Angular displacement is udwp;e +py ,r3z4b)dycsually express in units of

  Angular velocity is expressed i:1wf aijk6 7lifq cm91cqpl, ,n units of

  Angular acceleration is expressed in un7y4 +el, ov-fa c,dln/fdbqe.its of

  A boy and a girl are riding on a merry-go-round which is turnq xm4wh g8qs* / *9 kln9skux996ocjyning at a constant rate. The boy is near the outer e*9q 9 nou6sxxghcnk94ymljkq* 9w8s/ dge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridin9rsuoe.+fvcru1r 9j9)b m,pp g 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. 9or9 p.pfsb v,cmruj r)1u+9e Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a cons6umh0:hqtfs79ifm e*4 /k fbotant rate. The boy is near the outer edge, and the girl is closer to the centeihmm*4:hfs7 t0ufob/ekf69q r. Who has the greater linear speed?

  A boy and a girl are riding a merry-gogoz oy*b4h48 d-round which is turning at a constant rate. The boy is neazo 4g*yod8bh 4r the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which ie9 sf :t04x2ahh q9rjktf8 2nes turning at a constant rate. The boy is near the outer edge, while the girl is0t f8r:qk9n22ejxsh afe9 h 4t closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Whic,y3xkfy,mp/ j h of the following is an accurate sta, ,y3fmy/kjpxtement?

  Rolling without slippy ry77-b 32vym4o zqci.vp mp-ing depends on

  Two equal forces are applied to a door. The first fo*7l,wryc7i-it ,t hnjxd8 sn6rce 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 *wit,rtcxh,in7 d-6ls7jyn8 exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is app* ns11ldmwi k3lied perpendi1 l1dim ns*w3kcular 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, pe1 4jq,ntdi vi.p kz8a2rpendicular to the door. The first force is twice as large as the second force. The ratio zij 1ka q,2.dpv84tniof the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance u*z j-7ly yz cs9y50cia5)s ljto changes in rotation?j7lc-yj c9 5 *izals yz)u05ys

  Consider two uniform solid spheres where box1 bcva7lww8/th have the same diameter, but one has twice the mass of the other. The racwa8lx/17w bv tio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but * u ypiowl.-i/one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of-*l/wpyo ui.i the smaller sphere is

  Consider two uniform solid s7pb(x*5n m aoipheres where one has twice the mass and twice the diameter of the other. T x(7a5*nm ibpohe ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. Ifd3sqi2 fuh mrs+h7yw3 3 (i)lv these are increased to 2M and 3R, what happissq(2v+w m )hrd 7hu33iyl 3fens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied tu . k7c;gx:iufr. y-lpo an object, that object will

  The moment of inertia l3fumh v,dkf0z;lwmh1gp)pf; g13; eof 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 of mass 150 kg, one wheel of which has a mass of 10 kg an7 tun1rq (pf-0c vslr3d a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translat(l- tncfr137pqs 0ruv ional kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of massd z h9apjlfw)8-f n2l, M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends o2lzj8 wlaf ,)f-pdn9 hn

  Suppose a solid sphere of mass M and radius ;p2f v r(r:5poahu bbz3;2wmkutt6;a R rolls without slipping down an inclined plane starting fromt32k;hp;5;6rbau wzfrp:o (m avbtu2 rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes whid qx8p)eu4 pl5.ay, oen a net external force actsqp 5 )oaxd.u yle84pi, on the system." This statement is

  In what circumstances can the angular velocity of system of particles change witzn+48,/ d27hv 7oemssutg owthout any change in the syste+ontts8h o7 d7/s m2vz w4g,eum's angular momentum?

  The Earth orbits the Sun in an elliptical orbi jp ap :zc.;;g;jh-v s1bd.cllt. Ignore any friction which may be present. Whcj.b;djpc;la -sg z:1l;vhp.at happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit.xcz n li xo3mr+90a*x9 As the Earth moves close to the Sun, then which of the following best describes themza c0x *xio9l39n+xr orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hii3ls,7 vl5l ihs outstretched arms close to his body. What happens to his angulasil3,vl5hi l7 r momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc-+c9js / noe haxt-6nkhed arms close to his body. What happens to his rotational /+snnx9taoh c-6-kjekinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling q6,ku8w kbxf) in his outstretched arms close to his body. What happens to his moment of inertia abwk,q) 8kux6bfout the axis of rotation?

State the law of conservation of angular momentum.q*g uo5: x fdpyhw q)+p.7puf+

  What arc length does the Earth tr )b5yk6dubgbtaap(1l xxk y4. s: 6p1javel in a three month period in its nearly circular orbit about the Sun wityppgkb)1du5la jakx14s( .x :6tb6ybh a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 vml3 z s5lm:t3m. What distance does the tip of the second hand sweep through in 3 minutes an l3v :m35lztmsd 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to8 awjxzul egl;1mf)+z y)e y.*?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whatrd)ixjib j(:w t e2( tye13cl4 is the frequency of the wheel's r2j y(tlir:c31bti4wx)de (e jotation?

  A pulsar (a rotatingq;g is) q *h/tc n-bz;k42lhbr neutron star) emits pulses at a frequency of 0.40 kHz. The period of its ro i g)btb*l/crnh qz2q;;sk4h-tation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn i -(; epadvp-:d-b ynqvn 0.20 sevq-( n-v:adpp ;b y-d?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a o* c5-mx -)tmgmh 1khppoint on the outer rit) 5gmcm h -*hok-1pxmm move in 2.1 s?

  A bicycle wheel rotates uniformly throu- bi2k5kk nnp9gh 2.0 revolutions in 4.0 s. What is the average angular sp k-b9k 5pni2nkeed of the wheel?

  A bicycle wheel rotate;r/i 2jol6i /b./z ku dzsv)zws uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the. dsr /o uzk)/2i;6v wbzlijz/ wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 ktfmg ./hwo.n:c9s7y 9kbk90ouey pd 0m. The 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 minuk:e 7b hd909y.toksnm/ oucgpw9f.0ytes?

  A wheel of radius 1.0 m is rotating wiei-5mvc ce64rz2z i1.77fil torbwboyx1 9y 2 th a constant angular speed of 2.0 rad/s. y 1o viocwfbr e7i6.ci2l x-7brz5etz4y 91m2What is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is zaa31(j 3pbs qt6./ jn lct(fh0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the3jh6/ n sfp(zbc31talat.jq( 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 dlrsj d,pb6x3 x1g.4mf+)+jmfm: zoarad/s. What is the centripetal acceleration of a point on the wheel's ri + 3d xj6pxm1,.jfsma +dml:rzo bf4g)m?

  What is the centripetal acceleration of a point onk (*n4p 6fxtu0v6 xw0zhe il0u the perimeter of a bicycle wheep* n4 6kehu00itxlzuf6x 0w v(l of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stathq4sh -*id- yh5fie:b38g wxy ion (r = 1000 m) rotate to produce an artificial gray4- ywe*hbdh35qi x-8h sfi :gvity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curvno7e*x -td2e wyg4p o6e of radius 50 m with a speed of 20 m/see-g* t pywo72xdn6o4 . The 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 a flat circular curve of radius 50 m wit8 ycnq9uwxpow1u n(1z ,a+bj1h a speed of 20 m/s. Thez8jo1qcw + u9 1,(uaybpnwxn1 maximum centripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attadz hp3q63h,zqm/ey) k ched to the end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the stq3dhe63k,qpz y/h m )zring 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 without/e2wnykr6:udwc l 19i slipping 10 m down a lane wyc9k :d2e/ir6w1unlat 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 wv4hx .bv/x3q3 j+*a)atq wqg ;v u)dsdith 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 with a constant angular accesz0jv- -.kc ftit6l:aleration 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 starting frztbuac en728qr n2)ti- ts-bgalb961 om rest and accelerating at a constant angular accele19tut8)2-segna2ctnq ib rb 7zl -ba6ration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, an22z hy uv(7 pvrzsi31(afmx m(d 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 decelqq* 3y2./ujkmhon*tdn kh dv 5 v5(no-erates with a constant angular accelerat n ydhd*3/ tnvhojnq .kv-qo* m55k2(uion 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 turning qa:r8ofa zuvf .c::w) through 2.0 revolutions. What is the average angular a 8 :.waqfz:f)vr ca:oucceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest overc((fch( d7xb e a distance of 115 m. What is the total number of cex(f d( c7b(hrevolutions the wheel rotates in coming to rest?

  A wheel of diameter of 6nex td81 cj8h -b0lxasg.1u( b8.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 11b h -caeg1(dbu 8n0jt1lx8xs .5 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s d,p:i; sl+yhm to rest over a ,msi+y:; ldhpdistance of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationazgx6xu537 , ck0eh.pfmj bkhpm2x:c6 l speed of 3600 rev/min. Wcj .7h5p :zm0x m p f6kxh,62xukcbg3ehen switched off, it rotates 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. If joj(3 lxxncrgw c-t8 9fmd; *3a 30 cm long wrench is used, what is the magnitude of the force lc3fo8n(c j;9x -3rxtg mjdw*required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tighteb4+m98zel1yp:y iuwjning 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 applied aije+m yuy9: lb84wz1pt $53^{\circ}$ to the wrench?

  A wheel with moment of +st9e.whcw1j 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 follows: maskowr62b9ufl l9 2gy l/wdcc/ -s m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. Whabr2fcl/ w2 o c 9wgy/-6ulk9dlt is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoug0h5l4cv rii0 :r r*zy)3 cwqrght the center O3: 0qr )ciic5yh lrr 4wg*rvz0. 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 ab(r caxd*zm /r hv8+k:uout a frictionless axis thought the center O. A rope wrapped around the outeduh mc x:r8r(v zk/+a*r 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 in then j.v,mi 32la jksti96 horizontal position, and then released 6.3lj tsimaivj2nk,9 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 mas. m,m7yd tcw :xnp;b+ts 1.5 kg. Neglect the+mb.;y w d,m ct7n:xpt 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 without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disklz y)ti:3:ga(zk f 1nz pulley of mass 7.07 i:l1:nykta)z (z fz3gkg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aro yvyf.kd5 p0*dn 1v1laund a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accelerd.dvvn15* k1f0 yp lyaation of the mass?

  A rotating flywheel can b f-kh :a9)gs/hzqc8nge used to 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 inelp7-qr5ag bv 1rtia 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 0.0te ,xcdq+yeq3e 4c7q410 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 rxc4+eyd,7 e ce4 tqq3qeaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a sph 1 -yfmu,tth2 q+vn9u/kiz4jeed of 10 m/s. How high up an inclined plane can it clh 1, j 4qy2hz9-mukivutf/tn+ imb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest a+d em5br0j0:oc p6a qr-uw :olnd allowed to roll down an inclined plane. How fast is 6qbecw05oj:rr a0up +o :dl m-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 dm sy)oz4rj )(slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of imd(r jyzso ))4nertia 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 chwe9dn2t4q9if anges 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 inertiw0j;,yx9 cawwa 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 extendmt m6 0c+ qlewm-d;k2ved has a moment of inertia- mmed0q v;6ml+kw2tc 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?