Angular displacement is ux-3mgy+u3y9 ot5 flw ksually express in units of

  Angular velocity is expressed in una3.lmzxs xr 6g h),,hmn-ssumgl/ -qz08 vo2cits of

  Angular acceleration is expressed iod6/di,hq dd:wv9 iq9n units of

  A boy and a girl are riding on a merry-go-round w*-qm1atcjumpu0xv7g j2 0 m( which is turning at a constant rate. The boy is near the outer edge, and the girl is closer (0 uj7-0gwxmmqt2c* mpua1jvto the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turnibsfb0r/ hh 4w.2m +nbxng at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular .w0hrf2hb4mbsxbn/ +speed?

  A boy and a girl are ridin 0pc/k9o z ylb9/-c-3ctlobw h.ntl.og on a merry-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 the greater linear spee-bct 9./0-olzkcyc 9/ lpb ntlow.3h od?

  A boy and a girl are riding a merry-go-round which is turning at a c yh,bg1ei /r0)ixmh7 chz +a;ronstant rate. The boy is near the outer edge, while the geh;,/ c7byihh0ri x gz) r+1amirl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is tufta uy1/9 tuo1rning at a constant rate. The t 1a1o/fty9 uuboy 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 lru*m:dbpz: w3 -1g0 bgr;q ueod0j,ffollowing is an accurate stat*u0 dz0d :pfbj1ggbe- r3ulro wm :;,qement?

  Rolling without slippih+/w vt 1i7i.6zhbi6 ah- sekong depends on

  Two equal forces are applied to a door. The first force is applied at the6zd v1)b(1 ,s prndel ,odnqg+ midpoint of the door; the second force is applied at tvoe,+gndlq 1pds1b) ,(d n 6zrhe 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. z- qj*)mp 1swhqc+ /bm The first force is applied perwspzqmb /+ m)-j 1q*hcpendicular to the 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, perpei*r eoqgh7xyyi3 a; 6,ndicular 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 second i*q7yo63 gr;hxye i,ais

  What is the quantity used to measure an object's resistance to change dx ceb3b x,rk;-:b83k rn9il;scb:c es in rotationcx;9sekdb 3 8:b;b:x,l3 nerr-cbikc?

  Consider two uniform solu- gkt92x c 9di.fixq*id spheres where both have the same diameter, but one has twice the mass of the other. The ratio of u-2txdxcik 9 9i. qfg*the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have 9lz0c8p cls(a4-x o r cu)i0j-.yrzwr the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of ine rr-9lzpcosa0-8x0.4z )uij(wl cr ycrtia to that of the smaller sphere is

  Consider two uniform solid spheres t +i d8w,zao9vwhere one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the sma ovi8wz+,t9 daller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased to 2M anyi 8cv( +kedg2crjsmj x-8z12d 3R, whaj-jm+r vx2z(ck8c y18 deg si2t happens to the sphere's moment of inertia about a central axis?

  If a constant net torque isndp3kt2-0eoe: ev y4 p applied to an object, that object will

  The moment of inertia of a solid cylindehaco k p u+mw9lv- f1;i/mju0+r about its axis is given by 0.5 MR2. Ifuw+-;10au/9v+hf i lj o mcmpk this cylinder rolls without 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 has a21j(ojmp,dod 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 the wheels are uniform disksp(do j2d 1o,jm.

  Suppose a solid sphere of ma9 0jdtgkd5b 7yss M and radius R rolls without slipping down an inclined plane starting from rest. 9jbd dy07tg5k The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of massv 1s es.6(fhuyjcbs(mose9 )1 M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocit m)6e s1(hc1 y9b o(sfesuv.jsy of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes wt)6, arnvx *gv(v1 e9mcgh l/hhen a net external force(* en6hharg)v vl/ mt19gcx,v acts on the system." This statement is

  In what circumstances can the angular velocit; wj7s 5u.2v+j 9*x w:fybaipq:mhgsxy of system of particles change withoutvj*2 y:uxpj 9.xa+5:sfwg hmwsq;7ib any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frictifdz68vdmq+c9: vhz* xon which may be present. What happens over time to the Earth's angular momenqc zd*zxmv9v h+6d8:ftum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mg7t)yk1d4g 4ek2h4xsbj ,)kk xigf (p oves close to the Sun, then which of the following best describes the orbitingky tpk( 1)4 ihkg4e2sgbj,x7df)kg x4 speed of the Earth about the Sun?

  An ice skater performs a pirouette (a; x2 4-6el x+hbzfptz+5xnm 9ie inw)o fast spin) by pulling in his outstretched arms close to his body. What happens to e;+zixto54zx6fp )mb9 - wix 2ehnln+his angular momentum about the axis of rotation?

  An ice skater performs a pi3/tt/adk z6 yjrouette (a fast spin) by pulling in his outstretched arms close to his36/atk jtzyd/ body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette wizj.rg(a.6piuj 13mgtom nl 98u4r9 (a fast spin) by pulling in his outstretched arms close to higwmo3tz.4nu.ga9l p98ujimj r r(i16 s body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentuv*c x59busuz(jhw2.c m.

  What arc length does the Earth travel in a three month period in its nearhpa3 e1i-ur2 a6dfg l-ly circular orbit about t pr1f-da32h ialu6-ge he Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lenvp;rl,hxk(ac+i lcasd7s52k7f q2 +q gth of 0.30 m. What distance does the tip of the second hand sweep throug;qlhak x,l d++ksa 7rfs5pv2ic27 q(ch in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivan4fxj tgb6 q7omktxeh88 zmf174b),tlent to?

  A bicycle wheel rotates uniformly through 2.0 rok-)z8ib 4l pfevolutions in 4.0 s. What is the frequency of t pfi)bo8k4-zl he wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequencywqv+fj *;v u3fjd+cj* of 0.40 kHz. The period of its rotati ;*jvjj v u+dcfq+fw3*on is

  A phonograph record rotates at 45 rpm. Through what a3ocq po 9wdkl(zq ;u5bk2.lw ,ngle does it turn in 0.20 s?2d5o lpkukoc q3(wq; wlz,b9 .

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outer kbg3 zja-g8 : 0gaj0tsrim move int0-g 0g zb3jks8g:aaj 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. hcly7nec,-c7poe nf o-)k7 :a What is the average angular speye,7-- ckfcpe)onhl 7c7 nao:ed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolu ;t (v n.(:bhf6eugmlrv8oxw9tions in 4.0 s. What is the linearvx 6mwolv;89(n(ft regb:.hu speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. Thv xg6 3 w9i1uy1/skwh(af8+oct6xmj ye 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 minutesmfu+wicjgyvx6a 8sh6 91 3(k1wyo xt/?

  A wheel of radius 1.0 m is rot/peh0 h- .lewfjv17ivfe0vc0 ating with a constant angular speed of 2.0 rad/s. What is the linear speed 1wi0 h .e0ve j0hc/7v-l fvepfof a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengtgum t 6uql2j12h. If the motor rotates at t6jt22 qmu1lu ghe rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 bu13)dacluzl1 ku 5ti8q6-rim is rotating with a constant angular speed of 2.0 rad/s. What is the centripetal accea-i1il1ud 8 )lc3 r kqzbu5t6uleration of a point on the wheel's rim?

  What is the centripetal acce wxirv0zg79h wmal3/)leration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike wlar9ghw zm i )x73/0vis moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spac5.l7 jm 8vx.y zhcvuluje4j,.e station (r = 10,me vy4 vx.c7u jj.zu5l8j .hl00 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat cirn:29vto ,d812upcun n a3fbar cular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal f8f3a bp9tv ad212uun, : nnorcorce (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 ca2qj1ty 9q hvyas .(i6ircular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static j96i hqq 2a(y. svaty1friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the ercf)25gno;3,i f9y g l2avyoknd of a 0.750-m string, is whirled around in a smooth level tabok f2of2i 3vlc, ay)nrg5g9;yle. 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 radius 9.0 cm rolls wi fmhmnfnpp)m; w +840sthout slipping 10 m down a lane at 4.3 mm;0 mf 4w)fn+mnh8spp/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 accelerativzgey90n9 uk*;r1k pt on 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 const v)w,fvi)qs2 bant 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 25jf-gm;wqdf rotate after starting from rest and accelerati-jffm 5wq;d2gng at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, fx*e4sk- r8s oand has an 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 dec(xgs/vw1s9i oqu-da)g , 6 czuelerates with a constant angular accelerations oxqudwg9 g6zs- vc1ia(),/u 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 spe 5td69ui kza8o4 ubf :)0rqz gegzr/2ied of 6.0 rad/s while turning through 2.0 revolutions. What is the afoei zigr8u6)r49 tg2aqb 5k :0u/ zdzverage angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to ron8u9q +gy1s ch:l2rg est over a distance of 115 m. What is the total number of revolutions the wheel rotat+ qy:9gc2go rn81lhuses in coming to rest?

  A wheel of diameter of 68.0 cm slows dow(s7vmgoh0bp+o: s k.nn uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleration(pkgos sn.7h: vb+0om?

  A wheel of diameter of 68.0 c/yvdn 3 o9wu1e s,lhn/m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take fuh w/dnl 9,eoy v3/ns1or the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed j-,86qx 7h z6 f:ybu/gfvuuppof 3600 rev/min. When switched off, it rotates 50.0 times ax q u /8zfjph6:b6,7pgvyu u-ft 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 requir:t.gvyoylaj c2 ,rf5) gd:ft/ e tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force is perpendic :f2:oyc,t/d gj5v)rlfgtay.ular to the wrench?

  The bolts on a car wheel reqf :.fth-d-c fs-uxwc :)sgad) uire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the focuf-da hf::x.-) c-s) gdstw frce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertiv8o.j0 h+- popd1 rmjma $3.00 \; kgm^{2}$ 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, mass 2m id8- 8ef,tutfu gi,fjn,*ye 6qw2 edm /s at x = a, and, mass 3m is at x = 2a. What is the moment of inertfue,-6d t t/im,n8j8 e e,gudy2qfw*fia about the origin?

  A solid cylinder of mass 10 kg is p +wes jw76d1jz2d(olgi+ j 1- ycqtff)ivoted 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 exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylindq+-jos+t2jlfd gwi(w ) f1c6yzd7 je 1er?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axb,21xbmly2/v8 teepkis 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 an2l 1e2,bmtbyvkx/8e pother 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. The rod is i9 s56 x p(t1)ehg4 jpjab4ziatnitially 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 abou5(ib gth j1 4s9)6pze4jxapatt one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius ldsn a drn)i- 9u l7w*6n6c8dt30 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 radid nt*86uincdl7 r9a lw)6nd-sus 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 0j sz0mt + qst,yx)3tirope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of tyi tz)3 s+ts0xq,tm0jhe pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk p a 628rqtymg4sm ntx2uu 1i-x2ulley of mass 7.07 kg andmtm4 t6r-nqyxui8 g2 xsu 2a21 radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used togm4r :no1kp+fx ;r wq71b-wle 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 of in.m vqua x.m*u7 4wc,doertia 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 azlb 1kt3cku14nd radius 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 reaches the bottom of the inclined plaz 11ukclbk3 4tne?

  A solid sphere of mass 1.0 kg and radius 0.7)8mq7xqp;3l 0 swmvtye 5d0mma:jo -f2ux kz010 m rolls with a speed of 10 m/s. How high upx 0mw 0md3oap8;fkvjz)q2umeq yl: 57s-t x7 m an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass ojs.ovbq f;,9 of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after 9,q.;bjfovso dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 c.oq1p 0*qjqp l99gc /l(mpjyexmb, 0cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a pclb90ep/*x 1com.gyjqp0,ljq 9( mq 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 ch(q m t6b6hywy0anges 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 in-g+ sl muynl7h*y; mpi.k:ap6 ertia 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 has a i iqv l2*jwy:qipzuf5+( b:j .moment of inertii jy zw.2fvi (+b* q5pi::jluqa 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?