Angular displacement is usua4 4.wvf td+nwbd(+ sp r enfnx)c61k.wlly express in units of

  Angular velocity is expressed 3gm3 dc,;y84m/ e.gawzirspr in units of

  Angular acceleration is expr z pkpn(4dlp,:oio x5-z-,w naessed in units of

  A boy and a girl are riding on a merry-go-round which is turnic(7d-zoa1 fjv - 9zxuing at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displacemexa7if c-1-9jzu v (odznt?

  A boy and a girl are riding on a merry-go-round which is turning at a constan(8ywyccb1 j01su: ,nh1f mkoofts,) xt rate. The boy c1o,x,8u 1ym:fwohb s 0 scftkn)j(1 yis 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 t;; euwdgr2bc e6a0c1v7hq 6bconstant rate. The boy is near the outer edge, and the girl is closer to the center. Who has thhbae6b1c;7cu g0e wq v26r;td e greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a con*wcj5qb3:lsl rd hf55als n21slzt 3 g 2(v,tsstant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the great 2(bn ht2,flrtl13zsqvcdsljlagw s 3s5:*5 5er centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turn ij9z,6ocwse7l 6. ubwk) 9opzing at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Wz 9eo pkuww c,z7lb96 6ojsi.)ho has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the folelon0a9u6j-)), fj a;eb7nt h5 r jtcilowing is an accurate statemet,5h6trn9a joibe ;f))e-na l0juj c 7nt?

  Rolling without slipping depends on / bhxvob ch7e1k kk)w*lx3u-+

  Two equal forces are appliedj ci 371ocefbkn :.aq) 8xln3g to a door. 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 doof nngol3kx3bqcja1ce87i: . ) r. Which force exerts the greater torque?

  Two equal forces are applib a95l/kdyi ca/tg 0laq((7do9stqzz + 1ur/ bed to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e 99z/dy1(t70g dbs/5ckl(auaqbt o+z/ai r ql to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the doojz g9b4 f6 8gf2y8j.nw)rzvka djb 3n:r. The first force is twice as large as the second force. The ratio of the torque of the first n .zb jrky 8g2a:wgb86jn9z3fjv d)4f to the torque of the second is

  What is the quantity used t2iw0*(k,a8 cafnur nn. lx r.,- viooro measure an object's resistance to changes in rotation?ri n8n*u,co-0a x(2okw.frrlv, n.a i

  Consider two uniform solid spheres where both have 5* gri xi0n+q+6 1f(oyy rhlzethe same diameter, but one has twice the mass of the otho0+z6 *gq lre+i5 rf(yihnxy1er. The ratio of the larger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one h m0ux,2 ef,vfso7f m0has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sphef,70hxuov0, 2efmm sfre is

  Consider two uniform solid sphenku r zil9l9v 7agdryb9n,euh/ hv77x:(;ku-res where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to d/a(ug 9x7-kyku bin9n79v7 hzlrl,ru:hve ; that of the smaller moment of inertia is

  A uniform solid sphere hasg,.0 y/*b*6y lk q2fue(pphhdido53 q .fbjtn mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere',f..y* be0jl /ig6 d5no uy * bhq3tf2qdh(kpps moment of inertia about a central axis?

  If a constant net torque is appli n,n71(kf: 4.umd bc7:fqhu 5itftbjged to an object, that object will

  The moment of inertia of a solid cylinder ab s xr tr8/vk;ly7y91szout 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, 2yhv9 ib ;sr4x-/xz3yqqqwf8 one wheel of which has a mass of 10 kg and a radi4xw f- rs q;hyqzxqv /9y23b8ius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls wiui dxm*cu0ao )ps 2(2wthout slipping down an inclined plane startiniw) x2u2du os*ap 0(cmg 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 slipping down an incv) v f4fzkr8g , si3bpuew(6i7lined plane starting from rest. The angular velocity of the sphere at the bottuz i,pvfebi4(3ws)r7kg 86 v fom of the incline depends on

  "The total angular momentum of a system of partic8s/-qccs xns3les changes when a net external force acts on the system." This statn/-xcsc q ss38ement is

  In what circumstances can t25ztmp, exa(ihe angular velocity of system of particles change without any change in the ,2m t5 aix(zepsystem's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction whi(.(9o8s8kcrwy7xz snbc, +eta ykpt2ch may be present. What happens over time to the Eart( zyso ,9.t cyer7ktw (2+kcp8x8ansbh's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Eark5yxwiy5zcu /fqfwh 9);o w,6th moves close to the Sun, tc9w5fow)zqyhu 6y5;/ ixf w k,hen which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spink7qku fko n,/0t hh:9 ka-,nwi) by pulling in his outstretched arms close to his body. What happens to his angular momentum about th ,a-q9wkt07,hnh: iu nfkk/oke axis of rotation?

  An ice skater performs a pirouette (a fast spin) by +bu)zt/bs2 wnx s2 )wyr2s4matqff 96pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis z+6y9b)s2s2fqtxwas/mwur)nb4 2t f of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretcheb+:2o6 ;z4nu wv1t vlbpa yc9ed arms close to his body. What v nel4zu:y9;b 1a +62bvtpocwhappens to his moment of inertia about the axis of rotation?

State the law of conwag77 k94p egqidx*u(servation of angular momentum.

  What arc length does the Earth travel in a three month period in its nea6)md bv +zv2 bbhk1)s gnimmm/0/vod2rly circular orbit about v6 hmzo2i2v ksmn)g vdbb+b //dm)10m the Sun 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 the tipfh( ,5+ ;am3n b3*w ttmj )rfv )7nsgxdohn;nc of the second hand sweep through in 3 mt3ndnnj753txfr m*n );+w, mo )hcah;g fs(bvinutes and 45 seconds?

  How many rad/s is 25 revolutij* +yucj cp3w,ons per minute equivalent to?

  A bicycle wheel rotates ufdzu vvrm0eke0 o3+ (;+ zx) zp.4mdqyniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheel's rotation?+dp)o mf0.veyz m4( qvdrz;+e z30xku

  A pulsar (a rotating neutron star) emits pulses a je/: :c(8ec ano od7k*ya(rgst a frequency of 0.40 kHz. The period of ne(yd r acg8sao*k :jo/e:7(c its rotation is

  A phonograph record rotates at 45 rpm. Through what a8 y uek uf+oplej808su+ jef6 5qsz8x4ngle does it turn in 0.20 sxs5juyz8upeq8k 068of8 e4u+fs+ej l?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the o7 ofihw6w p28:l9lyeo uter rim movl 9:o6ilepf 7wh8w2yoe in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.dkv2 e*e( mrvk:kas96 What is the average an* e2dre (sk96mkka :vvgular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 reh:r+ bywt.:-pt y(mdf1v5 m w*4tz ojovolutions in 4.0 s. What is the linear speed of a point 05w1pv oy4z*+ r.yjft t -w:m:bo(hmtd.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distnpxhc v djup5m;;k+h2 l9u-a4ance of 6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assumingv-c ku9ph 2jmadxpn;h ;l5u4+ 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 rotating with a constant angular speed 1z jmi5heb:1 vof 2.0 rad/s. What is the linear speed of a point on the wheel'svh1e 5zj :1mbi rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m iql pqj4eg9.4dq . nd8tn length. If the motor rotates at the rate of 20 rev/s, what is the approxi4 dpq9tjlq .q4gn.ed 8mate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant a a:sljx(4/aexfxygf*d4a, +yngular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wf4ax x,+dx:yy* a4f(l asej/gheel's rim?

  What is the centripetal acceleration of a point on thr8n*jan;; ,rmoyzz zif+ 3c3)y,t tz fe perimeter of a bicycle wheel of diameter 70.0zy 8+ m;zo) z3zf;rn,farjn,ti* 3cty cm when the bike is moving 8.00 m/s?

  How many revolutions ps.wn dwx q/o;+1sab8rer minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial gr;+r w .oss1adqbwxn8/avity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m9iytw :oypz):9, ud,nm )aiwg with a speed of 20 m/s. The maximum centripetal force (provided by static d9n,uay )) iyo9:t wpgz:mw,ifriction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating 2zo rf)b 43rroa flat circular curve of radius 50 m with a speed of 20 m/s)oorr4 r2b3fz . The 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,my uex2u:+9hozsy)m 3n *-rpu is whirled around in a smooth level table. If the maximum tension that the string can withstanormym n-huzy*u 29+ s:3pe)uxd 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 r0t8rhuj 0)p zbhn 6s1rq,1 otuadius 9.0 cm rolls without slipping 10 m down a lanu )hu, q0trn8poh 6zjt01b1sr e 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 a:2y ntjd (0fn 9pdm5dpfdn5)qcceleration 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 vhh6l0s7 ;ezkhd w;w8acceleration 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 starti6.xu gf.dnp.z ili xt1kl,n7d( 5. higng from restii.ldnnth1. p7 x. (6gglxk5 .fu dz,i and accelerating at 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 accelenolug32s -.j2d*gfc6lf6swj *2rfx oration 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 accelowec 5zz m kirq5f4/(/yg2ey3eration oi2cm e/ ywyqg5or3f4ek z 5(/zf $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed5 uvt,0y5 doydion f+f2 lpyw9x;jkh2)( j*pe of 6.0 rad/s while turning through 2.0 revolutions. dt(*j5vp5h ikyo j; 0ylw2x+oenu2,dy9)fpf What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down 4 3 sjo2ldb*q.fha9u x6geqs8uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revogos bfxj6l4dq29shuaq*. 8 3elutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly f/d8o(05 wovvvs ez q0vrom 8.40 m/s to rest over a distance of 115 m. What is the qvsv z d/w0 5ev0(o8voangular acceleration?

  A wheel of diameter of 68.0 c,xp)gl1.ar o2(i owmcm slows down uniformly from 8.40 m/s to rest over a distance of 11mxp g.1 ci() oaro,wl25 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medi . 94/qf0enpvih*i keucal laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accekep .e9nh4qifi/ u 0*vleration 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 to*8.*amrx;czi8s mwxdxi l*1e rque of 90 Nm. If a 30 cm long wrench is8lmema.*xs** x8d1i ic;wr xz used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel reqd216trjvyl f /uire tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applie f2r/t lydjv16d at $53^{\circ}$ to the wrench?

  A wheel with moment of yw6iq mb /bzboy6g9ul 2oew*u; .) b6dinertia $3.00 \; kgm^{2}$ 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.a lzo0o, cs)v 2m is atzv sc,a0)ool. x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis th 7-kojzqft , 3tg:wj6 stmc/7dought the center O. A rope wrapped around the outer radius owt6 m/d-3,tgt7 j7fzs qj kc:$R_1$ = 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 pivoted about a frictionless axis thoug/ op*z*pp-ivx g 53n1 dr-yuynht the center O. A rope wrappn i *p- u/vrp1gpz 3n-5yo*yxded 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) 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 onebtxgc miuov-*n8z*ylsx2) 58 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 releasei2b85g8- zs* xvxolt uycn )*md? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of w 9*8kn( qu;fdexd4q bradius 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 achievk9u 8qb (e4*dx;wfnqde, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionle:7gh,jy r2zqp rl-xa /5/pyzmss disk pulley of mass 7,r7xa5py2//qgr z mpjlh-z : y.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulleyomel,-v r6 9db of mass 7.07 kg and radiu,d9mlr6 o -vbes 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to store b4;p ft 2/fxi7k c98iofff 0h:6sonop$1.00 \times 10^{6} \; J$ 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 inerv,1vqv x(lr5q tia 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 and rolls witt.7p i1 j9:iphkn0h ,wft*xfthout slipping down a 1.0-m high inclined*t:hhwtk 7i.i pjft ,x0 p9nf1 plane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rol k6k 8jqu-gefq6/c nb:ls with a speed of 10 m/s. How high up an incliqn /ubk6kg8jcqf- : 6ened plane can it climb before coming to rest?

  A hoop of radius 0.50 m anit,fwvu;qz8(.a2m dqwb d + -nd a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. Howt- a 2fd(qv8+di, uwn;wzbm.q fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg)(b-q t(nw*r.r19 pd7 jiwnsyyvr s:s:rng-h and radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The momrp.tdjhgrsn inq(yr)n-s b:w y- * :7w vsr1(9ent 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 th6 - 65v(k2c drxh9x8prpk az0rjzu1momentum 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 inerti9nmb 4t ntf2,;nzb glp1(o )mqa 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 a:o5;q),o*hgw9kl we,knln xrrms extended has a moment of inertia o:xn)k5hwqo,rwn*ke l l9 g;o,f
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?