Angular displacement is usually express i3psbhgahf25a *6 ;pwk n units of

  Angular velocity is expreshef *8davb0tccv 18k0sed in units of

  Angular acceleration is expressed in units of z:k (jwtmb 7;1hmv5ol8u, fpl

  A boy and a girl are riding on a merry-go-round which is turni; 6gy-soren7sng at a constant rate. The boy is near the outer edg-yogn6ss7e ;r e, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are;piz+ m- r1eaj0p:tkz riding on a merry-go-round which is turning at a constant rate. The boy pirz+j1e -k0pa:ztm;is near the outer edge, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are rid9 :c1lz2n3em9nlv nviing on a merry-go-round which is turning at a constant rate. Thzcv i23lmne9 nn19lv :e boy is near the 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- yyy(mln2 ng*o)9w,x3l5io ; m bv5cjxround which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has,9*2m y 3om5byxvyn nx(o ji; lgw5c)l the greater centripetal acceleration?

  A boy and a girl are ridi x:9( f3:zddzmt (twdcng a merry-go-round which is turning at a constant rate. The boy is near the outermdd: t(x3ztcdz9 w (:f edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that bmdby;, 8f zlf4/(bbii bodr*6u +0pt is rotating. Which of the following is an accurate sta6bf(pbl/mbz r,tid *40ubiofyd + ;8 btement?

  Rolling without slipping depends om9o; vqsv. nicc-8*owsq 8 x0mn

  Two equal forces are applied to a door. The first for*,bq czz4eludk j,7b0ku5-v dce is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular 40 ebukdz7*qbdzkc-,l5,vj u to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first fvha9sh9wo anl c71cx:6x7 4oqorce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the ga4xo 79l6cqc9os: wv 17axhhn reater torque?

  Two forces are applied to a doorknob, perpendicular to ths fc7 c+;bum+he door. The first force is twice cm7+;f+ b hcsuas large as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity l: b du9yjhw.p;3 pj:hused to measure an object's resistance to changes in rotatiodh;wj .3l:p uyphj9:bn?

  Consider two uniform solid spheres where both have the same diameter, but on9i y odg eguo::tym/age+k05:e has twice the mass of the other. The ratio of the larger moment of inertia to that of thek::dye+ t:a5 oeo0ug/ gmi9yg smaller moment of inertia is

  Two uniform solid spherey vlthbqa( 9+4s have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller v+q( ly9ht b4asphere is

  Consider two uniform solid a(5n8)sdqrtgmfdp*nvh1x jn 9,*d y /spheres where one has twice the mass and twice the diameter of the other. The ratio of th , vsxa95r*/djm 1q8fhnd nnpyg) t*(de larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hasp(g:f7;mpi5slx vz4g .pdh8z mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertiag zf7(dsil4x pm5p8hg;pvz:. about a central axis?

  If a constant net torqueiz )wk cx-r28s is applied to an object, that object will

  The moment of inertia of a solid cylinder about its a+*. u2,rcb5zwxjr 2me h yrk9kxis 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 z(rgpc)42hee c uv- an1nskxn14b7d38u8uq c wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ra4 ngckhux28 qz) c7uc8 e db-pu1(4rn3s a1ventio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius *rrnua:hdu8f1/q jqtr g;-d; R rolls without slipping down an inclined planeh;1 qdt /;*:un rugjr-d8rfqa starting from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls vs 1 g3q*uelq2x*e-mv without slipping down an inclined plane starting3gemq* e sq v1*v-u2lx from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum ofs;r jzn ,(ni;a a system of particles changes when a net external force acts on the system." This statemen,jans(n ;r; izt is

  In what circumstances can the angular velx t;.3s8e (u dy1gydrvms)azhp; 0e+locity of system of particles change without any change in the system's angular y g x dmveeru3; h;t(lpsz8a+0s1d).ymomentum?

  The Earth orbits the j-a4l1w;eukp l u uy uz:69-jrqi94fa Sun in an elliptical orbit. Ignore any friction which may be present. What happens over time4l9uuyj-lap9: e1-zr wfuqu ka;6j4i to the Earth's angular momentum about the Sun?

  The Earth moves about thr3va 0 wi0jzi:z4 mtwiwf0 o;*e Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the followifi 4*jwvi;mr zz00 wa:owt 03ing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a caya23ft7 xxhx1 6) aqfast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about a qh1axx6 37yca 2tx)fthe axis of rotation?

  An ice skater performs a pirouette (a fas;nd dokfj;3eq5e7 (cw t spin) by pulling in his outstretched arms close to his bodyjqdk7eef5 d;on(c3 w;. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin)pgz) 73 dq57wml vg5pp by pulling in his outstretched arms close to his body. What happens to his moment of ine5gvmqdwzl 5p3 p)g 7p7rtia about the axis of rotation?

State the law of conservation of angular momentumqlg62ij o d8vm*+ k2r p;y2jivis1b9l8ub9 iv .

  What arc length does the Earth travel in a three month period in its bm13 4z9d lfzldj7tn2yv3o7enearly circular orbit aboutdzj yz1b l3 ot7dlmfn497v32 e the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distaq9 v;0miqahk b9iwd ./nce does the tip of t qd aqi;vk09.bi w/mh9he second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equ w pt8l(g b1-dac2 b2qcj4ki:fivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What/he,j6odl -a k ;;fj j5llu/dt is the frequency of the wheel's rotatil/ jjh etudk6a-;f/ldo,;j 5 lon?

  A pulsar (a rotating neutron star) emits pulsej0nx:vk a;;g es at a frequency of 0.40 kHz. The perigxekn;v;ja0: od of its rotation is

  A phonograph record rotates at 45 rpm. Through what angleux(5 jusz) d:j does it turn in 0.20 s?:sjz5u(jux d)

  A wheel of diameter 26 cm turns at 15 0v civ2)s*)hi ,qohro00 rpm. How far will a point on the outer rim move in 2.1 s?hr*c iois,v qh2)o0 v)

  A bicycle wheel rotates uniformly through 2.1qx+c7md k 1 h+.wtksu0 revolutions in 4.0 s. What is the average angular qt +c.7wdx1+ hukks1m speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions ins/ .nc. x7j7a yq1a i(p;qpkhb 4.0 s. What is the linear speed s(a. /bjcq pi k.;1n7pxhy a7qof a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 gotd . ia(+u vnwu.e /hs;;-ekkm. 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 ti( .uvgu.kont;ew / ;he-a+ds he trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular spedv6 2j 53 4oa 4fbvcy96ylnbo9hbad*yed of 2.0 rad/s. What is the linearn *9dycyob6 j9b544flvb adha v3y26o speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.1.ukn.dsa xv u(w *v66x6 m in length. If the motor rotates at the rate of 20 rev/s, what is kw.svd6x(au *.n6xu vthe 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 rad/s.ysjg7vlj 6n.k(ubb 5i. vww/.23umpm What is the centripetal acceleration of a point on the wheel'su/ju2( v lwybmm ..g3i. 5s76k pnvbjw rim?

  What is the centripetal acceleration of a point on thzi y)v+xf6 o/be perimeter of a bicycle wheel of diametfi+/) xvb6y ozer 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (kmq8d,m(na +3ooy 4so/ 24 t; hlnmylorpm) must a circular, rotating space station (r = 1000 m)3mdo;/am, slno 4hoy8ytlo (qmk +n2 4 rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiatingpsd-jf* :ui88bkkae7 a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (diupk8 js 8eaf :7bk-*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 of 2069tz2use- mfk5l6 shi3guu 4kl9kn/y m/s. The maximum centm/ lz9 lu -356khue6s 4gut9if2nskkyripetal force (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attmx)orhg jo 7 bzp6x9na. (8g(mached to 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 the mass have if the string m(6b.ao r)8zg(xnjh7op gxm9 is not to break?

  A bowling ball of mass 7.5 kg and radius 9 1 p t3hss):2c+ +jjaxjgo-5*msz czhf.0 cm rolls without slipping 10 m down a lane at 4.3 +zh3ss2sxzftjopa-j 15):g+* mcjhc 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 constant angul9(5yq( 8jf+ gvj7tebb poscv0ar 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 wi13byw2 czbn6p th 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 0.300-m radius automobile tire rotate after h2oo; yf 0m kj( 6gozj6t1v-wtstarting from rest and accem6okz2 0wt1 yjv-ftj;h( 6goo lerating 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 thalubsqko ,fi t oyucd321+ f1+z;/0 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 accele mo9jqqloiorg+*7 rmx.)l)g39/ob z eraqx.397r /o9glloq*ib) emm+g oozj)rtion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reache9bpm o rthtcr6gvz j7-aa* ,2.s an angular speed of 6.0 rad/s while turningoz* 2p6ahgt m, .vabr7ct-jr9 through 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm jk3.m kb6r cdya+wn//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 rotates in comindy/ mkn.bw3ak+6j cr/g to rest?

  A wheel of diameter of 68l tr6(kwwixll.j6uz90 1 ywma wc,2 2z.0 cm slows down uniformly from 8.40 m/s to rest over a distance of 11 wl6lmwj6w1 yx i2rz.0cl ztak9,u (w25 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.0c rfjn 9je,jn5+f3g g40 m/s to rest over a distance of 115 m. How long does it9e 0nc,g5jfn+3g jf jr take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotationall/s u5g.e y4wk speed of 3600 rev/min. When switched off, it rotates 50.0 times ayug5 e /swk.4lt 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 a 30 cm l48jwsrw44 y v b(rqe9fong wrench is used, what is the magnitude of the force required when the force is perpendiculj4ev y(fb 9w4 qsrr84war to the wrench?

  The bolts on a car wheel requik)omykbz c)4hyr/k 90 3-fvd gre tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force rh)yo dkkkz9 0g3vb4cmr)- yf/ equired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ip(ypmc7gmk*c)b x: 2ex ,tjo:nertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follog7n he(ogxj 1+ws: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment o jeh(n7g gx1+of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the uottvvsfs 47e7 (qkh ;e9+8nhceh7ush 8tv nek(+ s74efq9v; tonter 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 axis thought the90w hf;tvyw b: center O. A rope wrapped around the outb9wf v ytwh:;0er 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 initia(eu8mtb rd)coq ) :s:d .-rhkglly held in the horizontal position, and then released as the free end is allo b-mt .k)us qhr:g:ocer)( d8dwed 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 w2 u,wxqo3:fx ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the w xxq fw3:u2,oaxle 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 disk pulley of wju52e;1xx g7xijt; zmass 7.07 kg and radius 66.0 cm. What is the ant5ju72;g;w i1 jx xexzgular acceleration of the pulley?

  A 1.53-kg mass hangs on p1p-do) jmki3 a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleration of the ma 1k3op-jdmi )pss?

  A rotating flywheel can be used to store energy. If id d-dx 7)3n.z) utcs60dh y7h kctizv9t 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 l8pf kv 4xxyfd49d41q inertia 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;f.gs;,dhtiq 1.0 kg and radius 0.010 m starts from rest and rolls without slippin, qtsif;g; dh.g 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 rolls with a speed ofogj+e1;bh/d:-jc e tm 10 m/s. Ho/oe1g:jm jb-ced t;+ hw high up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg i ll,ta5a:o 7m pi:x 1t,aa5mcoy4.kpgs released from rest and allowed to roll down an inclined plane. How fast is it movin4atm:laa ,.aol515:iy g, cpk 7tpxm og after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm 0x7dc 5 hroo5krolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of d5o5oh7c0k x ra 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 changeepz,di(wgo, m+5 zja,o(q2kus 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 io yu ddj1 w hv*c+44g,rbr,;v bvr6f4mnertia 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 e;tomnwik; -bv-(*o yq1:cmn/s with arms extended has a moment of inertin-qeyv ; ;co binmt-*:mk( 1woa 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?