Angular displacement is usually expr 9twxp:q5v l6aess in units of

  Angular velocity is expressed in uni*ow, gxai/6u fbrlf: )ts of

  Angular acceleration is exprft9maljht22 8dkh 4c7essed in units of

  A boy and a girl are riding on a merry-go-round which is turning at a constant a3:o) 4xu;t n:gpw jkprate. The boy is near the outer edge, ang;k: pojw34tp:uxan) d the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are ridino-u9tl 9fog)3u8a z45ntk jwjsku7 dsvz+u*.g on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl ul 5wofus3n7jtso u8)za* j-k4+kz9 gv9.dt uis closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on r1omak /7q1pgvm a/ h/i r a7:1jpmjgk(sq60na merry-go-round which is turning at a constant rate. The boy is near the outer edge,6rnom p: /kggs i1m/0 aj 1(maja7qr pkqh1v7/ and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a me q4u .x h3giy*gnrk0byqw fnk2d-2j2:rry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to thn iyyn0rqqgh2f4:2bk2ukd*3x w-j.ge center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry+e3uph .6q ueyz md67l-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+ lu6uh .zq6deemp 73y has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is yltc4i0 n-.wk;fbbb ;an accurate sy ftkl i4bbw;0;n.c-btatement?

  Rolling without slipping depen0ba(ia 2bgucn*9jju :ds on

  Two equal forces are applied toa w9;a1q4/ocgmdu8u1 y0ie j0y ov zp. a door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Bothqa4ywm0 /g dy10ap uo.; ej8uo9 ivcz1 forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknod4glj (hw,)o ib. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which fo4d),g (iljow hrce exerts the greater torque?

  Two forces are applied to a doorknob, peys*0.jjxo6 ar rpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the fir6yro.* jx0ja sst to the torque of the second is

  What is the quantity used to measur) l j47m.hmbcee an object's resistance to changes in rotation?.mj4cb h7l)me

  Consider two uniform solid spheres where bd(c6nj.uv q9oun/* hf511 tnz mnzdd7oth have the same diameter, but one has twice the ma u9vcf nn5n(7 .h/1nmq*d o6uzzt1jd dss of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice u -dya*klo/ovc9 u3c+the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphere c ycd-kv9o3o l*a/u+uis

  Consider two uniform solid spheres where one has twice thhf: jpf7n*2g6bc un9d- g sqp0e mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the small *npsqf6fb20nj 7c9hdp-: ugg er moment of inertia is

  A uniform solid sphe;vtg+wg l 3/iqg4g o1jre has mass M and radius R. If these are increased to 2M and 3R, what happens to the g jgq w1v4i;ol3g/+gtsphere's moment of inertia about a central axis?

  If a constant net torque is applie 4o0kc3lew 1edd to an object, that object will

  The moment of inertia of a solid cylinder aboug(jpwc: i7: hjt 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 a s-9y2u )gaxemnd a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of a2-y ex )msug9the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls w3/of) lyzjr*,1 :tnkim nd e;hithout slipping down an inclined plane starting from rest. The linear vzthe 3;o,idm:rj f*lky /n)1n elocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down a9c8ac,p 64es xw2sle cy01d2zb)pvdcn inclined plane starting from rest. The angular velocity of the sphere at the bottom2 4 e8pz2acw yv9dcx0esbc)pcl16,s d of the incline depends on

  "The total angular momentum of a system of particles changf+b)98ar oh0 rx(rz ktes when a net external force acts on thexr08h k(a o+fb r9)ztr system." This statement is

  In what circumstances can the angular velocity of system of particles change j.yxnja gyt9*d.yc/;q )ue h3without any change in the system's angu/3ejd*)t9 x;quh.a cg y.jyn ylar momentum?

  The Earth orbits the Sun in an ee0encnqgg/9ppl s1(i 8,6oi elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about cii(qp6e0 / e ,8negpgsnl o91the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves nzkrj:)4ncme4by+i8p ro 7 2hclose to the Sun, then which of the following best describes the orbit2 nz:jpr4bnr 7o+k4ie)cmy8 h ing speed of the Earth about the Sun?

  An ice skater perforknov j+-2t 1, vwb2l ga6to:uvms a pirouette (a fast spin) by pulling in his outstretched arms close tw :vgov o -bv6u2tk j+,tanl12o his body. What happens to his angular momentum about the axis of rotation?

  An ice skater perfor1qyn5md84 f mpms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational qf8p5 ymnm1d4 kinetic energy about the axis of rotation?

  An ice skater perform8- b lvz5fy ) xwmlos/g1:jsa1s a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axi l1bo)y1j - w z:8fs5/lsmagxvs of rotation?

State the law of conservation of angular mom h :/y4a,/ibgvekw*o bcal+j3 entum.

  What arc length does the Earth travel in a three month period in its nearly cgmv i-io wnv -z z*a7h2i*(e3bircular orbit abob 7i*mioi (eg a h3--v*w2zzvnut the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a leejnw*8p; +mamua g9: ength of 0.30 m. What distance does the tip of the second hanuaw: me+j;n*p98em agd sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revec.(+zu ngj 5qwp 2l1dolutions per minute equivalent to?

  A bicycle wheel rotates uniformly ut/ +dqf :og liq4/3hsthrough 2.0 revolutions in 4.0 s. What is the fruqg3lh+:4t// f qosd iequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Th9nlphqp hij;b a e-:q,);+nsje period of its 9,nq l pspqin-j:he)+a;;j bhrotation is

  A phonograph record rotates at 45 rpm. h4fu l2w+9zff Through what angle does it turn in 0.20 s?fh 9fwf4u+l2 z

  A wheel of diameter 26 cmpo/t b2tp4059ccjqf;5 dwlk f turns at 1500 rpm. How far will a point on the outer d4k; 5fwt/c2p5cfl t 0 opbqj9rim move in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. wz1uq:e0rl ex8u5o ,lWhat is the aver1x8 e wu: oue,zllq05rage angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What ;j1,son ;at ysis the linear speed of a point 0.10 t,s;oysaj; 1nm from the center of the wheel?

  A cable car at a ski resort carries skiers a distan;inly dj*pa,z7p+q . ece 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 pulley rotate for the cable car.i;na z,q*pldp 7y+e j to make the trip in 12 minutes?

  A wheel of radius 1.0 m 1 +hjb1z: b8idc)9 ;bisnllmu is rotating with a constant angular speed of 2.0 rad/s. What is the linear speed of a point on the wheel's r u9 1bmbi ;idh8z+ln:jc)1lsbim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in l lwd::) rfu /;e dbzpf) e9fcr1pex5t+ength. If the motor rotates at the rate of 20 rev/s, what is the approxi/durpbfr; edtx pz)9+5lf:1 ) cef :ewmate linear speed of the end of the cord?

  A wheel of radius 1.0 m is ,n,0t:bm pjs+a7mdlu rotating with a constant angular speed of 2.0 rad/s. What isl,man,7m: sptbuj+0 d the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a po *;yo q)kn xz8a(s3hbpint on the perimeter of a bicycle wheel of diameter 70.0 cm when the bikeo sb;kp3(x*qza) nhy 8 is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space stat 0jvz2t1 /x/k5cf-9ef9ac,sj tf bhpoion (r /ec9fkjs1b -5v ptt o,0xhzf9c/jf2a = 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/sq(61/7wcr f+ y3h) vb2ho v ohvei0aom. The maximum centr /ech+ 1i 3wfvarmv0qoh76o hv)ob(y2ipetal 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 with a speed ogls-v4 ( szz8k6pti-pf 20 m/s. The 8 ss lk-t4g-ippzv6 (zmaximum 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 to the end of a 0.750-m string, is whirled aroj5d wff:4;;azn0lt kx pv; )fiund in a smooth level table. If the maximum tension tha5 wzdjn lv:ki;40x;) ftfp;fat the string 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 c7)ddf(y6gao 2h wf2d qgdo9d.dyo )/di(a .owithout slipping 10 m downoi c.dh.fd(y29f odga)ya26ddwgo )oqdd(/ 7 a 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 7/9k +b uaa;4ez8o 8yptvnlcuh 5;iw ha 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 accelemd;w-5uh;o q pration 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 afte4jyz 5 im-xx+er starting from rest and accelerating at a constant angular acceleratijxxe 5 +m4-yzion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelerke-l84 yox,4wv ba5 kaation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating qto)p6)8djrrfh5m/ ,* ffup r8 +noggat 20 rad/s decelerates with a constant angular acceleration ojf, po5qo8/rt hf+6g)rr8f d*gum) np f $-5.0 \; rad/s^2$. 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 v btf1f89- im2jc)j;dnwpo) y while turning thvf;jt-9 cfpj)bmi1won8 d) y2rough 2.0 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 t:,w;0yt ;gmcxq 5qu4fh4o p:iqov bi/o rest over a distancev;i50cqmiyg 4/ hu pbo ;4: wx:foqq,t 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 rese7 ql5doe67 q).13zf mczwvypt over a distance of 115 m. What is the angular acceler voe7lye3 mczqzq56dw. )f7 1pation?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/iffs.n q*clvxf rw ,c-*..4y zs to rest over a distance of 115 m. How long does it tl., .xqn*ivzfw4csf c-*. rf yake for the wheel to come to the stop?

  A centrifuge in a medical laboratory rot avm;x83 fulut:z-t t; )s*fmqates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 ti;zf)fv * qmttustum : l-8;x3ames 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 requn( tczr;*xm i*01zeehov-1qdire 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 ;on 0merxi 1*-zqeh *cz(td v1force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. x btn fn8f:b2-If a 30 cm long wrench is used, what is the magnitude of the force required when the -xb f:bn8nft 2force applied at $53^{\circ}$ to the wrench?

  A wheel with moment tkn y ro1a,l/: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 modeled as foiq:e/x6uyx j 8llows: mass m is at the origin, mass 2m is at x i8 xxu/e: qyj6= a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionzcoqh: gmr b*f/w*y+: less axis thought the center O. A rope wrapped around the outey g/:*bzmqhw:c*+rfor 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 g:y0 sn(wq2:qc t5 wormass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius wtnwqs:y(q0 r52o: cg$R_1$ = 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. ,xr5dl5qg eh7dcr8w1p( 7ywm The rod is initially held in the horizontal position, and then relea5wc1x7mrl r,dy8( 5 gd7 hwqepsed 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 nt*,p7lgwrgkk8/;*2cjsps :l w m.5( qvlzs acm 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, klj/rtp s:,nza8.c lw mw*5psvq7g ;k g l2s*(assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrappeb*sr v:n+ ddeq2fvie,k* :k.t d around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pull evd:q :+*kv ,stebi2*.rnkdfey?

  A 1.53-kg mass hangs on a rdapg 7oi8 ng./vj46uv ope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration vggv4 7n diuo p8ja/.6of the mass?

  A rotating flywheel can be usedibv jpz;d0z:gu6du,/w i me3) 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 inertia 5(xe1.gmktw g:x 6bceof $5.00 \; kgm^{2}$ 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 masnb:q))mz h/lm i5da*ps 1.0 kg and radius 0.010 m starts from rest and rolls without slippi)bnhaq dp /:zmm5*l )ing down a 1.0-m high inclined plane. 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 0.010 m rofbmq r nb1 7c8d66nmn/lls with a speed of 10 m/s. How high up an inclined plane6nbqn8b 6mcf d7rn1 m/ can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg iso8 6uij*dvp6)yz lf7tiialb 8b5/ 0gi released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance5uly/7db0jiiaoi *6t gf8 iv6zpb)8l of 3.0 m?

A solid sphere of mas hs:lw04: bwb0faumj.s 1.5 kg and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia 0fj 0wh mb.:us la:4wbof 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 by /l)vsua1zo o 8o95qtf $20 \; kgm^{2}/s$ 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 (zm(xuo -tf ku3d(k6qtot tyh)4 /0rdmoment 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 rotating at 5.00 rad/s with arms extended has a moment 4b3 ;snzr s9d,ihw)zlof inertia ofws49 n,3r bizld);szh
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?