Angular displacement is usually express tpyk ;6b9mzouxc8*; en 08shgin units of

  Angular velocity is expressedmnl8f q3eg)v 9 in units of

  Angular acceleration is expressed in prbqej iu93lxk9 4v 9*units of

  A boy and a girl are riding on a merry-go-round which is turning at a consta.k tp 4y3;u*; m)st(+qwlomu ocf cu*ont rate. The boy is near the outero fp ulto4 o;(3mu*ucsc)+y t; mwq.*k edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a .t 28bo x aqbwg)2,sbeconstant rate. The boy is near the outer edge, oa qb )2 28w.ebgsbt,xand the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a:+8wp cq8uckj constant rate. The boy is near the outer ecc8 :jwq8u+pk dge, and the girl is closer to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-0vjrg1+ clpwor m8)/mfi ls44go-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 centripetal acceleration?8wirrg4l4m)om f/c+sjv lp10

  A boy and a girl are riding a merry-go-round whichtylor6dqw0p:ny a /81 is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the o10q8 ypt /darwln:y6greater tangential acceleration?

  Consider a rigid body t*xc6huq a w:5xhat is rotating. Which of the following is an accurate statementqa :cx5wxh6* u?

  Rolling without slipk qfgdn7kt+yru: oj-3n v2u- )ping depends on

  Two equal forces are applied to a door. The first force is appliedicgc36k..s -tbna4;l7lhx z kmb1re1 at the midpoint of the door; the second force is applied at the doorknob. Both forces ar;n tm7 hei s1br.4ca3bzklgxl1-6 ck .e applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first forlwt *zxo g2 z)g4qnq7-ce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the goxn*)ggq7 tql zw2z4-reater torque?

  Two forces are applied to a doorknob, perpendicular to the door. The first forcc5hgmt7uhcxq+9* ar z -59xrye is twice as large as the second force. T-cu957x hayt*9+crqxz rhg m 5he ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes in ro;rwrz6) px-wx tationr) r6wwz;xx-p ?

  Consider two uniform so-tu9ctjgh9f*. ohf. p lid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger momen uohpjg.*9htft 9fc-. t of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same/:nree9l r5kltk7iz+)9o ;jq4 jl tz r mass, but one has twice the radius of the other. The ratio;j7tj)q:9n+ o5tlr/k zr9 kel izrle4 of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform41m-5 .yjdxpz gg, qea-;uahj solid spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment gj j5.; a-a,xmedhy-zp 1qu4g of inertia is

  A uniform solid sphere harn gy rryf-r 5p)j rhvs*.+412iy7 slgs mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central a-fgv rys7*n +gj 42lr syr 5ryp1r.h)ixis?

  If a constant net torque is applied to an object, that obj9:*u dve)pq ezect will

  The moment of inertia of a solid cylinder about itxci 5+ux:j e-es 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 whic0bhbf3e/f ukge )lc9:.k0n, mb mwn tw9oh+;b h has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels t ec9wb9u/.b t h nk +mgfomk):nlb0f0bw3h;e,o the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M ajs 1ov pl1(fq3nd radius R rolls without slipping down an inclined plane starti1pq 31sfov( jlng from rest. The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M anbi4u m1 re)t*ud radius R rolls without slipping down an inclined plane starting f tuem1u i*)4brrom 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 whh x/ge )m(nam h (zo1,ngunf4*en a net external force acts on the system." hn u/ g1(em()znmf oh, xg4*naThis statement is

  In what circumstances can the angular velocity of system of partic. si u br.1a0gpc0aby*m +w*fxu ;th/zles change without any 0zuxh i1c+fa;0 ya *g /wtb.bms .pu*rchange in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. okj+x k( x0411t sam;zakipe7 Ignore any friction which may be present. What happens over time to the Earth's angular moment1ztk4smx jai7;x(ke+ ko 0 p1aum about the Sun?

  The Earth moves about the Sun in an elliptice4 a*mjyia+ bu)0co6gal orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed ofo4bay+6 ui j)a0m* ecg the Earth about the Sun?

  An ice skater performs a pirouette (a fast sppdue0f a q+:5tin) by pulling in his outstretched arms close to his body. Whatq5t0epuadf :+ happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouea1dpp4 1 3yf+ewyf6ln+oba c-:acs)vtte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis fy)d 1 c:yp-36 +f 4npoabavcwe+1a lsof rotation?

  An ice skater performs a4lx4/cj*zx im4n x)jb pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotation?/xmj bxl4*n izcj4) x4

State the law of conse+yj yu0 hvno.cxr))ol7t u6l0 c4v9burvation of angular momentum.

  What arc length does the Earth travel in a three*os 3f :x: v2ycmhjv tc(:tn4v month period in its nearly circular orbit about the Sun with a radiuscmj3: 4vnvot2x: * f:tv ycsh( of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distag0l +,j*pwudbe7+ hq18gblp qxbf/+ab yn6x 0nce does the tip of the second hand sweep through lb+*n pgdq ,wp + y0 xbj7ufbh1g6leqxa80 /b+in 3 minutes and 45 seconds?

  How many rad/s is 25 xh1 .2hmejiz/revolutions per minute equivalent to?

  A bicycle wheel rotates uniformjb5-do+i qwto1 wj8; ply through 2.0 revolutions in 4.0 s. What is the frequency of the whei 5o8w;-1 d+jptbjqowel's rotation?

  A pulsar (a rotating neutron star) emits pul44ctim z*2du ytt8(jt ses at a frequency of 0.40 kHz. The period of its m*d t8c4it4(tutjzy2 rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0.20k+ izz r 3,ed6jl+hec3 6z+3lhi dzk+ejr3 c, es?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on thofs.)b 8pt9e g skg)c)e outer rim move in 2.1f)9b.o gp ssgce)k)t8 s?

  A bicycle wheel rotates uniformly throughyc 7f9btkjv7k-e)jo 0 2.0 revolutions in 4.0 s. What is the average angular speed of thf)7kky0t7 -bj vj9o cee wheel?

  A bicycle wheel rotates uniformly through 2.0 revoluti9(f4(olnohhh-ny ,hrons in 4.0 s. What is the linear speed of a point 0.10 m from th4l o9 (on,(r-nhyhfh he center of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cable whi6*rf s1((ldnp pg0r klch moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must the pulley rotate for the cd(n1r pfl* 60lgrsp( kable car to make the trip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constant angular speed h2e+)bs. (tfzh 7mdchof 2.0 rad/s. What is the linear speed of a point on the wheel's rm 72hbec(hd) sfhzt+ .im?

  The cutting cord on a gas-powered wcnc p/m)p1,-avw5 .r(o x ehxmeed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate cpr hm x(-5m/c.an1oxe),vpw linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant anggui0o.*f,if2fd ha ,iular speed of 2.0 rad/s. What is the , i02ofai. f,hfigd*ucentripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of -u 2bc7s;278d 8ros -zlw9l/suxex :ii sgxds a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mosl/ 2u8xxg8xdcl:- 7 s ;o-is7sbise2z9wud rving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rott1 gck txf0hhk)9bhaa)a ++,pating space station (r = 1000 m) rotate to produce an artifip+ h)kcab ,+xt0 kgfah1a)ht9cial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed osxao uw2. )/husitk 3+f 20 m/s. The maximum centripetal force (providus i t sh32w)ax/.k+uoed 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 spee (uh1 )1wl1x sjq:n myeni. a8vjn52yud of 20 m/s. The u 2wy lj1avh5qn(1s )i1:unm.xj n8ye 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 to the end of a 0.750-m string, is whi z9- lkvg.-k2ws i6fv.yrh 6lvrled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, t9k2r- ky.-v w6h6gfvvsi.zl lhen what maximum linear speed can the mass have if the string is not to break?

  A bowling ball of mass 6p qn ynlu y.i;fd50u;7.5 kg and radius 9.0 cm rolls without slipping 10 m down dfq.n0lu;nyu5 y i6;p 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 a constant angular acceleizj -cs(v, v0e -3en)w2 weddsration 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 accel +zeymv +gx39zeration 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 6-jtn(kf gmf7 tire rotate after starting from rest and accelerating at a constant angular accelertjf6mk gn(7 f-ation of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and h,d-koldjes9prl7/3 o as 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 decelerates with a constant angular accel7*t k4 av4ugywgja8at3z21e peration o4zta*41uy8v3pk twg 7ae agj2f $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an u:*h (hu*aain8csjz4 angular speed of 6.0 rad/s while turning through 2.0 revolu8suai*zj4a nchu * (:htions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68du-(cz:01t; otuexg kk j+/ge .0 cm slows down uniformly from 8.40 m/s to rest over a diso+gk0 e etk( xu;zcd1-:t/g ujtance 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 /.n m(ty)eys ndown uniformly from 8.40 m/s to rest over a dist) eyty nm(ns/.ance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cmn7spml4-2s cv q 1vo1h slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come too7 l c1s-n 41pvmsvqh2 the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed9iy cixu; p:jz4 l bw/;pqw,w0 of 3600 rev/min. When switche4ujziwwi;l0:;, /xqwcy b9pp d 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 torq g ftc219yzld78shkn: ue of 90 Nm. If a 30 cm long wrench is used, what is the magnitutyc9slkg z2871 nhfd: de of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a tor,fb-svpz1,vi . ll*/ 4vq; wm*xyo ewqque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude le vx.-*/q q,w *pwv y;z1sovb,i4flm of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment yaz(qt zp03 g3of 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 bx( hagk 9)59my ei0dofollows: 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 aboyx)0 ib g99mo5kad( heut the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictiopslr1h1 jih :+ fhg2i4nless axis thought the center O. A rope wrappsr 211fi:jghlh+ 4p hied 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 /g *tdh8q2cu4i4 iucspivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius 4* u4dqg2ius8i/ccth$R_1$ = 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 i6l.a eqhqib+3 n the horizontal position, and then released 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 3q6l+ah .ieqbis ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and nd he)an-j z:j1.dwz:mass 1.5 kg. Neglect the mass of the axle and sprocke.nnjhw:z : j-ze)d da1t. 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 w.-ea d.enth4on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. w4e.a thde -.nWhat is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around y)rk8rthxpwf0:)5iq a frictionless disk pulley of mass 7.07 kg and radry p5r0)tf:8q ihk xw)ius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requirdxtls68yh;1fs) (/2zw gpk;y*oia dm;mk-g ied 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 ofp9d1o /+s mzwyvpfv qa sl;;n-h m50)x $5.00 \; kgm^{2}$ 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 wie69 i hw+iwwe;thout slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottomiwee ;w ihw+69 of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rollsjwyg-x ry0sbyu9-* v -0nbsw, with a speed of 10 m/s. How high up an inclined plane can it cljbgy-*-, yxwn syrsb uv90 w-0imb before coming to rest?

  A hoop of radius 0.50 v7tr9c vjqr9yrx:8m( m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast isy :t9v r rcjm(x7qv98r it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radiusfkvv0nxvx.dv lkevi2; y/6/ 3 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment ovv e v d6ln/kkf2 0;y./xxvv3if 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 changes9 avb)v jxjq:z )yi,m6-gi ,kn 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 mom79 t;lo+rs gedent 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 ext7ys(sjhnbm:gkquh(4; )f(h9m g mw,tended has a moment of inertiy mnhu(b jmghq gk9)s ;s:whmt,7f4((a 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?