Angular displacement is usually exp6phaaevd07tbpp b8*-u qu mjw i3;4 )vress in units of

  Angular velocity is exmmbe::n -g1; 3 prwcxnr7qa)a pressed in units of

  Angular acceleration is expressed in unioz4li9w sgx80d2 jpb2ts of

  A boy and a girl are wpw 2,9i s ghz6(nwo6driding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the gioz26wg(9w nwd,s6 hip rl 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 th.c1z;k1dq l 8 jyv(egm.z ku;urning at a constant rate. j zhq8( dz11luky k.me;c;v.gThe 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 coxx89 y*g bdau7nstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speedxb*9yau7 dx 8g?

  A boy and a girl are riding a merry-go-round which is turning at sa*bsdzbp2*ee964zng d 1+ :a 2phw jia constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration2 nsdp+ zsj2bia w4*h e:*adbe6p1g9z?

  A boy and a girl are riding a merry-go-round which is turning atjc w;zymx+;5o+mb mh: a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential accel m;zob j+ mwcy:;5+xhmeration?

  Consider a rigid body that is rotating. Which of a 1sz4epnhz )))nx* cothe following is an accurate statem z xpha o1n)zec)n)4s*ent?

  Rolling without slippingd, ;jw c3sp,ljha.(oe depends on

  Two equal forces are applied to a door. Thdxfwx44 fkc:.j man5wmf1; g;+;ccoke first force is applied at the midpoint of the door; the second force is applied at w1xjockfk 4d afm;m; c4fnwcg.+ 5x;:the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied koto 3a7h3 fl*to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to to3fl7o ak 3t*hhe plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular vqsn) : in,,abto the door. The first force is twice as large as the second ba:viq)s n,,nforce. 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 resistanclqis,r *ur,r 1e to changes in rotation? rusr,1r qi*,l

  Consider two uniform solid spheres where both have the same dixe7ty- xo u6+7 dtuvt/ameter, but one has twice the mass of the other. The ratio of the larger moment of inertia t7tdxxuv+-ye7t t6 /ouo that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice the radiuswi ;oc dr 9cde45e+n+i)mqw 2k of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphrce2;45wmd +9qonwi+ dk ei c)ere is

  Consider two uniform solid spheres whej,k0s4 c.yharre one has twice the mass and twice the diameter of 4 hy.jrk,ac0sthe other. 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 rads 9h b+,n zg5v on7:i2+z f3vr)gvinffius R. If these are increased to 2M and 3R, what happens to the s nvfo+,n3)zf9hvb +:gz 7i sif 25ngvrphere's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wixg5l.kc co8y)ll

  The moment of inertia of a solid cylinder about its axis is given by 0.5 fe,g7lq6 m 4ojMR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to l,o4q6 e7jf mgits translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of which has a mass of 10 kg4w*+g noq ;o d 4oiyu5nav(u6r and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total44iawonug;rq o*v+5u(ny o 6d translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radi; hytbe7r 8ii d:y(-zius R rolls without slipping down an inclined plane startii7hi ;ibdyr(y:t- ez8ng 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 without slippi3;l.6c)mh zp1cw sxdl ng down an inclined plane starting from rest. The angular velocity of the ssh;dcmxz6lc p.l1w 3)phere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes k1,mq ,bo-mpd3w7 (o bzdb v+dwhen a net external force acts on the system." This szo(3b,w-,mbv qd po7dd+1k mbtatement is

  In what circumstances can the angular vel . kzp7:w,hhezgex:: l (j5qegocity of system of particles change without::ph,l. xj h5zgq k:zg7e(ewe any change in the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbittg,ri x 4yhql0 d3x-q9. Ignore any friction which may be p9qghldt i3r0 y -4xqx,resent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth mour94 cgx34we vfks ,c9ves close to the Sun, then which of the follo s 4vuwk949fx3grc,ce wing best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast s. mt6zgx+lz x3pin) by pulling in his outstretched arms cl. zm6tx+gx3l zose to his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in cdrsx)q zm 69e-o. hn +nnds6c+o1gr5his outstretched arms close to his body. What happens 1e.nxomd+o6cngds r+ 95 -sq6hzn rc)to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) b6kk w;) jr(wpry pulling in his outstretched arms close to his body. What happens to his moment of inertia abopr)jkrk(w 6;w ut the axis of rotation?

State the law of conservatio9yrzp0 3ti ak7 1mwmiy;)d:ay n of angular momentum.

  What arc length does the Earth travel in a three month period in its neart fe),ab7ictuu*, 5ptz o)d s,ly circular orbit about the Sun with a radius of, boi st,tt e *z7cfupau)d,)5 $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a lengvfi/h 3si:j z8th of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 / 3s :ifj8izvhseconds?

  How many rad/s is 25 revolutions per minute c,6 n rpniyd.eowa0 ie99a48sequivalent to?

  A bicycle wheel rotatepkn: od i, a5u:p,s:zis uniformly through 2.0 revolutions in 4.0 s. What is the frd,5 ,n:auip i:zsk op:equency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz.td yw(m +;j)dvlieh*2 The period e+*(v)dty ih d;lmwj2of its rotation is

  A phonograph record rotates at 45 rpm. Through what angle do18abdl *hu16/lj o iznes it turn in 0.20 s?ih a n1jz1u6dlb* /ol8

  A wheel of diameter 26 cm turns at 1500 rpm. Hovm ed4/,z wvx3w far will a point on the outer rim movev/,4d3 mvzw xe in 2.1 s?

  A bicycle wheel rotates unifor::ckveh br,e 7hm0 :tumly through 2.0 revolutions in 4.0 s. What is the average angular speed r07m:h:bku,hce e:tvof the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutiontg1m6r) / cqcpump0 o;08gme2bv cx,cs in 4.0 s. What is the linear speed of1 0cmvqx 0,um6e2b8c) m porggcp/;tc a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries ski6ai5xys:nm6 l ij6(jhers 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 t(sn 665iyh xl:ijaj6 mhe trip in 12 minutes?

  A wheel of radius 1.0 m is r1fp2 k+(n9s)td upja qotating with a constant angular speed of 2.0 rad/s. What is thqtsj)+( 1 up 9f2dapnke 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. I f (kce9vm/x 1. kd3+f8nunq;vwikgz +f the motor rotatewf/kkqnim.ked+ 9+g; n(x8vv3c1 u fzs at the rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular spevt au -qn* l5e(jqymu0 :i2s)ved of 2.0 rad/s. What is the centripetal acceleration of a poma uq (i- v5y nvtsej2ql)u*:0int on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicycle 6 w2p-w r9.r7x rmjklawheel of diameter 70.0 cm when the bike is ww-pmr 7j 629la.rxkr moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space statiorma7d(d wh+ j3 lsvkh 4n *)6c4urhed8n (r = 1000 m) rotatvdhkh +d4crjl38m6h*) ruas dne7w4(e to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating are2k*y nq z*3kba 8x/keumru./djr5 5 flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) is 5e k3kn d*r./ae2qmzukj8bx rr 5/*yu $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular curve of radius 50 m with a spee*i:kaf-5g vhc go07k77 lli okd of 20 m/s. The maximum centripetal force (provided by stg7 7*g of-av5k0 clk :ihk7lioatic 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, yi b co* q8lx/.p,8fkais 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 .c yx8,ipbl/qo*kf8a have if the string is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without ykj,nob)g+o ux ;s: /9tr-ffpslipping 10 m down a lane afojx )fk9/st- br ; ,op+ngu:yt 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 wi; b .re;bm(y)us*ap mzth a 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 consts rcy ++y+oft vky+9n;ant 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 starting:6j ; mrjwnz k1xbyi0* from rest and accelerating at bm6k zyn0xr;w*ji1 :ja constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelet ;5+b:xpk p u4 vmc4cwdxh-o8ration 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 acceler8t -2uzdd 3r.*xxikusation of s2x*.8 dui zx durk-3t$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest -k;p j)v(vncqf:f io3and reaches an angular speed of 6.0 rad/s while turning cq3 (i;-:nvp) ok jfvfthrough 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slrr biy6o* ivpf p nm m5x upp+/yt43:ky9(9l,cows down uniformly from 8.40 m/s to rest over a distance of 115 m. Whpf5uimc6y4 p9y(or*b9 y 3/tv,:mnpx+iklp r at is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformrilj t/x1. d04 uwwk/dly from 8.40 m/s to rest over a di kld. wd401//xuwi rjtstance of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mbw:p 0ia 4cw4m/s to rest over a distance of 115 m. How long does it take for the wheel to come :ma wcbpi0 44wto the stop?

  A centrifuge in a medical laboratory rs7 lt7p/simo8 otates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times alopm8st7i7 s/t 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 whi iv762/exttk/s: lrheel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requthr6leks t/ i2/xiv7:ired when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque xok: z4gh )c0+y5,ymu/n)q idvto sh;of 90 Nm. If a 30 cm long wrench is used, what+y goqos4,vhmikn ;zxc) h/)uy0t 5:d is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of vt-;lwpzh /vizp , ,hq;wlv72 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 origin, mass:njwy29n: 6g(ydnl duuo1 b6l:x9dfv 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inejd flx(:od9ungb1u:v2l:wdy n96yn6 rtia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a fric +8,+tzc ys(n27ttwid d;e plotionless 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 F2s 7(e pottn w t;ic+2zl+8dyd, = 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 a+wui r22qa8 ijxis thought the center uq w8+jr22iaiO. 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 rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hib1r,tug-9z944tjfz7k 9 t2xo shxjusb 3+bxv nged at one end. The rod is initially held in 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 1+szbjs txux92z9k4h 4u,vbtxr3-7 9objtg f of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and masczep8fpyte8 l:5hr6uv3xp ots +4r( :s 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, assumcetzspu+4o: r6hp8p( yr 85e x3tvfl:ing it rolls without slipping?

  A 1.53-kg mass hangs on a rope w )eg.*-qvbz1 ,araw)5)dpc:u vdocpx rapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?z pe1o ,gq.)cv*wu dxb )-ar:5 vdpac)

  A 1.53-kg mass hangs on a rope wrapped around a frictionless y 1kv0zbrdz33x:n n*u disk pulley of mass 7.07 kg and radius 66.0 cm. What is the acceleratioz0ndr bun3zy1 xv 3k*:n of the mass?

  A rotating flywheel can be used to store enpg9us8ruvu : y1+ybwl.n c+vco*rw(+ergy. 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 r + vduc2tj.6a (zhir)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 radp x/vs ,(e1le5td fl1oius 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 t1(,ef1p etsxl5 vlod /he bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls wsp:;/l 8 qpdxp.8ywr f7w 5domith a speed of 10 m/s. Hp8 /x.rf;7wdp 5 ql:dspomy 8wow 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 is releax qub*yxztf2y*+byt3,r.7 hp sed from rest and allowed to roll down an inclined planhypq, 3bx.xtfyy*tb+* u zr27e. 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 rtml icjkt*:c8 v,ra uba2)6m9olls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia olkb2tu89 atm ,jmcc iv)6:*arf 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 momezmb byx.py6u ,f7.y0 entum 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 momentui1cq wq7w5-y3 p2f-d en wr.c 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 4d5( hd5+:z n3ptnz b ef)runn5.00 rad/s with arms extended has a moment of inertia 34( t dhzbfdzp:+5e n)rnnu5n 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?