Angular displacement is usually xreaw)80x,ee4ov uv;express in units of

  Angular velocity is exp0b3h6l4bzioy lec ., 2tzsgk.ressed in units of

  Angular acceleration is expressedamaw og-wh racl*f:9+0vk72k in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant fz zvm z5eml k,/v19oqj; h5;orate. The boy is near the outer edge, and the girl is closer to the ce jkoh/z9z; vvmmleofzq5,1; 5 nter. Who has the greater angular displacement?

  A boy and a girl are riding on a4bwsf. n)h)8i emts2o 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.4 h8osems2tfwi)n b). Who has the greater angular speed?

  A boy and a girl are riding on a merry-gox7o2oi r+gho rq/*l-p-round which is turning at a constant rate. The boy is near ther +g-o o7px*o/lqih2r 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 an/jrf gg.6li6 t a constant rate. The boy is near the outer edge, while the gir i/n66lfg rgj.l is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-roujo*;z:xx24: lgszz slnd 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 tangential accezx*zlo ;gx:l 4 js2:szleration?

  Consider a rigid body that is rotating. Wajnsinwsf o5 0*k*d ofz ;k(7;hich of the following is an accurate sns;5 i7*sj(oa0kdfz *nk wof;tatement?

  Rolling without slipp;mtc yo)2. iv ugc6bn6 zx7e5cing depends on

  Two equal forces are applied to a doo) y wb5k1c 3l3yjs8y whui06oor. 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 torqu38 5uy s)ch wl1o6kj0yiwyo3 be?

  Two equal forces aresgdww 5( n,4tl applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to thegstw 5,d n4l(w plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first;0 5xampjylq mk-bk dg1cy8* 4 force is twice as large as the second force. Th5qm*lxgyyc d p48 0-ab kj;m1ke ratio of the torque of the first to the torque of the second is

  What is the quantity nexmb2w(v41zused to measure an object's resistance to changes in rotatix2m 41newzbv(on?

  Consider two uniform soli*e3e4,jpsvg t-fnb * td spheres where both have the same diameter, but one has twice the mass of the other. The ratio of th3t-*4n *p sbftegjv,e e larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one hi db-vk 8fp w*tlx0yiu,fc+qt 7yq/+*as twice the radius of the other. The ratio of the yp*i-u+ /fyvtq* 0+c 78xqw,fbtikldlarger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres w x ;/bfbiyxpf,et-,0 k/q,i fshere one has twice the mass and twice the diameter of the other. The ratio of the larg p-xsib,0f, ;y ib,/kt/ffexq er moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hay1 gg(v,7sk lxs mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of ins(xg1v, k ygl7ertia about a central axis?

  If a constant net torque is applhl 1i2ukikvie si 3mr96(2o l;ied to an object, that object will

  The moment of inertia of a solid cylinder about its axis r0gph7t0ksh(o, j c8q( ildw7 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 oj/fxvwu 5 0v5ifb +2zvf 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 bike? Assume the wheels ar5 vuvi 2/wxfj5vzf b+0e uniform disks.

  Suppose a solid sphere of mass M 7 s97 pdbma)xiand radius R rolls without slipping down an inclined plane starting fri 7ax)pd9s bm7om rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius u6v g)ehqk c+4fk2 0iai7jqs* R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline d si+ci4*k f gkjv60u2ahqq)e7epends on

  "The total angular momentum of a s+ xw 8i0/dk 1l qjzbuii1o3w 3i2q+dqbystem of particles changes when a net external force acts on the system." This statem+i/ z8bqbdiwqu1qdiojikw x 20l13 3+ent is

  In what circumstances can the angular ve 9qrde(z+pc56c4xc w flocity of system of particles change withodz59(r c pc4wx6+q ecfut any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore aad pd1 6l9n6nmny friction which may be present. What happens over time to the Earth's angular momentum about the Sun?napn6dd ml196

  The Earth moves about the dmfxl9wt -(v t98rbg0:8n ta hSun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about tw l9-m gd8t0fat(v:r9hn 8t xbhe Sun?

  An ice skater performs 9 gaf3 gt2*(o4j2ad dsmhyfd8a pirouette (a fast spin) by pulling in his outstretched arf2ag8f9j dm od4t s (*gd2yh3ams close to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretche: igz th xfprtl:u(cq:g .9c36d arms close to his body. What happexgr96tc( zh. t u:pgc:lq:f i3ns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched j-u7g8.s y twxxuxc(+ arms close to his body. What happens to his moment of inertia aboux7gwcxu.u(8-+sxtyj t the axis of rotation?

State the law of cond,+mci77s6, usdf: xs sut7xyv*. xrxservation of angular momentum.

  What arc length does the Earth travel in a three month period wt14lr nbgv 71gwumvpycgv68)7 b2q:in its nearly circular orbit about the Sun with a rad2lq4tn w6g)gu 7g1mb8:7cywvrbpvv1 ius of $1.5 \times 10^{11} \; m$?

  The second hand of ao18jmu5ftb7 wht 2a4 j clock has a length of 0.30 m. What distance does the tip of the sec h a2o4m1 wbjt8t7f5ujond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per miaf224wo )ez1vz. b-fzwz*q z vnute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in ci*zv c6v)ff7 4.0 s. What is the freqvz cff7v)*i c6uency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a freyt 8 n3htf9-6hujj.nzquency of 0.40 kHz. The petnhh-3f j8 6yun j9tz.riod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn ilyj yv fgu9oodj/uh,3 v )8fx,,56pxmn 0.20 , xo p/lv)yfudyj g8 3hvj, 9,m56uxofs?

  A wheel of diameter 26 cm turns at 1500 rpm. How v,w50ayh0asta8yv/ es78en- vui7osv gg5x;far will a point on the outer rim move in 2.1 sv/xaya, gi5tns0 vhas7u8 ;5e vyswg8oe- 0 7v?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is fw +em+ 9olr +f5ewrd2the average angular speed of the whw2fl +r f+ee5do9 +rmweel?

  A bicycle wheel rotates unuts0sj9d (hr:y,fox+g aeb7 , iformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the cent:h(,yeds uos,a9bjfr0gxt+ 7 er of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. d/z pr39u 6 jndm, :scvc.dmb, The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast musn/vsb .p6mzdcr u3c,dm,d j:9t 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 co,od:dvs q+tpglc(c 4)nstant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's +sc4td:dcpoq , l)(vgrim?

  The cutting cord on a gas-powered weed )yuvy;tzm-epltg,5 6 cutter is 0.16 m in length. If the motor rotates at they y;t6zt p-v,m gu5el) rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular s e :4q*zrhhbzg/3d0,2zcszojpeed of 2.0 rad/s. What is the centripetal acceleration of a point on the wzzhe:zs,o/d4b 3h 0zgrqc2j*heel's rim?

  What is the centripetal accel9 pz xlc3hrs44eration of a point on the perimeter of a bicycle wheel of diameter 7044zcphrs 3x9l .0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating spabic v wy,q.55uce station (r = 1000 m) rotate to produce an artb .5,wyqivc5u ificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flatgy m1f o5ja e1(kss1/ms k59cx circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force sa(o /gfmsecyj11s9xk551 mk (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 curv9zr y dfr3c qn,4nf/*ve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (providefnn, c q4v/ 9*df3zrryd 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 st:2;ah dl1fedn ring, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what m dhnaf:2e ;1dlaximum 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 sf:i,g 2*wg xjkw-(:idl: nugzlipping 10 m down a lane at 4.3 m/s. ju*:nwkg x: :-gzdgwi(i2f, l
(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 witu/u f yk.-61dedtjc/ ,y)kzk/c xz,roh 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 angu8 .9pkqds 7w 7 4(u9qf4kea)n2zvped)v dyugxlar 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 rotate after starting 7c79vu*s eiyrv,-yd ifrom rest and accelerating at a consrvsvu7yie7 y di*,9c-tant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has acz//kna :j3f tv12xwxm ,q/uvn 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 decelerates with a constant angular accel4+vi8 illo /saeration ilo ais8+/4lv 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 wef4r *p hmz6:phile turning through 2.rz*pe4pf:h6 m 0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to resj a-9xkl*5epp t over a distance of 115 m. What is the toxp ep*l-ak95j tal 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 3hv 3kbnq 4j48m4g3oz8svwt cto rest over a distance of 115 m. What is the angul 3gvj 4tmz3n4sv3 8k4hwco8qb ar acceleration?

  A wheel of diameter of 68.0 cm slows down unim3)p8 h f6e;m8 egcszhformly from 8.40 m/s to rest over a distance of 115 m. How long does iteme z3pcf 8h8 ;)hs6gm take for the wheel to come to the stop?

  A centrifuge in a medical laborat3yos) hfoot6()pi(rg6u 5q boory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coogyoq6iooh3p)b )6( s(f rt5uming 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. vp u0ohz7)b g4a (rc:u If a 30 cm long wrench is used, what is the magnitude of the force required when the force i)g (rb:az0vhop u4 uc7s perpendicular to the wrench?

  The bolts on a car wheel require23iqeolhh1 4z2n f.p d tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcnqe1po 2z2 h4fdlih. 3e applied at $53^{\circ}$ to the wrench?

  A wheel with moment ul m*4mr,z;ekeb 6 r4mof 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 modele aqfmbgd 567lsdb-ha8b)6 le :d as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia ab: 65daaldgh f6sl8e 7bqbm )b-out the origin?

  A solid cylinder of masi8u3 h m*qozv 05zqa*ss 10 kg is pivoted about a frictionless axis thought the center O. amuq3q z 0* v*szh58oiA 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 the 5 cvgxarfjfa:k(q/( /xx;2l vcenter O. A rope wrapped around( v cx5//l:g2kafrq(xa ;fj xv 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 in 72:x;y5 ukcuc,ynpmk/cmd 80 fa5k xgthe horizontal position, and then released as the free end is allowed to fall. What is the angular acceleration as it is r2kmk /kxapu cydcu;50n :,mfx 5c7 gy8eleased? (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 any qfatxef+b438x;wab13m8qw d mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 Ne +b t31 4;a8f3xwm8ybqafq xw 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;i1f ;ng 4szij frictionless disk pulley of mass 7.07 kg and rai;1sg nzji4; fdius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a friction- tvhu,cg, i 9w 6+/r-dg 8snqb/zaephless disk pulley of mass 7.07 kzgs6h/qi - ahv w8/gu-npbte,,d+cr9g and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it5i ba)e31jv cj 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 inertdkm58 k)+a eqez*v+ yzia 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 and rolls bj+ 3fus -w 2mro1m,towithout slipping down a 1.0-m high inclined plane. What is the speed of thebo wtm 32f om+rs1j-u, sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 1c 6n be(i7u,ttndn0c n5dc0x30 m/s. How high up an inclined plane can it climb before comin5 tc0 3tdcn6c 0euxd7b,(innn g to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest a+/lk5mnkked 7 .t.5mhv9uu o and allowed to roll down an inclined plane. How fast is it moving aftlm9ud k k /v5ke5ah+u.n 7.omter dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipn,i q7,gr,(oxpk a 0cpping down a 35e anip, p o(r7,k,x0gq cincline that is 7.0 m long. Assume it started from rest. 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 changes kc7.mlpddftl1 il8 .si c:41 vby $20 \; kgm^{2}/s$ 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 i( h7jn (/recao7 be7njnertia 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 armsp vew4yl jn:un/uwlc/(; 4ft ; extended has a moment of inerti4jvu ;4 ;n(cnl:w pfwt e/u/lya 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?