Angular displacement is usually express in units o:xi bzp-7r 9 to,dc tvb)3+wgdf

  Angular velocity is exp zu (32cv6qw7.cqvkqoory.. dressed in units of

  Angular acceleration is expjiy; 3om/ 3s +3kmmdowressed in units of

  A boy and a girl are riding on a.9 ntkx ns bm(gi6o;3wr7ag; l merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closero9t(n7iakn.bl;6w xm gs;r3g to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning .**y gtny,fs, qo .gcmat a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has thg*.nmt.qy s,f *yc,goe greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a8gp5t:y:zj sl constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater lineagpyl ::8sj 5tzr speed?

  A boy and a girl are riding a mex+2i 6r)x fesnrry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centix)rxef+ 2 sn6ripetal acceleration?

  A boy and a girl are riding a merry-go-round wx1rc:b 2t1t;rm )sgrzhich is turning at a constant rate. The boy is near the outer edge, while rczs t1 1) t2;br:mrxgthe girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body azt.e o3) c8ym -icoplk4s8jw,b* 7nethat is rotating. Which of the following is an accurate statement?sm)w8 ltn4j,*-zo ycb.3ai c8k7e eop

  Rolling without slipping+ f,l.j68yihkwp+tzcaz+v- x depends on

  Two equal forces are applied to a door. The first force is applied at the621g*q . rhu fz:qv ycliqjw)/ midpoint of the door; the second forc: q62*hvqrq.i jz lgwu /1)ycfe 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 door at the dovv 4)fmkxt vj.. 0f-weorknob. The first force is applied perpendicular to the door; the second force is applied at 30e vveftx0w4-f j .k.)v mto the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, rdymq pj g87 8p9k:z(uperpendicular to the door. The first force is twice as lar(dp9muy8rjq8: zgp 7kge as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to5q4 g5e68vhykocnn/k measure an object's resistance to changes in rotationo4e6y h 5cgkq /vnk5n8?

  Consider two uniform solid spheres where both have the same diameterha lfnfb; o904 e*x 26xevdv.i, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of d;l. vxef6v092iaef x4bhn *o inertia is

  Two uniform solid spheres have the same mass, but one has twice the radiusat21fhpb ydr- fpd6xn w4:a/. of the other. The ratio of the larger sphere's moment of inertia to that of the smadn pyw-:p1a. ba4/fhd2f6 x rtller sphere is

  Consider two uniform solid spheres where ona8t( erbg 34t5*zxaece has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of zegr34 t aex(t *c8b5athe smaller moment of inertia is

  A uniform solid sphere has maskvhr kn f13 m1b,px3q m-8oz,qs M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central axis8,bzvmnmo1qr3q 1 h-pk,3xfk ?

  If a constant net torque is applied to an object, that object 9v;uht-c srcp i 89sebt;/s n9will

  The moment of inertia of a solid cylinder about its axi x85vqkr9iufugw tr (v 1e683es 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 massvni4 0fv9jea0 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 bikv0 0nfviej94 ae? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slipping dzuib 4s +j 5jk5(hv7ykown an inclined plane starting from rest. The linear velociz uy+ b5jj ivks4k(7h5ty of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rol 1hj6+wkvr m7vls without slipping down an inclined plane starting from rekmh+ v1j6w7v rst. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particlc9j:l (gv fm+40 /ayok:nzmig es changes when a net external force acts on the system." This stat gzf m ginym4vj0k+ocl/:(:a9ement is

  In what circumstances can the angular velocity of systm1 f k+q/ lnd6 b.vl2lgtfr+ui-)f e6jem of particles change without b md+6l6jvr1kifqf)lf-.n 2t+egul/ any change in the system's angular momentum?

  The Earth orbits the Sun in an ellipticcts6j8 i/38y wa gard: u90pskal orbit. Ignore any friction which may be pres k r6p/y9 cidgs8:w j80suat3aent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptpa )3gl34*/ezusstx ys3 g *rfical orbit. As the Earth moves close to the Sun, then whic*ggrxsy s /3*pz33f)4 aleu tsh of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a 8 ha5s v u1tgqjsxpks2s8e7o zti6,.2pirouette (a fast spin) by pulling in his outstretched arms close to his bodyxksosei5 q8,u th6spv8 t7za2.s 1g2j. What happens to his angular momentum about the axis of rotation?

  An ice skater performslrr +m26fme)o a pirouette (a fast spin) by pulling in his outstretched arms close to his body. oml e2)+rrmf6 What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hig/k: .him2bcd s outstretched arms close to his body. What happens to his momebc gh.:k2dm i/nt of inertia about the axis of rotation?

State the law of conservation of angular mom gjjx xp/,a-;r:un9ry entum.

  What arc length does the Earth tjrr 1x b+ aj;;1kxes3oravel in a three month period in its nearly circular orbit about th1r ;as1bkoj3;xj xre+e Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has ahz/v2bn9yla:pw w- 49n p3i yg length of 0.30 m. What distance does the tip of the second3 ni-/pbnha ly4wvy29 pg9wz : hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revpm-pn ux2 (ew)olutions per minute equivalent to?

  A bicycle wheel rotates uniformly throu j +xk ).mmq kwvq091 js-iik)fw0kj,rgh 2.0 revolutions in 4.0 s. What is the frequency of the wheel's)w90xvi.jqr k 0)mk-k, qs1 jkjwm+ if rotation?

  A pulsar (a rotating neutron star) emits pulses at a fre8t/cuf2p imrzrir+t:p1 4f b5quency of 0.40 kHz. The period off+2irrcbu1f: z/pimt548 tr p its rotation is

  A phonograph record rotates at 45 rpm. Through wdu7lu-cs5/e46.jp fxep ic. what angle does it turn in 0.20 . u.ece 47fipjl5/s 6d-wup cxs?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the outuotp 0:d ,i1teer rim move in 2.1 s?t u,:det0pi o1

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. b2je 9f/ wk3.oowt/qj What is the average angular sj2//o3 okj .wefqwb9tpeed of the wheel?

  A bicycle wheel rotates unifog/ oqzqx vler- t k3jj8,o2jct;5i 1 qq+i1,xzrmly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m fz,- qc132oqextj /ti,r8;k+ogqlq5 1jz jxivrom the center of the wheel?

  A cable car at a ski resskk8 cx4d dn2mq/,h 8sort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no8 qhd,m4d 82 kcsnskx/ 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 /c6c7oahf7s mrotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's rim?c6o77a/hs fcm

  The cutting cord on a gas-powered weedwuxf. uxf:n5 ( cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approxi5fxwn(fxu: u .mate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a coadn;zcrq /mx )//e4 3u jvs4(yvs/nkgnstant angular speed of 2.0 rad/s. What isx/nesmz 4vdy4j/q kr(s;n/a /v gcu3) the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle whdydd /qv -upg,k:inx4ujk/2 ,8slsv/ eel of diameter 70.0 cm when the bike is moving 8.00 m/sk g,iu/pyjv /v d,8:xl 4qknu/ ss-d2d?

  How many revolutions per minute (rpm) must a circular, g (ivth39 koxwrh*yhy7(b 3)r rotating space station (r = 1000 m) rotate to produce an artifiro3b y(9h7ywg()3vhtkx h*ricial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ookt1xr6 1rkh 0trtykd. *ez79f 20 m/s. The maximum centripetal force (provided by st.td10 t x* 7okr yr9hkre6z1ktatic 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 radius6t zir ,-38xa+wf ecala*6 ead 50 m with a speed of 20 m/s. *3e +i 86a,eacadz aw-t6 rfxlThe 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, attached tocz;:k y48y ldm the end of 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 what maximum linear speed can themc:;8y yzldk4 mass have if the string is not to break?

  A bowling ball of mass 7 epd)qnah7k v12lxn3*.5 kg and radius 9.0 cm rolls without slipping 10 m down v23nphxn q 17ad) e*kla 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 v /0v7xu dts(kp1ks2dconstant 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 acceleratp/3u.*taib4b5pyz enz+p s p9ion 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 auxeos o. (aet,12w iq0jtomobile tire rotate after starting from rest and acceleratino0t2soaj(i,x.1 qe ew 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 ang zzhb*/0-.e1zl dc4n .fyd oszular acceleration 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 +btz :oyipo/3z*y )ln a constant angular acceleratioyo3pnb z+*ti zo/y)l:n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angularb,3(4mm;ldtbksho yk. s8 u. x speed of 6.0 rad/s while turning through 2.0 revolutions. What iskyuo.x., b 43(k8bstsdmhl; m the average angular acceleration of the wheel?

  A wheel of diameter of 68*x+p fub)j,ff,mpdqa; *gv q4.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel f;x,fj dpg)m,*q+*qbapuvf4 rotates in coming to rest?

  A wheel of diameter of 68.0qgy7u08mt4ha xs:;m g cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What 8sx qm;uh: ygg0t7am4 is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to 2yhty9u 8:c qrrest over a distance of 115 m. How long does it take for the wheel to co ht q2:ru8cyy9me to the stop?

  A centrifuge in a medical laboratop)t*t g.o 4i3azv0 bnlry rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at 403 ltv ba*tgnp oi)z.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 vmw, 0 hvlg1g-3v w6f k:vool-Nm. If a 30 cm long wrench is used, what is the magnitude of lo1o-lv 6: w-,wghvk vvf03m gthe force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 6 uxe di:-k-id90 Nm. If a 30 cm long wrench is used, what is the magnitue6 k-iid-xdu :de of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment jz35rl1j b k1(*j ,ohyuz ngn+of 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 modepat+3cgkzbts,t t+z19pc v)+led as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m1p++ cab pskcz)v3,t 9+zttg t is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axn6y++xxr t* 3 *1lj:vqls .nqlj v 7bwenv;l*xis thought the centej*lwqbvn37+16*e.lxq;l xsn *x:r+t nvyl vjr 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless amyw9dk+9 r4yf rzgy*z*femqzw9x (-t2qpl 2( xis thought the center O. A rope wrapped around the outer ryx pyy29((r qgrzdz -fkww*fz9t *ml4m2e9 + qadius $R_1$ = 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 ros6);c /sq.s7 exssht md is initially held in the horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as itsse6qms); x.7ssh t/c is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be av zw822ohpb7qxtb 7o) 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, h2)q28bb77t xwzoov p assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionlesso iwsy56f(5:le49/ipiqhq tw disk pulley of mass 7.07 kg and radius 66.0 cm. fosit56 :ey9/5h4qq(w l piwi What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs )shs5 do3 fep9w +(meqon a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm.h wds5e( mef9 q3+pos) What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it i tz i3 o(bx1mjf+m4b*gs 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 inertia c .ipe iq(vl7pl5.u /2mkd3oeof $5.00 \; kgm^{2}$ 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 rfi/(twikg c59 ui*s ege.h,m6moow 2(adius 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 rt i (io*hkg(26smowc.f /we 59eg,imueaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a spe iyns6na,4i jo0iutb(ej an7;vy5f ()ed of 10 m/s. How high up an inclined plane can it cl7 uafin 46()ebji t ,(oynvn0i5;ysajimb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fro3e 40b)0smv1vw bxcogw9s pl l;f1w9cf (w0mbm rest and allowed to roll down an inclined plane. How fast is it moving aff0gb 4o (v01evpsx3 bwmbwl9 m 90s l1wcw;cf)ter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without sliphg80b1g9agiot.5m g e ping down a 35e incline that is 7.0 m long. Assume it started from rest. gb0matg1hgio .58eg 9 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 chanv ooyak79e8tg e /a6;cges 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 8k1(xf 8pqm /lknvxa -gc,piq 5 1io3dmoment 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 rotat;3yl-)ncb oz2 sl lw+bing at 5.00 rad/s with arms extended has a moment of inertia-bbc s23 ll;n)ywz+o l 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?