Angular displacement is us.9w1hmsh(a5 +qz 1/syhzk u tiually express in units of

  Angular velocity is expressedmu b9g /jfu7e-,ht js4 in units of

  Angular acceleration is expressed in unit(qsdj53 ;rq x jz fqnd61q)kj:s of

  A boy and a girl are riding on a merrqk7xql;1ks g+:1q:ewa eg tz,;jzt.cy-go-round which is turning at a constant rate. The boy ilk,.1agz; t:+ke1js 7 wq ;xqtgqzc e:s near the outer edge, and the girl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a mer(/w/tj5od:gi/ ovz bi +se ro1ry-go-round which is turning at a constant rateo o(/ j:5b iw1trd /iez+/svog. The boy 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 riding on a merry-go-round which is turning at a constant r5 ya atonx9hkfto,k* sb)/0 s/ate. The boy is near the outer edga) x9 h,nokystt 5b/0ko*s/fa e, 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 (j ncxr1q.h( , gth6aga constant rate. The boy is near h 1rh.6xgqct n(j ,ag(the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a meyun,9 :/ybet8x kx:ot rry-go-round which is turning at a constant rate. The boy is ne:xk :t, y9xu 8no/eytbar the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the follo.yvq+ped9 bt0h m(z amk 07e4k231 efh hfy9lbwing is an accurate statement?90e+h(be4d pm039zkhvf2.ftyka 7e1 ym qbh l

  Rolling without slippij)vklxf5 gfh:q:j +rl1fl3 *hng depends on

  Two equal forces are applied to a door. The first force is applied at the m.q-0b+xa *b4 ao8bmab b*hlw gidpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts 0 olm-*ga*w+qaxhbba b8 bb.4 the greater torque?

  Two equal forces are applied tosgqt 2i:r-/ pa a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?r sg-/qp:ita 2

  Two forces are applied to a doorknob, perpendicular to the door. dbu-o; u 1hvl/ The first force is twice as large as the second force. The ratio of to1v- /uhlb; duhe 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 rotav0fhh1a2 i j;r+yrd* ytion yaifyr2r*;h1jh+v0 d?

  Consider two uniform solid spheres where both have the same diameter, but oh ,1vbipodjsj3948 jxne has twice the mass of the other. The ratio of the larger moment of inertd jphj1x,o i4js3v8 9bia to that of the smaller moment of inertia is

  Two uniform solid sphere u 0hf.884n wir)jyq)dm i.bdls have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertiaym j8. 0nd4w)r8q )lfdi.uhbi to that of the smaller sphere is

  Consider two uniform solid s,gf+t 2l0 t:a ze7iyywpheres where one has twice the mass and twice the diameter of the otherw+2ft,i ytz 0eg7 yal:. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and r1y)lh*g wth)k( ku;v radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertiak wy(*rhh) ku;lvt 1g) about a central axis?

  If a constant net torque is applied to +huhc pc2mt8xd1h(6fan object, that object will

  The moment of inertia of a solid cylinder about its axis is given n5l *lbri4)pi/f q0my by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to l/inpl)q fr0 5im*y4bits translational kinetic energy is

  Consider a motorcycle of mass 6bh )lmuhpon 7ed.0: i150 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? po.0h ui)7 :mnb l6dehAssume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slis4+st+ +enq2e vxghln dgpxk /. m34-ppping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom osm+n2.s 4+kg3-txp ngxhv4el/pdeq+f the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without sli;kz- bz51x0s(se1 b+8 ns: fd w akck5isvu;ocpping down an inclined plane starting from rest. The angular velocity of the sphere at the sd o:(81weicz;xu kfz0155s-k;k+n bssacv bbottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net e9rl*kg5dh o qv8zae5 ;xternal force acts on the system." This statement dlagk5eq*r v95;z8 ho is

  In what circumstances can the angular velocity of system of particles chang, nhcj(iljo.fq,s9p6fkt;z +e without any change in the system'skf( cnpizo.6jhf;, ,stj ql9+ angular momentum?

  The Earth orbits the Sun /in2 mv z3t9ubin an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's anguzu/3 it v2b9mnlar momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earthd m;4,/4k sm, z8 ,dftadocdr1dq( zqd moves close to the Sun, then which of the following best z, m,dsqz4 /oq, 8 (kf; a1dmddtr4ddcdescribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pull-/sla -hpo 737e, dwjpleb8t ning in his outstretched arms close to heojw nt 8pa/b - l7dhe7s,-lp3is body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hisk66d0bw;97rvdifg iz outstretched arms close to his body. What happenz06g;kr d 796 idvfbwis to his rotational kinetic energy about the axis of rotation?

  An ice skater perform:/aae3vil ,rg+dt a /hs a pirouette (a fast spin) by pulling in his outstretched arms close to his bodydi+/r hgv:t,aal 3ae/ . What happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular momentum6if5j6fxpup j/xm , 8k.

  What arc length does the Earth travel in a three month period in it, gm 8 6h:7v-j .ewyjdjte, glk5)yipjs nearly circular orbit about the Sun with a rahwj-l)y.vtg8gpj,m, 5:kyj j6 e7e i ddius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance 3ooseu5 u15 ufw;j8xzdoes the tip ofsje;uu 8 uf 531o5wxoz the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equ cu; jg;6tn31c/zm:oz+m*a c* r9s0nyglzui f ivalent to?

  A bicycle wheel rotates uniformly through 2.0 r4p+ :vc,btn, q8ajd :vf j7jzqevolutions in 4.0 s. What is the freque:7:a,vpjcb 4q n8vtz+dqj,jfncy of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 k.9:7 t2hhx5og mx xhjj yke1-ym/ydn/Hz. The period of its rotationhon7/gtj91xyx/ :5dy m ehkmx 2j-hy. is

  A phonograph record rotates at 45 rpm. Through what angle does it turn i) d qhd:17ie/q.q,yvu je2 qyxn 0.20 s?q eqd2)/7h.xyi:,de1qj v yuq

  A wheel of diameter wpy3p3)ee l ;m26 cm turns at 1500 rpm. How far will a point on the outer rim 3 3lwpp;eeym) move in 2.1 s?

  A bicycle wheel rotates un -umfxp* z;(yriformly through 2.0 revolutions in 4.0 s. What is the average ayx; u*zf(mr-p ngular speed of the wheel?

  A bicycle wheel rotates unifyxc4. npt: 4tzb35uqzik9 p c/2pgrt(ormly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.z2nytc4u3qc :gpr4zpptk(t5 9/.bi x 10 m from the center of the wheel?

  A cable car at a ski resort carries skierq uh2a.ll1x)o s a distance 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 to make the trip in 12 2 uh.la)xqo l1minutes?

  A wheel of radius 1.0 m is rce)vj:)mmj lqw5y i89 otating with a constant angular speed of 2.0 rad/s. What is the j)8ij m) 9m:wlv5yceq linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If thea w6pq wbn/p.0 motor rotates at the rate of 20 rev/s, what is the approximate linear speed of p q0a6bn/pww. the end of the cord?

  A wheel of radius 1.0 m+:4x a t 2kj s/. cv:b;5bcsnm0gieeat is rotating with a constant angular speed of 2.0 rad/s. What is the e2i : as:s/ej+k5vb xb.nt c t;0mc4gacentripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bi6 / dsa-xzwfu j63phj4cycle wheel of diameter 70.0 cm when the bike is moving 8.sx6zjap w /6h 3j4f-du00 m/s?

  How many revolutions pe 574hlxdefx4 mr minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gravity x5dm44f7 lexh of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ofqg43l wi9z zcb+5 r+ r3 wr;q/g4vedaj.d/rh d 20 m/s. The maximum centripetal force (provided by static fric 9+g; ewrqddazrzqji 34/g/.h4r bw l5dcrv3+tion) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating s4r fq2,ajvu )a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal 4,q 2fjvu)r saforce (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, p(fxtek/ xn:/fbt-lovv x )7)is whirled around in a smooth level table. If the maximum tvnv(7 xtofpx-):l)/e tkf/bxension that 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 without:,bypn-5f) 8 6epnr/cgswdjq slipping 10 m down a lane at 4.3 mg)fcbqep ,s:djy 5 -8nwn/rp6/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 angula6 ce0cg hs,v(tr 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 d 0 zq6r9*xwuyconstant 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 startinl,0fs tx27 uzbg from rest and accelerating at a constant angular accelera 2uxlfs0bzt 7,tion of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, an i)*-smeoj;qh d has 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/be0 / +z(nfa++kgf3 tmoy nd7cs decelerates with a constant angular acceleration o0kze(+b of ++3tn/7yncmdg faf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed oy+ 2kunf-k u;tf 6.0 rad/s while turning through 2.0 revolutions. Whatntyf - 2k+uk;u 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 rest ove 1ke- :9zqiknxqv2. kar a distance of 115 m. What is the total qaienk:-1 zxkk 2.qv 9number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm sqq fd(c 5c++:7u4x sjbql,gs rlows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the blr7jc4 +, s(xf5qqd+q:sug cangular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly fl 5h-cqic*8wlw t -a;brom 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to t*5ct-;w liwa-c 8bhq lhe stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/m:ndyyi 4fse4* b3/ kfain. When switched off, it rotates 50.0 tiye/ ba:sfd y 4fnki*34mes 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 torque of 90 Nm. my6, .lrhf gj1*jbk 0e3j(iy ty3 i,cwIf a 30 cm long wrench is used, what is the magnitude of the force required when the force i3b*l6r(fyk,,3j wigjy h.0ijm t yec1s perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 cm lq+5dsfe(l(oh4ef p py /o3 1ddong wrench is used, what is the magnitude of the fo /o5 dfpd(l yd3 oh4f+pe1esq(rce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inobf0dg0k h(ye/q,y c8ertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modelezsfrtu *q7su)-jmf :-- 7x ucud as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a.-:ftf sq ruu* m7uzxs-7u -c)j What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted abo6nfdp *g(d) arut a frictionless axis thought the center O. A ro*gda6dn p()rf pe 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 Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thou2s2 cwd 4at; i,4pkdvzjhxm0)ght 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. How many radians does the cylinder rot 4)m0;ti2c 4j ka2,xdhpvzwdsate 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 injn+ .ct7u,muy the horizontal position, and then released as the free end is allowed to fall. What is thetc .umun,jy+7 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 ringw)hwp94f5 1lan-j.j c onuxc2 of radius 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 fonxh j pc-o2lwjf9aw.)c 4 n5u1r 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 frictiony .ft -ya3p8zlless disk pulley of mass 7.07 kg and radius 66 fat8- .zyp3ly.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ofq ge7x/(s qm8m jdx)x9 mass 7.07 kg and radius 66.0 cm. What is the acceleration of the m9 gmxxqx7sq( 8m/ )djeass?

  A rotating flywheel can be used to store energy. If -sxyt rk ug4a7 h-s(sc *.r:srit 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 inertiam3)nwi d5*qt ss7 auis(it9t5 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 akd1ne 02j(gega. tn-end rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches nt -kge0gane.ejd ( 21the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/pggu*n-:g uq1r:2 vt cs. How high up an tv -uurpq*ngg2c1: : ginclined plane can it climb before coming to rest?

  A hoop of radius 0.50 mkl.oj75(xr c,x sf6pb92z okp and a mass of 0.20 kg is released from rest and allowed to roll dow9po,xpc5(.s6kxrjl2bko zf7 n an inclined plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withou/xa;rn/ pz th*9ub5 ):e) uc7fxuib fft slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given b5xucp 7ubhffxu/ne ))/ at9 ;:*zrfiby $I = (2/5)MR^2$.
(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 mommvz1 .h)s1burentum 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 inertiaybw 3a0v,f(ml 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 ha*k vfe1ujil.h9 5 ks:xs a moment of inertia k9*ifkjs1xeh. :luv5 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?