Angular displacement is us/as ry: b d5ekvhd9dxui9i208ually express in units of

  Angular velocity is exprb m)o *ers8h l7nm+(yax;r3qgessed in units of

  Angular acceleration is expressed in unitsv+o -p h,pot1b of

  A boy and a girl are riding on a merry-gou6c 0tl tmmursi7+ 33r0n2dsy-round which is turning at a constant rate. The boy is near the outer edge,d3rr63t2uyi0 +0s7mlns tu cm and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constant q5xr)v fj jne4 efoiw xk8 bh5:d;+h+2q6c(bfrate. The boy is near the outer edge, and the girl is closer to the center. Who has t2fxd k h v b(4fhxqcr5 e )+qiew;65nj:bo+8jfhe greater angular speed?

  A boy and a girl are riding on a w h6- ucp8a5;i9ol allmerry-go-round which is turning at a constant rate. The boy is near the outer edge, ali9o-8pl lwahc u5 ;6and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are rid0(oq)tu tbx ,lb m2lwr52at9ming a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the 2mroqt (, xmwu 9)l250tbltab center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constanp+5+rbp*yuej r kf7f/sf0dp6 t rate. The boy is near sfy + *re+f6jfp/k b0p7dp5ruthe 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 accurate s: pjdoh-nr 03frow2-ktatement?n-3kpj whf2od o0 :rr-

  Rolling without slipping depends onkn:1b*wyie cv6 x0ju1

  Two equal forces are a4; *;hw(crw fjyrx v*tpplied to a door. The first force is applied at the midpoint of the door; the second forcety r;jcvw*( f*hwx ;4r 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 dooroj7 o2h(gmadbz5zgf54idz36 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 grezia57 ozgdfj 5o zm3d6b(gh42 ater torque?

  Two forces are applied to a doorknob, perptf (.l0 fso:h4l 7gmy8 q g5lg+7 sunfp;0gaxdendicular to the door. The first force is twice as large as the second force. The ratiogl l ngpaf7; x+8dtsulh( y7. g5004f:fqm gso 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 in lidz/evo51 np:0 s-pv3f5 pa brotatiszpp1d-pv:ae bvfln3 o0/55i on?

  Consider two uniform solid spheres w4qmqnm1 q+1l5ch p:azhere both have the same diameter, but one has twice the mass of the other. The ratio of the l5mpq:zq+ m1an41 cqhlarger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice(da6l4;xyr lcw ) euj) the radius of the other. The ratio oxl )(juwe)ay;rl4d 6 cf the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twvo ,x+wi ,fdb8ice the mass and twice the diameter of the other. The ratio of the lax+i8 , ovwbd,frger 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 2M (xd9 ncb2*tna8 usaxz7/( qxkand 3R, what happens to the z(7 8q xxa9nx*snuk badc/(2tsphere's moment of inertia about a central axis?

  If a constant net torqco-p0 a4w9trp 0dp7xk7kg :xzue is applied to an object, that object will

  The moment of inertia of a solid cylinder about its axis isdj)w bv;wk2+co x-c 45)i mfn+lgykjc+ bo()u given by 0.5 MR2. If this cylinder rolls without (ox) km+y+ o bkj);cc 4c)w-jdbn l5vufgi2w+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 a mass of 10 kggd -iur /-g qyfde8p8;)iu-u e and a radius of 30 cm. What is the- peq g-dryudu/8 )fue- gii8; ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mas: dy2ehk uj.vzia)o88s M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of th2 u8hvo diaz.y8k:ej)e sphere at the bottom of the incline depends on

  Suppose a solid sphere of 0m6*or8qs qzyh 7zb 0s2 /zv5g2g csjumass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocityu2y0m 58zqo r q6s*0c7 2vbsshzgz/gj of the sphere at the bottom of the incline depends on

  "The total angular momo s28jq9e4g pventum of a system of particles changes when a net external force acts on the qe2o9s8jpvg 4system." This statement is

  In what circumstances can the angular velocity of system of particles : gy- f jvsjmx5*(-jduchange without any change in the system's angular v*5g:fxy dmjjjus-(- momentum?

  The Earth orbits the Sun in an ellipticalt gb,,qnd.,mw*q nu-d orbit. Ignore any friction which may be present. What happens o-uw,qnmgndq,. ,d b*t ver time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eart:f4 q03m )v hnp0gpj55qlsq/)ej pfesh moves close to the Sun, t :f)5q5hfsjj4 )g p3qqpse/mpnv0le 0 hen which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spivj-pz*up5fmvt8g( k f2h 6 6tmkj++g mn) by pulling in his outstretched arms close to his body. What happens5 ujt*m+-f+gmh(k j m6 pf 2vgkt86pzv to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin)/ 6hd4zxnw 3ae-xssn m 9j:7gv by pulling in his outstretched arms close to his body. What happens to his rotational kinetic n49nxg e 6 z3-m:/wadhs7sjxvenergy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) wtn1 0 1):s hni3zepquby pulling in his outstretched arms closeq h1npwe3 0ns1it:u)z to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conyc:6odf za he9-cq)+j zz:j 9lservation of angular momentum.

  What arc length does the Earth travel in a three w 2o x5c937kd:a0v3.ykcx0tsy lerts month period in its nearly circular orbit about the Sun 0cx c7: ot3vsk0x 2arl d.wt 5yse9k3ywith a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length t5 r5:mj3w* ypriavk3rn2rk9of 0.30 m. What distance does the tip of the secovra nwt53rk259rj3p i:k*ym rnd hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 257j ;*k/ blexhn revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutiki dbo88eyr82x4j c1b(1 xmdeons in 4.0 s. What is the frequency of the wheel's rotation?81824 xe1j d(8ix boecdyrmbk

  A pulsar (a rotating neutron star) emits pulses at a fre8 zmv**vxewab (w,,taquency of 0.40 kHz. The period of i ,zv txev*8a* ,b(awmwts rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in utn02egw172p tpni/k 0.20 s1t ni027u ntg2ewppk /?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point oet 08bc7p:x pzs-e xn7n the outer rimpxpeet s xzb780 c7n-: move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0k 8ydj-y* mdq6sgd7 g e4sx36m revolutions in 4.0 s. What is the average angular speed of the -me4*7d qkdys8jdsy 3mxg66 gwheel?

  A bicycle wheel rotates uniformly through 2.0 r(5gd7fv9 grc+ b 2i5sc.hiy rwevolutions in 4.0 s. What is the linear speed of a point 0.1 w(irh5r+fis7 9g.d52ybcvcg 0 m from the center of the wheel?

  A cable car at a ski resort carries ski5(j/w,oot ro. j j;pahers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diaw./hoa;r ,5oo(jjj tpmeter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant anhn49ox/v)ts xg5lipq,p 17iqgular speed of 2.0 rad/s. What is the linear spe v7 g51xhlo/)qs4p,iti9 qxnped of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the moton;y28 o7- r1hhtl;cizrdr )mwr rotates at the rate of 20 rev/s, what iz;h 1r87 - i)dr no2th;lwmcyrs the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 y-o4rebd8p8utw8x(g rad/s. What is the centripetal acceleration of a po(yxoebwp 48 gudt88- rint on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter kzgj/e3bt) ) tof a bicycle wheel of diameter 70.0 cm when the bike is moving ez/t kg))bj t38.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statiuwh 5jl/ 9fq/ron (r = 1000 m) rotate to produce an artificial grav /wfuql/ hj95rity of $9.80 \; m/s^2$?

  A car is negotiating a flat cir 1jvd ;:/va2 z5lwoe-bfvur k:cular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal forcefu 2vlo j;d/w1r:vz:k-5v abe (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 cu :wb)u-f- haoz(d0 q s-9huqpnrve of radius 50 m with a speed of 20 m/s. The maximum cen qb-f(wqhz9ap o0d-: -u)hsnutripetal 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 ar1: y5ci(bij cxqp8yofp :*/ siound in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maxim8: qpi5y po(fci1* :sxyicjb/um 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 rolwe20v gd8bds; ls without slipping 10 m down a ddv;8sebg 2w0 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 angular acceleration of ek/nfd 08 v2,tdf h)ot$4.5 rad/s^2$. 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 ajp58uc8a z -ilbu 9bs7ngular 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 a mniq yrot66l+r)15q rotate after starting from ) l tmroyn661aqrq5i+ rest and accelerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, .qskk,:2touk;y,2umb i jj;k and 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+,h wdb 5hpeity +93ko/s decelerates with a constant angular accelerakweo3h 59hyp +t+bdi,tion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches attngw:u m( ;*bn angular speed of 6.0 rad/s while turning through 2.0 revolutions. What i(w t gubtm*n;:s the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.4/l6 f fv+-sifp5rn7tznl4 ,yl0 m/s to rest over a /z5ifffsl6+r ,4yv pn7 ll-n tdistance of 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 down uniformly fr03t6ah2rpdx vom 8.40 m/s to rest over a distance dpa6 2xht0 3rvof 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down un*zi.f pdi)f 6giformly from 8.40 m/s to rest over a distance of 115 m. How long do*6if f.zd)i pges it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 re) ue94/lckhoi k,q6vkv/min. When switched off, it rotates 50.0 times at a cve 4 ,qkh6/ lciuo)k9konstant 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 cm zdyty /,(yso:fngcuau59 20y long wrench is used, what is the magnityy ac oy2g z(/:0t5fd9 ,unyusude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenvjycmzmt;5 93 ing to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the fo5 3jctym9 zm;vrce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia /b3hf mhx 1f4cr0sut+$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows:wl kbk-*f;-i*ag- h zs oqiqw2,wv7w8 mass m is at the origin, mass 2m is at x = a, and, mass 3; ih -87zkwwlw-2i-, aowbkq*gs *vfqm is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted(x2kxi3mn cn 4rd4.m7)7s s2hm xlnvt about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a forcir.n2 nmml)( 7xs x4n4s2v k7 chdxm3te 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 mass 10 kg is pivoted about a frn6 mbmq9e zg,.pxfq z d791o4wictionless axis thought the center O. A ropqf.n 76ow9z1 94 mxqp,mgebzde 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 from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially hespo 1):aq 5pklkzu ;ug1j,au -ld in the horizontal position, and then released as the free end is allowed to fall.zkua 1u lpu:o) p5a1sq-k,gj; 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 wz7mpg2v. 5 xzhxtn m()heel to be 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 sprocket of radius 4.0 cm for 4.1 s, what linear speed does the wheel achieve, assuming it rolls v xp.m hxnztm()5 gz27without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless d7tj1ijkhg e58xb b24 nisk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of t jbkj t7i5e2hgx1b8n 4he pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless/yrdh--vvi )ss)kwm w6b ,51saqw2 ox disk pulley of mass 7.07 kg and radius 66.0 cm. What is the aw )65aqsyh)kb,x is v/w-dv2 ow m-s1rcceleration of the mass?

  A rotating flywheel can be used to store energy. If it i/c nt,44uj/l(q9 + ccgyqiabfs 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 inerti bfe-1; wzg.sja 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.mv6o /2rrm pxzvdr1+/0 kg and 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 wd 61ro rr vpv/m+xm/2zhen it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg ancje9q 7) oj,mz9l -lvod radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before cl) lojz7-j 9c m,qevo9oming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allw:o.ihodo+ 7g i3 r/ ccl4 hmu23ws(oeowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m/ e+4wiihr( u.7o c: goo3ms 3wdholc2?

A solid sphere of mass 1.5 kg)le rfq 8.ve9 tpztw(9 and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rz9 .q89 prtfevw()et lest. 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 cgtja0. r, /(fpox:z+caitai) 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 inertia of +) 68 gusyuhau-gg-nb $5.0 \; kgm^{2}$ 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 rotatcuff .+rd)cg2 /0 yniy.q op1ying at 5.00 rad/s with arms extended has a moment of inertia ofr) n/u0ydfog 2fcc1. y.qpy+i
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?