtwcx of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Thdw +2erx31xz/. jrbiue 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 zrxx21b.d/wj3 +ueriin 12 minutes?

  A wheel of radius 1.0 m is rotating s d45( g*dvsw-gt+e rmjb2f:kwith a constant angular speed of 2.0 rad/s. What is the line v* ged-gdtsmkj2 f:s5+r(bw4ar speed of a point on the wheel's rim?

  The cutting cord on a gasm ;g(2agdc,3rbx r l3l-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speem3rg,g2rx3ba;( dcl ld of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed fe1u ;msc( 4vdof 2.0 rad/s. What is the centripetal accvmsec14f u(d; eleration of a point on the wheel's rim?

  What is the centripetal accele6+blzt) u y6,gdzyw 8cration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is movin zbuzy ,c86lwgyd )+t6g 8.00 m/s?

  How many revolutions per a2m+h,ioss )ij34j eeminute (rpm) must a circular, rotating space station (r = 1000 m) rotate to pro,e e3smjho )ij4i2a+sduce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a7/a (qht cu+ njo9e6sth: is ;qkg3ml+ flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by shql7og hje(+si;s+ u96a c t3nm /kq:ttatic 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 radiuj p:k-sw22oj b- ;gni1jv3q (bn ves)zs 50 m with a speed of 20 m/s. The maximum centripe;(jk vz1) s2-onws-3qnbejbi v :g2pjtal 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 0.750-m string, is whirled ah9tyx2.4ud) femrvhusss c(t 1k n,-3round in a smooth level table. If the maximum tension that the string can withsh21r ,4u-9svts3kmyn .du (sfh )cx tetand is 250 N, then what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of masjta7r0c(13 j g ;gstzws 7.5 kg and radius 9.0 cm rolls without slipping 10 m down7sa( rj0gwtz;1cgj 3t a lane 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 ang ,o +uzd (;h;n-ppq:uupm7 iyjular 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 accelerg on(sx:m h-r,o 7uk9qation 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*9fng62km9t g ze8ci5qla ljr1p(*t ,p9m mos after starting from rest and accelerating at a constanta1z9m(lp g q,jcltn9 m* igk6mot5r*pfe 298 s angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angs8z l0u 3hi1oepn/b9nular 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 angu h rchbmt *2)4ifvfc1b9bac( (lar accelerat)ab*b 1ic rf(vh (42t9 chfmbcion 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 rad/s while(snj- toja8a js-(6y*jz b0u e turning through 2.0 revozs-e*6s8uj j0 y( aotb -n(ajjlutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0v)cg5gzyqe k4l pq4cs6p 2m77 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the tota7 pge sk5q6gmz 2v47)yqp4ccl l number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows do*kbtjh:6qpg:avd1 vx /c n ,w)wn uniformly from 8.40 m/s to rest over a distance of 115 m. Whatax:q1h)nb g6v*/kjt,:pwvd c is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 ,not0akld3:ro h5m 2xm/s to rest over a distance of 115 m. How long does it take for the whl:dr a 0tho k5,2nomx3eel to come to the stop?

  A centrifuge in a medical laboratory r m;oukhi1my( (otates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 t ((m1kiymuo; himes 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 of 90 Nm. If a 30 cm0ts, d58via m pnii.4m long wrench is used, what is the msn i.4m,vtpm0i ia8d5agnitude 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 3ec :dr3sdm;a cx ;;2zq0 cm long wrench is used, what is the magnitude of the force reqq;de3;a2mz sc;x r :cduired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertqxg d b0o6)7bktycp h3bm+1)kia $3.00 \; kgm^{2}$ 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 the origin, ma1fm dgqt14v0zss 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about themz4 1vq1 dt0fg origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought yyhj )a*ra,sm 5*19sb5m q jbfthe 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.*yr9,s hayqa *bj5m5fm j b)s1) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a9lb;k/v4ssh,ub iiif)y xn 2; 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 fo k /ihinx bv2,)ysl bi;fus4;9rce 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 jb 9,coxz6 hepbrn )4+one end. The rod 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 released? (The moment of inertia of a rod abo9nhp )rb6x, 4+cbe jzout one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radiusdke u).q6tzc)w8e ,z q 30 cm and mass 1.5 kg. Neglect the mass of the axle and sp q.dzqu,6t)c8 keez)wrocket. If a force of 20 N is applied 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 wrappedq;;rnqgo*u 7b z)aze4 around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pull4er )ganb zoq;u7* z;qey?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless diskm0z- ,- )ropnkvr5wne pulley of mass 7.07 kg and radius 66.0 cm. What is the ackw,nno v0-)5 rzemp-r celeration of the mass?

  A rotating flywheel can be used to store energy. If it is requireu 7xn,bi1 bh)zd 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 inert,/ g- mv3xkpuqia 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 sta+sl9aj j pht:(rts from rest and rolls without slipping :ls+p( jhta j9down 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 a speqh u/4g1ok-pr ed of 10 m/s. How high up an inclinrqkgpu o4 /-h1ed plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of p7d; 5 j98omvec-ge wz0.20 kg is released from rest and allowed to roll do;dcv -w5e9p 7z8m ogjewn an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kgis7je9nvg)yas,3 uy:n6k - pr and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m loasrkeuy n:vji ys 3p-6,n9)g7ng. 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 changes slzgcvsak h:jcn93d82 :2xf/ 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 inertwl k0 +p-:g-wv 4; zzl*phjcutia 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 xw n*9 u,ya an :qfam*q9l;4iirad/s with arms extended has a moment of inerti; 9*wyqnlm*9i: a nafxq4i au,a 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?