Angular displacement is usualzjk;-klx j/ 0yc7sn4m ly express in units of

  Angular velocity is expressed in uny u b6/9ntjew9its of

  Angular acceleration isxphpw;6 t)xl57t4 vf u expressed in units of

  A boy and a girl are riding on a merry-go-ro 9 :s7vx t+eso 4r4m.e5otcsfkund which is turning at a constant ratfote:4x sscs k4.+ t7 m9rve5oe. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridinda 6:7 *vv lp-dtr-7hgapz vf4g 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 thvrvpa7* g d f:a-zp-6l 74dthve center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which lv rp5 mkma,3wqiwjh 40:i)y+is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the ,5 j4miq)mk0hlaw wi3yrp:+vcenter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a g6g 5ut3/emiiu zm86w constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal a6t 3w5mgm 8/u uiiez6gcceleration?

  A boy and a girl are riding a merry-go-round which is turning at az cgyg h/7-n54m9zegs constant rate. The boy is near the outer edge, while the girl is closer to the center. 5zm /cgyg4gzhe 7 9ns- Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whiwjl rg17m**z:sdx6b dch of the following is an accurate statem mrlgbd6:*szx jw7*1dent?

  Rolling without slipping depends o8:xbfmyaz + nk1b)p:vn

  Two equal forces are applied to a d+9 - --xxrd5zsm.smngyh /,qbjk 1gavoor. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torqu91-g- mxzg hjy,ds.-x5/ qnva mbs +kre?

  Two equal forces are applied to a door at the doorknob. The first force is9e8ee4o, xo (yetc, jp applied perpendicular to the door; the see9 yctpe oe(,x4ej o8,cond force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, o0ptjeg:;6za80 pu fs perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque o a gu0zp86se :ptofj0;f the first to the torque of the second is

  What is the quantity used tok)ir 8yb2nq1d measure an object's resistance to changes in rotationbriyqn128 )kd?

  Consider two uniform solid spheres where both have the 7da7srjk 5 3s;u z (3x1 fkmmxw.ps5zmsame diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller momerwjuka3pf1z d sm3z . s;5m xs5xk7(m7nt of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radius ohj7x.8zu,1o h4)umq9g n txxef the other. The ratio of the larger sphere')x 8mhe,9uquhg7o.z tj41xxns moment of inertia to that of the smaller sphere is

  Consider two uniform msaos8 g53wd 1solid spheres where one has twice the mass and twice the diameter of the other. Th1a mogsd w8s35e ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M as65n s s9u6volnd radius R. If these are increased to 2M and 3R, what happens to tn9vuss65s 6ol he sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object5o:s6xctln2f9uwy *p yzk)4f will

  The moment of inertia e+iwr e0 k0:z*c7*dbxyl ) rkpx.e;fkof a solid cylinder about its axis is given by $\frac{1}{2} MR^2$. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle ofdeqgxr* iqw 02fi 1*y3 mass 150 kg, one wheel of which has 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 bikx d1 yr2if*iq eg3w0q*e? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M andwghh6- i qho6; radius R rolls without slipping down an inclined plane starting from rest. Thwio6q 6 h;hg-he 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 slidz6uv. 0zd3(t35gnceu ex0fc pping down an inclined plane starting from rest. Thec 0x d5d.ct3e3zeufz (u0v6ng angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net j.tkw-na1,7x5u5 m 0avubopgexternal force acts on the systp1 5tjwxgo a k 7nb,a50vu-.muem." This statement is

  In what circumstances can the angular:8nywo t eq0b3 velocity of system of particles change without any change in the system's angular momentumn3ewytq0 8b o:?

  The Earth orbits the Sun in an elliptical orb0d+bfq4f)vucj/i/t pyt x4+ k zs(l;x(qie,uit. Ignore any friction which may be present. What happens over time to the Earth's angulaf0 //ep+j l); qxs x,qfut ivytuc4(zibd+( 4kr momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moap .16 igcngi/ves close to the Sun, then which of thei.cn16 apig /g following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his oupoa. xby1l1wn0g9(xbtstretched arms clos(l go1. 9abxpnwx01b ye to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouets/3s r9)zs7cw1py ft3kk,c yr te (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotatio 1 cp)fkrsr /3kytc9y37w,s zsnal kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fadui7oo ybnxx-34 5jq)st spin) by pulling in his outstretched arms close to his body. What happ5)ybx4oj on-7ixq 3udens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum.qhrz d g,y3v k on69yh2k2k*a;

  What arc length does the Earth travel in a three month period in its nea-78aelfqt36n 8-fwauqhozm8 0t - yswrly circulara y- 7ewm6ff38quoh-l 8naw- 0z8stqt orbit 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 mj4 cc/kk/yl6flp;263avwd j m. What distance does the tip of the second hand sweep throughc/6jl k4y;f d mjp6w2vl/3k ca in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to?lyk ,2/6uqy )l/3;lseoyafs, ua yif)

  A bicycle wheel rotates uniformly through 2.0gvw6d-e -1nl h revolutions in 4.0 s. What is the frequency of the wheel's l-nv w1hg6de- rotation?

  A pulsar (a rotating neu9ua( c bvgzuknywuagn :))o51e)s7( ttron star) emits pulses at a frequency of 0.40 kHz. The period of its rotati uotn):7sgk9n(a e y)wuvgz)c1b(5 uaon is

  A phonograph record rotates at 45 rpm. Through what angle does it xldta3tx6:-m4 0zf 4jzr pv)kturn in 0.20 s 0x6vtjx3:4 tfz -dz l4mak)rp?

  A wheel of diameter 26 cm turns at 1500 rp b;ks(.,(qd fl 5tz nl,pog7p.ijcrh8 m. How far will a point on the outer rim move in 2.1 i8bkcp (,gtz.;p(r j fsod nh57lq. ,ls?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What i e/jti,rhp -*k8ly0 bzs the averagjhzlbepr*,-ki 0ty/8 e angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0r ufi+e)y/g am+dr9g+ s. What is the linear speed of a point 0.10 m from the center odgr/i gya++r9)u+ efmf the wheel?

  A cable car at a ski resort nbg - e*f:ek:dcrkm 25carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with d:f 5m-r*2 negb e:kkcdiameter 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 :l, aditn2jqyh f1jne8itx(45 0g 8smis rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheelti5 am(jh0,j 1fldx 8i2t:gy q 8nsne4's rim?

  The cutting cord on a gas-powerfj::pr s8lo) ced weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate line:r lc:fp )s8ojar speed of the end of the cord?

  A wheel of radius 1.0 m is rotating withejl z)45als 0n a constant angular speed of 2.0 rad/s. What is the centripetal acceleration e0al ) nls4jz5of a point on the wheel's rim?

  What is the centripetal acceleration of a poin9ahw5k5o8h p ffca8m 5t on the perimeter of a bicycle wheel of diameter 70.0 cm when the bikek55chw 88apohf9f ma5 is moving 8.00 m/s?

  How many revolutions acttep16in 4 ,wo9r 2pfu a/)sper minute (rpm) must a circular, rotating space station (r = 1009 pnt)6 , 2ir/spauwafc4t1e o0 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/s)gk7/al +/sv ant /w6z/uecms. Tml7asnt)c zu/va/+g6/ wke /s he maximum centripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating: apa-/t gd0t;5qdk lj a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction d-dta0 ;lak tj5:p/qg) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end offonyw7ed * +wpj 5ei geg8ib9l022a.k a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then whao eb.*ignk75 pj29l2gw8e+fawi0ye dt maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and rad pl5,)y 5yvw:-9w5 aw7 ekxetwyuase,ius 9.0 cm rolls without slipping 10 m down a lane ,7a s -eetyex :yp5lu5ywa,k5wwvw9 )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 witiad0)-/b6pf0-j vsy stz 6 evsh a constant angular 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 wyw 1na+anvj9e/ j *cz-ith a constant 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 0.3fdlwewuv mi83swvho) 4+k.vd 1 8:qr)00-m radius automobile tire rotate after starting from rest and acceleratinlwkddo4v i :vv8+f.8 3m u)w1we hqsr)g at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration of66xua2d x1+m b0pqxcg $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constaf7y jmv0-ov49 ;qjnef nt angular acceleration ofjjye9;n 70of4fv vqm- $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angu b.raf c-7q26kkk 2unj29wpaq lar speed of 6.0 rad/s while turningf7a9ncj 2kqqkw2 rk26 p.-a ub through 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly0nia-le5e;mrk9v6;s.rv5 8 a d mnczj from 8.40 m/s to rest over a di -e 0mj kvrena zn d6si85m5lvra9;c.;stance 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 from 8.40 m/s to rest tl. g:yeuo*,m 8 dvk:cover a distance of 115 m. What is the angular accevme:o: *d.gl8ut,kyc leration?

  A wheel of diameter of 68.0 cm slows down uniformly fromat piq10bc5alzk9 ;anie g;;7 8.40 m/s to rest over a distance of 115 m. How long does ;zpa 1iicebn9l tq0ak;;5 a7git take for the wheel to come to the stop?

  A centrifuge in a medical labora nrg(8t8 j4+*fanp nw-t)qzoo) mil;ttory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to rest.)n t+gf; al8)jwo npmno-*r 8(qi t4zt
(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 requit2rrr o++aiu qv, n*9zre tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what * iznqra92v rtr+,+ou is the magnitude 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 30 crq(m0 d56i2 iam hu3t 6uj ieqsk:mq0)m long wrench is used, what is the magnitude of the force required when the force adi2 i 60u:u3m6t(e 5s iam qh)jqq0kmrpplied at $53^{\circ}$ to the wrench?

  A wheel with moment of rbwms;38 3ict8c td,u inertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as followsd;b.tkra os/rrci 10 7: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momentbi7k;.rordsrt0 1/ac of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted axh1t7pzkbe qc)f );t) ;tn+n ibout a frictionless axis thought the center O. ))cx bntntfte k71zq;; +p )ih A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought ;ovxzu5:hc8xo38 n wnthe centerow8z;o3nhxc uvx8 5n : O. A rope wrapped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 held inaq/p3 n1bp1tc2jw zir f;g2 +g the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it 1z2qf rg1ap+ j23;bt nig pc/wis 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 cc ;3sekthnb/ r*+hq(wp+ ts2mass 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, assu/swc(3 h+ n2sbh*tpk+e ;rctqming it rolls without slipping?

  A 1.53-kg mass hangs on a roppukx)m4r o6z*g3za* f e wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of tk6x*auo p rg mz3zf4)*he pulley?

  A 1.53-kg mass hangs on a rope wrapped arou(mw65npw gg9s5 u z/pund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What9sww u5/6 upmpnzg(5g is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is r. rlj3byjk; )sequired 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 inertia89s6snzq, gov 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 myhz.2tr+7 1l:xl9 k jwqy6wkstarts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it rjk1+tmy2 .z6l7q wxh ylrk:w9 eaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kdnlki7jp )d )3g and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb 3)knpdljd7i)before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is : dvprol.emw; 2-3 dvef(4nfrreleased from rest and allowed to roll down an inclined plane.drv;p (elor 2ednfvw:f-.m34 How 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 slipping down a wp-t:)h xl) 3cbtf uw+35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of x ct3b+h) uwp:ftl- )wa 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 mom*-:vyzoe *ix vr17spi entum changes 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 momento*l m3hu 5sj(x2zwh4l of 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 rotatingr eca e8(qp:*o+zcx. c abmb9- at 5.00 rad/s with arms extended has a moment of inertiam+cqb-r9 x8epa *ec.zbaco:( 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?