Angular displacement is usually express in iz-;cnnt; /w,tpo:h p1ovk c8xp-u+l units of

  Angular velocity is exprd..0fb n db7czessed in units of

  Angular acceleration is expressed in units3ry+(xeq pzii2; u 3ui7ye6na of

  A boy and a girl are riding on a merry-go-round which is turning at a constanq u;6:jl2 2r0dp4st3eqvjt db t rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angurtjtp b ;d22due3sqv04jl6:qlar displacement?

  A boy and a girl are riding on a merry-go) o+e :tdfndz/znysbf-+ 8.e g-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who ha .nf + b:dgs+ oze/t)y8n-zfdes the greater angular speed?

  A boy and a girl are riding on a mew l.l5s o*ut:grry-go-round which is turning at a constant rate. The boy is nearu5o *t.: lwgsl 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-round which is turning at a constant rat(mjfjtz, ox,g w1z:s .etdtqw92zg3+e. The boy is near the outer edge, while the girl is closer to the center. Who has the greaterj.t(,2+qgemt 3:1wjxzwzdzo9g fs ,t centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turn fc0tfy/ hpqh,vg8 w /0afb/1ping at a constant rate. The boy is near the out, /1gq8hybfhfp /c t w/0vap0fer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which884unpbzlq8 9:qrdrt 2 c nmw/ of the following is an accurate statemenwq/pr:q 2r8 tbc8n8z 9lum4nd t?

  Rolling without slipping depends or-3bj, ,p drpln

  Two equal forces are applied to a door./zbnyv+x1 dl0tm5 n8mwbm6 /s 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 /mb5dmy w+mv/bl06n 8sn1xztdoor. Which force exerts the greater torque?

  Two equal forces are applied to a doorgs v(;3dnwhs15)qukc fn1 2d q at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the pla(2vnnws 15sh;k13q udqgcd)f ne of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. Thew6c7mql2v)cgcqh8l*3 .sa p r first force is twic)m*7vq w38ccclhgl 6ps.2 ra qe as large as the second force. The 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 rmuyc 41mr id89/5(; g dvwcqqzotatim 4ziddc (891q5uv/w;cymqrgon?

  Consider two uniform solid s6e mdk8l n5.ttpheres where both have the same diameter, but one has twice the mass of the other. The ratio of l8dtt 6me.5knthe 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 the bmr f:n g-/8ezradius of the other. The ratio of the larger sphere'sr-ngf:ze b/ m8 moment of inertia to that of the smaller sphere is

  Consider two uniform solid sph:;u2*mbxass , a0odif5 d:dqjeres where one has twice the mass and twice the diameter of the other. The ratio d,5xaajf20m; b :sidouds*:q of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. 3bi kt,65ma)q2ysqm iIf these are increased to 2M and 3R, what happens q5 b3i k,si6m )yqt2mato the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that objqzg a b woq4+;+8kxr(vect will

  The moment of inertia of a solidzp:iwq5t 81t(xcbc kq--ql+ te3,ipv cylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of,pc t:p 3(xtc8qtizilwk e- -qvq+15 b its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass oixq hc;mji ; j9 i8,6yyjx,7xrf 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translationix 9yi r 7yjhmj 8,;;x,xqijc6al kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere0 yb zq iag*bn)0 h7t)n)noll80axa22. wmewh of mass M and radius R rolls without slipping down an inclinenn).wtn*2oebah20wya qi lbz)70a) 8x0m lghd plane 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 rad qd/wf,vo 4yoyn0km ,2ius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere a04 mok /wqyonfy2v, d,t the bottom of the incline depends on

  "The total angular moment0j r b0i znt 786q7dvubu)zuy2um of a system of particles changes when a net external force acts on the sysvyuun2bq0 0z7t d iu)zj7br86 tem." This statement is

  In what circumstances can the angular velocity of3 t(5uo;fb wr y5r*tot system of particles change without any change in the system's angular momeobt3yw5*t;rf(5ru t o ntum?

  The Earth orbits the Su z4p, v -ww9p;q+cbcagn in an elliptical orbit. Ignore any friction which may be present. bp ,c+ wv;cg9z4p-aqw What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. a6r tw2ngb3 :aAs the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earbn:ar26wt 3 gath about the Sun?

  An ice skater performs a pirouettem/k:ol9mg(*ub, c, qwzz 4cfn (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotati(c*fuc4 b9zk z,w:,m gmqn /loon?

  An ice skater performs a pirouette (a fast sgl.+tc 3oqc imo-o q. q1p:s(lpin) by pulling in his outstretched arms close to his body. :-3 l ocms1( qiqo.+o. lgtpqcWhat happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spi h- y:iikk87rqn) by pulling in his outstretched arms close to his body. What 78kq :khiy-rihappens to his moment of inertia about the axis of rotation?

State the law of conservation of angular mxv6hh*k,a 9r momentum.

  What arc length does the Earth travel inc.yz h3z) fotn: wg./u a three month period in its nearly circular orbit about the gh/wo yuzt:fc.z). n 3Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance does q/g.b myj2fp+kycnf8/dn;c 1the tip of the second hand sweep through in 3 minutes and 45 second2c1kybgf8/c/ fp ;jn. yq+d mns?

  How many rad/s is 25 revolutions per minute mior-gq:u ;o6equivalent to?

  A bicycle wheel rotates uniformlakw.k,h/8 vu v *p:hujy through 2.0 revolutions in 4.0 s. What is the frequency of vu,a*kwj8ph: vuk. /hthe wheel's rotation?

  A pulsar (a rotating neutron star) p lcjwxh5. /6hm3wl- ro+0x efemits pulses at a frequency of 0.40 kHz. The period ofljxwfm+5r p ecwo hl/ xh.-630 its rotation is

  A phonograph record rotates at 45 rpm. Through 2a6ylq5 ehh z4what angle does it turn in 0.20 sy zhqa52e 6lh4?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a pou 5b+; waj *ydfp.(rokdleimr;( s(s7int on the outer rim move e;( d ;*+s pmbad(fkw. orr5jils 7(uyin 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolution a +g1f7z)tke:g;9u*g o(bvf dvlhc -os in 4.0 s. What is the average angular speed of tcfub;t va )goe1g7k9 l:dgf- zv+*o(hhe wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What isy9u9lqv c9-ix the linear sp9 yi-q clx9uv9eed of 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 km. The ca. bf)uxg0 0nkfble which moves the car is driven by a pulley with diameter 3)g.0uf0f nkx b.0 m. Assuming no 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 rotatingg c9a i+9li jx0-coev +3oh.wh8ktd/n with a constant angular speed of 2.0 rad/s. What is the+l+.jogihwe cvxdna8h/9 it390 - ck o linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengthq3zkal2m/ :uo . If the motor rotates at the ra oq/ k23:ulmzate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is ;aduf by 9t(8brotating with a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on ybd (ua;8tbf9 the wheel's rim?

  What is the centripetal acceleration of a point on thb6 :biz tmdte/(qt1g, f h+uo5e perimeter of a bicycle wheel of diameter 70tbu+dzt o(6q1g ie:5/thb ,fm.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per mml4 an,74 jcmow68e)syxg;xt inute (rpm) must a circular, rotating space station (r = 10 m7j xx aesg); yl4t,6mcwn84o00 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius zq ;md s-*ap3 t)si*ii50 m with a speed of 20 m/s. The maximum centripetal force (provided by st- psi;s**taimzi3q)d atic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular cu4gx mg(mh-rvoa )3 agj1 i0j4grve of radius 50 m with a speed of 20 m/s. The maximum centripetala )41xm g(jg3vgo4ag0-im hjr 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 a4jl,+bm :tfihnuyp*6 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N,pn+uylfj:ib,h tm64 * 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 without slipping pavw)b5 g.d5v 10 m down a lane at 4.5pg 5ba)d. vvw3 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 angul tdyyk, t;klo)39.a )twbu :kgar 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 ang t8tzwdzmoh500 1ii7wular 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 automobil-e em 6 r1,ega/(efknie tire rotate after starting from rest and accelerating ,ef 1k/6rn a(imge e-eat 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 of /k kycz03zitcy45p7m $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s p(jfhwr l *bv4x/, 7phdecelerates with a constant angular acceleration ofj7(,fv/ plwpbh h *xr4 $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from f jf6p5jrq2gwv -da/2bb)9o m):helsrest and reaches an angular speed of 6.0 rad/s while turning through 2.0 jw b q6 )g)2mhdf-rv/sb :j5l2eoafp9 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dowizic.bv)y6 (z n uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total vizby z (6ci.)number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly f vf+j(rgt ik uc,2f7x7rom 8.40 m/s to rest over a distance of 115 m. What is the angular acceleration?i77j2f( gxk+rt,uc fv

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m+ku lr hpuv(0r: 5 ipwdxba81-/s to rest over a distance of 115 m. How long1rh-x ba d08+pp(ruwikul5: v does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational spee4bvzr(f /-yeo;ro a .v1d bbk4d of 3600 rev/min. When switched off, it rotates 50.0 times at/v;r.4abe1 dko rb4z-v oy(b f 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 torqupbmr* 8k 2-xque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the bk m28 p-uxrq*force is perpendicular to the wrench?

  The bolts on a car wheel 77eb, 1q1)pvgc wk0qp ri *fxorequire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force r1g fo07p pb,)1c *v7ixerkwqqequired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment mov66g)t+fk5ibav x 80 a2njytk8z.mof 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 follows: mass m is at the originw8vvqa v3x); e, mass 2m is at x = a, and, mass 3m is at x =x v;vea)q 3v8w 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is piv0w ndu* uf f9a:5f9dysoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See sad9:y09f unf*fu5 dw Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted abw 4o6 r51cqbl 1p.ptqzaou/;lout a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another sectiontu/ro5a;4b o l1qwlp6 z 1pcq. of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. 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 ip s7z f0w8oj,ym8pqp ,s initially held in the horizontal position, and then rele8fppo,y 78p, 0wzjqmsased 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 radv t j3*;li/u7sslh um5 2qfvj7p.pjs(ius 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, assumin2vf5*qj u 3/p vilu(htpl7ssm j.js7;g it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk h c6w95b1eb iepulley of mass 7.07 kg and radius 66.0 cm. What 9i56hbwc eeb1 is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on y; .ly3fj-cr ft( kdht((q7qca rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acce( h qfy ;(ltck.(q t73rcdfy-jleration of the mass?

  A rotating flywheel can be used to store energy. Ilcw.i/yn; 4ma f 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+htq6isny x/ztfr 0 03 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 w(2loch a8; krradius 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 reaches the bottor8cka hw;2 (lom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m kx9gr ,uhkm;r9xv24/pti- b drolls with a speed of 10 m/s. How high up an inclined plane can it c9t - /4xhr ;dub m2v,pixkkg9rlimb before coming to rest?

  A hoop of radius 0.50 m anv+r, 11.0bdo/ t bbz6miytnx id a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical mibbr. ity10dto,z + 1b6vn/ xdistance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 6f4bh fa:hd vs3 sy:pb)hvzj (*;3poi35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere isbdpyi:oha 6hs33b:4vs(* ;jpz)hv ff 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 momentuja -i/f127h x(vjbcpbm changes 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 in(11 c l8 0/tighwtoxtwertia 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 extendekk e0btpptj.n,tt0 ji* c/ 7-hd has a moment of inertia of t0ihbnt*p k/ e-tj, kpj7tc.0
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?