Angular displacementiz-m0pgj7 3(i l9vs -o -gmizy is usually express in units of

  Angular velocity is expressed inc oi;mbonn)pyge: )-cud -6r-km,d+l units of

  Angular acceleration is expresseevg5kph;g1d .d in units of

  A boy and a girl are riding on a merry-go-round w0 vvu1 rxf o;(wotyf:dht*8t73w +mjuhich is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the cenf (wro1jth:u uv y ;xm3fw0vtod +*78tter. Who has the greater angular displacement?

  A boy and a girl are rb,/t ao6zxt+ g- but7uiding on a merry-go-round which is turning at a constant rate. The boy is near the ou-o7b u,tbta+xgtz/ 6uter 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 constant1b,su evasw)u 5u62;c+vhxm j rate. The boy is near the outech svj u6u;s5x)+,baeuw1v2 mr 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 f1z:ytj,*amv tazb- 3o hxn:;p +j un(a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleratiphnm3:ajx1zn- bf:atv (*z; t +u,yj oon?

  A boy and a girl are riding a merry-go-round which is turning at a constant ra;zqnyyv7),xc+n ,0 co o;mlpzte. The boy is near the outer edge, while the girl is closer to the center. Who has the gre 0v;,;czm q7+olyy)oxzpn cn,ater tangential acceleration?

  Consider a rigid body that is rotating. Whiclt 6qlbci2p1 dgj( *3dh of the following is an accurate statement?*(dld 612cjgq bpl3it

  Rolling without slipping :+;/ epv t(fg.tn uf+ gzpwrx+depends on

  Two equal forces are applied to a door. The first force i:ds y, i mlqa8qpf+(5xs applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicul:,xqdf8a qyl+ (5pismar to the door. Which force exerts the greater torque?

  Two equal forces are applied to *g .vx 9xny3lda 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. Wnvx.g3 d9l *xyhich force exerts the greater torque?

  Two forces are applied to a doorknob, pet: g*suj/k* qgm/ib6ot0nz, hrpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of sbj*u/o/* zkgmgi ,q06tnht: the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changem4 su8 ;o6ryz +cd*wsoobou+.s in rotatio8 z;us cywoouro+bd+ ms4.6o* n?

  Consider two uniform solid spheres where a 3hg93:env kqboth have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the small e3q3vha 9k:gner moment of inertia is

  Two uniform solid spheres ham: he,v;z 7es ywoz 6cxf v5u*2gg3b4mve the same mass, but one has twice the radius of the otw;5:74 y 6xmfve3vggb,z e o2 *mzchsuher. The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice2 g tepm0m*f:c the diameter of the other. mcet mf20:*gp 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 radius R. If these are incraj+ dn(g 0x;k3 h+is1 gjqwd2geased to 2M and 3R, whn w(1;+02k gh+da3 sigjdqxjgat happens to the sphere's moment of inertia about a central axis?

  If a constant net torqz//mvly *.b+w 7.o :xhruyjtn ue is applied to an object, that object will

  The moment of inertia of a solid cylin/do (ztgif 5 ykrzol3 ik4a+36der about its 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 olqno;x81q *p ck1v5u(o ,vwgvf 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 8,wvopv (c1vg5nlx1q; kuq * oenergy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius sa;acypldr d-vu s /9u+4/t-cR rolls without slipping down an inclined plane starting from rest. The linear d-c- l4y;dtuu/9 r+acsaps v /velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippin/ nu os-9mihk )c) o3e9:zpwycg down an inclined plane starting m )e/9whcozny o s:3i -9upc)kfrom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of 6nfnm0j 6: p 5i; :pouwc +a4b,lywhafa system of particles changes when a net external force acts on the systef 5 h6pp;6bo ,:waajy +l:wfi0u4nncmm." This statement is

  In what circumstances can wave.y.e. np a+)zagaw) 1g8n.vj(gvthe angular velocity of system of particles change without any change in the system's angular mw. ae)e.yna (z jv.v.vpa )wg+1 aggn8omentum?

  The Earth orbits the Sun in an elliptice 8pr hwkv8m2hs54m :fal orbit. Ignore any friction which may be present. What k5v2:mfhwres 8 phm48happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in ang0y ,2rlyo ;qh elliptical orbit. As the Earth moves close to the Sun, then which of the following besh0ro,q2 lyg y;t describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretnj wcd))s ((k ,jkc/urched arms close to his body. What happens to his angular momentum about the axi) c,j) /(kjw(knusrdc s of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc/eg,s9cqxr:d dsrk1ds9 pl2 ,82fqc hhed arms close to his body. What happens to his rotation / pc 1de9sgsqqlr8s9dx,,h:r2 k2cdfal kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast sp 19y xxy8 bv7oit2.b(jivl4 siin) by pulling in his outstretched arms close to his body. What happens to his momen.xi(blvyvt8 2 7 b41iio9xjsyt of inertia about the axis of rotation?

State the law of conservation of angular m4 ee+6z*j yiz:5mx4t5plxwsl omentum.

  What arc length does the Earth travel in a three month period in its nearl:fb2la3 ptvx. *ot hmdua+1z 0y circu1+bxp lz:. at0 dauvh f3to2m*lar orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clocuviu:u7bzla-+5 :eem k has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minuteslu-v7 b +:5u:uaemezi and 45 seconds?

  How many rad/s is 25 revolutgpl*da:zjbxi* 7 -5slions per minute equivalent to?

  A bicycle wheel rotates unm edu*m*xr 7j 7iwrn9+iformly through 2.0 revolutions in 4.0 s. What is the frequency o uw7r+9nijdm7*xr m* ef the wheel's rotation?

  A pulsar (a rotating neutron star)s(dt wf j514 m.pfhi:va))cyz96iaij emits pulses at a frequency of 0.40 kHz. The per) 6a )95.fp d(satiiz ciwjjy:h f14mviod of its rotation is

  A phonograph record rotates at 45 rpm. Toy lv/n gmz:xk)fxq,4g2; * vhhrough what angle does it turn in 0.20 s? *;n,)qy :xxkhfmlv og 4vg/z2

  A wheel of diameter 26 cm tlgsl g;vz2 iyvuc( 469urns at 1500 rpm. How far will a point on the outer rim m izl 9g 6v4;uvgy2cl(sove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Whaq 0qot 5sj3l3vt is the average angular sp qjqst3l 5vo03eed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is3 : (immdr;j*zbnaav );3oopq the linear zo 3 mov:)bd(p*i am; 3qajr;nspeed 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 k*f t2vlzly- .) rt2z,btpsp*sm. 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 mtszt2vt2b*sfy) -ppz ,*ll.rake the trip in 12 minutes?

  A wheel of radius 1.0 m is rotatinghnttg .4al,-i with a constant angular speed of 2.0 rad/s. Whalan.4h tgi,t- t is the 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 the mo5 wokr6r8f+ xftor rotates at the rate of 20 rev/s, what is ther w+ xf86ofr5k approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with r)ryj pmsttpj+ 8d)g3.jh dz2 i,gx(.a constant angular speed of 2.0 rad/s. Whasp yjg(pmjt r)dd g.zjt8. ,r2 h3)x+it is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a bicyy ;d5.lm 1mr-qssjz .ycle wheel of diameter 70.0 cm wh 1md-r;sm.yz qyj .5lsen the bike is moving 8.00 m/s?

  How many revolutions per minu:zchku* mb6sg8d,o5 bte (rpm) must a circular, rotating space station (r = 1000 m) b m,c58ogbhd6 zk*:s urotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a sxggek w)e w6+9peed of 20 m/s. The maximum centripetal force (provided by static frie e9g+ w)g6wxkction) 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 oflw0 hyl mx(0g1wi: hyrj6 f7)m 20 m/s. The maximum centripetal force (provided by static friction) (lm w0f6h7hg)lji xyy m 0:wr1is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, isdt(u6d/ 3n 1flj4f.egkxw* qi whirled around in a smooth level table. If the maximum tensidn4f t 6(kfqxdjgi1ewl*.3/ u on 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 9yqsu0-c dv2xlgz3 3 p9b aw1)a.0 cm rolls without slipping 10 m down 301 3luqdx-abvcza ws p2g9y )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 constdaqv u5 f4zrp(7cfw+; ant 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 witr bur/6(cqsnsg9e1(+ jk q;t 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 k*n km7ircf)unk7 l2;0.300-m radius automobile tire rotate after starting from rest and accelerating at a constant angular ac7cn;knurik* )k72lf m celeration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accnjkj26pgj/ i(5*wa s meleration 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 co4hqudkx a/)z sn1;y :enstant angular acceleration of k )n xs:dh/1uq ;e4yaz$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest 7 .ytd h;dytto r;):odg d+j*land reaches an angular speed of 6.0 rad/s while turning through 2.0 revolut7o:+ jt;;).gydtd hrl*odt dyions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniforb*el7 n0mb :-musv+4cbua1 bimly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rot-*an:1bc iblsmb uvu70 m+e4b ates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s re /)pm: dgl*oza9o8y y l6y*sto rest over a distance of 115 m. What is the l9ezor 8)p m6 * *yalysoy/d:gangular acceleration?

  A wheel of diameter of 68.0 cm slows do5nidc8ik -vjfvc -x* vzl 5l1.wn uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for5x8f *icj-5cv vkdl liv.-1zn the wheel to come to the stop?

  A centrifuge in a medical labg/pk)1 bwhy r;x n2;dtoratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 g1ndyh pb2) ;x w/kt;rtimes 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. Ifut0qeb*v 1 z(g03 iavr a 30 cm long wrench is used, what is (bz0ie va rv3*gq0ut1 the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tigh5 uee)cnjpt,4f6 :ac ltening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force reu :5p,46 ) ltfccejaenquired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertf3w(u4qj rju* 1 mnr3aia $3.00 \; kgm^{2}$ 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 ( o x):g;izv -+)rhsi2ncculb at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the momerhg-z+:2u; ) nsviic o )l(cxbnt of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axisw(;9k4 prdqow thought the center O. A rope wrapped arounwk4;dq (9pro wd 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 matafnrp*,g9lgl:. is 0ss 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer ra09lfgr: ,.tg salipn* dius $R_1$ = 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 one4.(iaxk9w zsx kg f.7h 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 acceler7fgz4k9( haxskw..x iation 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 rad/e.+;bpb)l l*yjmy q zd- +nc)e;crkuzzw8q (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, +m)+qk z* . )r bu- zz;e8ql;e/bycj y(ncldwpassuming it rolls without slipping?

  A 1.53-kg mass hangssh+d- (qtynh* on a rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of +hs(* ndt -yhqthe pulley?

  A 1.53-kg mass hangs on a rope 7gqd bs+vj6oxe2pg)z c x*f7h*a3i .iwrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accelerata 2ob6c pg7i*)v.q xd 3hzxi*j+f7gseion of the mass?

  A rotating flywheel cah3(b /f3j 1cgeuyi:gy.pwi4n n be used to store energy. 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 ofd 2 lfgeh,/0tv $5.00 \; kgm^{2}$ 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 diu 9.gspm.; qrest and rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the bottosq 9m .i;u.gpdm of the inclined plane?

  A solid sphere of mass 1.0 kg and rad9jr -l sh8wfcj,k :dw4ius 0.010 m rolls with a speed of 10 m/s. How high up an inclined planes flr 9d,-jk4 whjcw8: can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is*mz (4 kj9fsxb;)qmzj released from rest and allowed to rolszmx )9k bq*m j(jzf;4l down 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 ro .rghv3 pab3x6b4j;re lls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momena 3hb6;rbperg4 vx.3j t of 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 momehz hs mj (i3z66 .f,oaez 2ao/mpjx5p7o;hf:pntum 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 inert1ubgj.;5f- fa1fmm kb ia 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 has a moment of i0do / ms,e(dlbnertia o /,bl(ms0deo df
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?