Angular displacement is usually expres -3ruut+iju 6is in units of

  Angular velocity is expressd-d* 5 pu mln0vpiu2l8+7 apqeed in units of

  Angular acceleration is expressed 0be a+9d ;l)bx1 icukdin units of

  A boy and a girl are riding on a merry-go-round which iyk rmw p/x 114d7euyrfp641fdx niv:(s turning at a constant rate. The boy is f1up1 44y (7dwevd rxkx:f16nmi/ rypnear the outer edge, 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 i)qiut h g1cv:+x6keb5s turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater 5)u6 vi: cgqt+kxh e1bangular speed?

  A boy and a girl are riding on a merry-goewm ofg9z p*ojt; (hus .e4fx9h7hy7--round which is turning at a constant rate. The boy is near xshzhuof-9(jofteempwh. ;* 79gy7 4the 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 /-n6(ea-xhw cj0jdqkjvs0g;(wyb 6s at a constant rate. The boy is near the outer edge, whileb0 (6va-xkns/6 e j-(wj0 dhwjycgq;s the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-elvz qtqkbw p, vb84*x0r9+l ;go-round which is turning at a constant rate. The bo4e bl+qk8q;wz,trpl 0v b*vx9y 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 ua:btw ;5 h8/l mr-zsffollowing is an accurate stam-8fhst5u b:w z/a ;rltement?

  Rolling without slipping5is4p w hj1t xumxnw1*v,bb+0 pbtw- + depends on

  Two equal forces are applied to a fgb (lvyn99 el (5e6o4tyldf b/y b2y-door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Bot2(b5yl9lbflye9v6t nd -(bg 4yy/ eofh forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to 7/pns+jx (w;n ijyi3 ca door at the doorknob. The first force is applied perpendicular to the door; the second force is appy;p i/c sj+nj7nw3x(i lied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Twbn r5u.df96j lqo0z 7he first force is twice as large as the second djo f 90ql56nbz. r7wuforce. The ratio of the torque of the first to the torque of the second is

  What is the quantity used ty; gej q7wg1+r5u:jzzo measure an object's resistance to changes in rotatiogq z jrgzj+;5 :71eywun?

  Consider two uniform solid spheres where both have the sam1q yfhk1034 jt zuo81.jqao)iin n* txe diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to x n jt0fi 31a4*uiq1.oqo nk1hz8j)ytthat of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twic-skk m7gp:bj;pka( f7n+h4hve the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere ishb m7-(+sak kppjgk7v 4 hfn:;

  Consider two uniform solid spheres where one1j unmh)73n3ch0fd xz has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia33 n)dz17c fjn0hmxuh to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. I)zmqn:* (o gij3nfxyyg10-r jf these are increased to 2M and 3R, what happens to the sphere's moment3qoxyyim z) n*fn(gg: r0 j1-j of inertia about a central axis?

  If a constant net torque is applied to an object, that obje.95qurzoke-s y d;0qs ct will

  The moment of inertia vsl,7o(6rr/ jh .mham(yv e*h of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to iy6/ ,raje mvlh(*7rsh ( vh.mots translational kinetic energy is

  Consider a motorcycle of mass 150 kg, oy2b 8caqbr,4pzsb 76 fne wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kineticb2 rfba s6q4y8pc,zb7 energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rollsy 7/8) y4 zystbxfexd5x6h u8dy6lzd3 without slipping down an inclined plane startiex 7t 6lf)4 zs5uyxx8dy yz8dd/h63by ng 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 without slipping dohwtr-ygrli.n elfb6s4. x13oh 1 62s jwn an inclined plane starting from rest. The angular velocity of the sphere at the bottom of theh4 f6 ygl63o 1sens2.xlwth .jrr1-bi incline depends on

  "The total angular momentum of a system of particles changes when a net extern;udn qoaa w z+m.v20n3al force acts on the system." This sta03u2dzw +a navn. oq;mtement is

  In what circumstances can the angular ver662,cuk3 hkgd/ mrtg 3ax jm1locity of system of particles change without any chah6,rk m x/61guct3k j3mra2gdnge in the system's angular momentum?

  The Earth orbits the Su dff4 o6s-lnf4n in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Sunfs46l4 fd- ofn?

  The Earth moves about the Sun in an elliptical orbit. As9*+ (4o jzmpauapm7 tc the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?t*poj7+ 9uamz(ampc 4

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretct k:kvmv .zd5*hed arms close to his body. What happens to his angular mo.: ztd*mvk 5vkmentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche2 eqdyb ,iir2+i 4z(vgd arms close to his body. What happens to his rotational kinetic energbiv2 rd+i gy4izq(, 2ey about the axis of rotation?

  An ice skater performs a pirouette (a fast spin)( eqxxp-a+h5 dux xo7 p t:l)+1zom/de by pulling in his outstretched arms close to his body. What happens to his moment of inertia7e-p(p/ ldat 1 ex+x5hmuqzx )o+:o dx about the axis of rotation?

State the law of conservation of angular momz bo/e0garq7qs*z (yw/ v3lz 1entum.

  What arc length does the Earth travel in a three meyc 8p4 i7mr,month period in its nearly circular orbit about pr48 m7myec i,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 the tip rn g)g47xq,hd48v dfp of the second hand sweep through in 3 minutv4grd7d hgqx8 f p,)4nes and 45 seconds?

  How many rad/s is 25 revolutions pe dtutg,y-9-z c0zg(rdr minute equivalent to?

  A bicycle wheel rotam i)4ij8s-rx.pko+js f(nt+xtes uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rof (s-.psxx4orikm+j8t)+ i jntation?

  A pulsar (a rotating neutron star) emits pudttz: a2*(ddhlses at a frequency of 0.40 kHz. The period oat2 tzdd*h( d:f its rotation is

  A phonograph record rotates at 45 rpm. Through what angk9f)y8.s e*kn zim(jy le does it turn in 0.20 s eks8i(j*.9n)yyf mkz?

  A wheel of diameter 26 cm turns at 15 ye8y1mqgc2u500 rpm. How far will a point on the outer 8cg ye52umyq1 rim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What -yxmr)v j.bp01ir2r kis the aver-pr yi2b1 r0mrx.kvj) age angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions 1 rd,jtzuzv0-(u(sw0cvxw bekm 9/z/ in 4.0 s. What is the linb-jr0ek/twzsuvc(vmzu zx 1(/d 9, 0wear speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distffb- ouh o)b f*imz8n*+u0j+yance 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 p+u 0bf i onfj +ubmyf-o)z8**hulley rotate for the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angula6*mhkc: dsz9pr speed of 2.0 rad/s. What is the linear speed of a point on the wheel's ri: chps6mz9 d*km?

  The cutting cord on a gas-powered weed cutter is 0.16 m in leqqtki2.bag) c+k ()lw ngth. If the motor rotates at the rate of 20 rev/s, what is the approximate linear speed of thqkl +g)i.a()ckbq tw2 e end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2. 2d65mpga*zbn2 is7yn2kg4o kfq+ z)w0 rad/s. What is the centripetal acceleration of a point on the wheel's rimz4 dn2wg g5pzki7kn*sqoa 2f) b6my 2+?

  What is the centripetal acceleration of a point on the perimeter of a bicycle wh4 ffsr-at7cnznu25 (9- hhstve ix64 yeel of diameter 70.0 cm when t i4u(fxvr7-nyez4stt 2-an sh f59ch6he bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) z; 3k(vz*(ak yphsscqrlyb3 o7 vhik *-20n1emust a circular, rotating space station (r =;zs13hyb p3-qalc(eovkk2n rs0hiz k(v*y*7 1000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 20 m/eb3pp*t ,ol lt:u1v:hs. The maximum centripetal force v 1lh pp u:,t3e:btol*(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 curvl 2pw55uf4enpe of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) fp 4pe w5nul52is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is ov1mz fcu ;hbcmx+-zbl 3(/q;whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, theh m-cz/obl f3+1m;;xquc( bzvn 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 withoikp, j7 fs:jd*g.h8.is ct9wzut slipping 10 m down a lane at :8*.shc ,.ikg9 s7idjj zpwft4.3 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 ldqtq9. 4 co0qacceleration 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 acceleratiik cjb+j8r-6z.3 bwwmon 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 start3r;x c7+db wk*(wss 1yrzl6axing from rest and accelerating at a constant angular acceleratio xd*l3 (17way6r;b+ws srkz cxn of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration 4qdhm+ *tlr.w 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 copjr*1x9p j ffafap6t p9. h-y6nstant angular acceleraapppjf - 966 ry 91afjftph*x.tion 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 gz8rlg)jdh *4r1yuscx)8 dwi3heo. 7r2nob8of 6.0 rad/s while turning through 2.0 revolutions. What d 8 3drh4zi8hlbn 7wrxs8 2goj1uye*c .r))ogis the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s tc +a h;.t/vuqyo rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in c.a;hytv +c/u qoming to rest?

  A wheel of diameter of 68.0 cm w0q 5j/z*7ey2g yezu,4y tbx*vuac1 r slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceleratio/acuyuez wv2gzy ,ytr5*0q4xe 1 *j7bn?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ,99ls9s+j irez8d mwoc3p ww*over a distance of 115 m. How long doe wdi3*msz9e,9p s98rjw c ol+ws it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/mvc8 ek m1 0 gqhb,srj3cr,(j:jin. When switched off, it r3rrjg,b c( km:qjve8c s,hj01otates 50.0 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 of 90 Nm. f *nk(vjy-er,If a 30 cm long wrench is -nyefj vk*r( ,used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightv, qmb1k *:l+n/fmgp4na9rltening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnpbll*mm+9t r,gqf4n1 kv/:naitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia zqgau 4jxc(izaot)u 7:na:3. - 3 lkmi$3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is mo2m7ix r+ :dgbxdeled as follows: mass m is at the origin, mass 2m is at xigx 27:bm dr+x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 1,lm9 wvxe) k :uvp,2tr0 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 exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular ac mtx,rk,v :)wv2 l9upeceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought th9ncp vh6rw r;:d* u5noe 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. How many radians does the cylinder rotate through in the first 5.0 seconds, if5*udcw9r;vr 6n o:hnp it starts from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in the o. e.fn .y,j2f ru.mrrhorizontal., .f2e. rumonyj r.rf 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 about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg. Negle wlp,+ydk(l 4xct 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 achievey, w(+k l4xdlp, assuming it rolls without slipping?

  A 1.53-kg mass hangs o c)-eg)y.zp.q+ 5,syw wnkja vn a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is theyke.jza5q+)nv p.)gw,c-wsy angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a fre p-u/e38gtbki/ l)ai *xh b/pictionless disk pulley of mass 7.07 kg and radiu/*)83a/plbt xhkbi g u-eip/es 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is r 3hecbial.z:a4/x;fxnff 6-t equired 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 inertiuv no uq.u*z.10azlo8a 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 andf0lj/x 4ha-nmebiqd4v uw.wuk a8,( 0 rolls without slipping down a 1.0-m high inclined plane. 40kqv.a0dfie/a 4m u-bw,(u8wjhxnl 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 0.0 k2ieamdc)b64sy e9fwrl-tn oa- 08g- 10 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before cdtyisnr8g6)b -0 wame 49--2k lcfeo aoming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest an0 :a/2f vvra ,k9h1vc+ev5dos(t n feqd allowed to roll down an inclined plane. How faqfef v1 arv(hav50tv cskn9:2+, oed /st is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.v 2uj8 /kabx,h5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momenubxjvk2 a h/8,t 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 c) tm 8mx(x-zec8 uut-( klex3phanges 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 o dr-xkxz+,; skr). ralf 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 has a moment of inerti9yr28i6gebst.k( 5 k8 wbx:p:s it gbwa of5:: s k 8sb er8kw.tptyi g69ibb(wgx2
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?