Angular displacement is us)z hbqxk8c ne8lkp+3rhl+ )j0ually express in units of

  Angular velocity is expressed in unjr3i on /nj;/bits of

  Angular acceleration is expressed in units, pmoz4g dlosfz)lfm 2y4 l)scc2.;/m of

  A boy and a girl are riding on a merry-h*3x wbkuw mgt(l78lttn 8,fz4x) -oggo-round which is turning at a constant rate. The boy it(ut8 glzoxt-flhgw w)k38 n47 b,m*xs 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 merry-go-r 7lyw3m h54 hrxyah6( -yhwe2nound which is turning at a constant rate. The boy is near the outer edge, and the g5xahy- 3h74 e mrhnwhw(2lyy6irl is closer to the center. Who has the greater angular speed?

  A boy and a girl are ryrxwu i918 oaxs7z /a8iding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater linear speeyirxw78sa u 1a8o/zx 9d?

  A boy and a girl are riding a merry-g *t1u avo y0m /1zwogyv:k c1js09vjd,o-round which is turning at a constant ratejsauv1zk t1 0d :vgmj /w o1,*yocy0v9. The boy is near 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 merry-go-round kjjl1vtxc /xsha1.o, cc3ryy+x 5v54 which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. W xj+.r /xx3c41h csvy,5ocl1vk5 tj ayho has the greater tangential acceleration?

  Consider a rigid body that ikfxt9ixo or78(j a8n.8 f*q xhs rotating. Which of the following is an accurate stat kxoixj* 87hf.ro8 8 afn9(qxtement?

  Rolling without slipping depends onmgo r84vys0inas gk k,y( ohb2w7 ek+jz6- .*z

  Two equal forces are applied to +d u+ xvd2-z1 j )wg8jboz,aafa door. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both fobj1,g-zd2+vu )wf jz ad8oa+xrces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first for : q4egj;hv23zr *rxmyce is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater tz gqe ;mx:hv*2j4ryr3orque?

  Two forces are applied to a doork8tnr k/m7+w xlnob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to ther78l kxtmn/ +w torque of the second is

  What is the quantity used to measure an object's resistance to changes in rotav;jadq, 2x0k ktiojk;vq2x,k 0 dan?

  Consider two uniform solid spheres where both have the same di ,hxhk;cxtq:m59 cnj;ameter, but one has twice tcx;, 5x tnmh9qhck:; jhe mass of the other. 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 has twice the rad hu1mkn p9zt *419df5cep: jrjius of the other. The ratio of the larger sphere's moment of inertia to that of thker j:du zmp1jcf9 5pn4t19*he smaller sphere is

  Consider two uniform solid spheres where one es8x6;pnf ux u mbmem;p5u982has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of if8ep ep nm2ubx8x5m;u ;m6us9nertia is

  A uniform solid sphere has masso p- )5grkhc+mm rf7+d M and radius R. If these are increased to 2M and 3R, what happens to the sphe-or h+)m 5mg7rc+d kpfre's moment of inertia about a central axis?

  If a constant net torque is applied to an object, that object wilft e4ir(3;bpg l

  The moment of inertia of a solid cylinder ab9 z o(4hi(e4huinlm/ n s(+rlnout 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 of which has a 2f4l; cqj 96boyzbt, kmass 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? Assume the wheq ;o9z6ky24 fbj bt,clels are uniform disks.

  Suppose a solid sphere of mass M and ra0s/dt /4c rmeedius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the ec4et/rm0sd /incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slipping down an ivtzvmx. ()+u6h*/gbhxl f xn9nclined plane starting from rest. Tu zmx xv )l(+nb*h /6h.x9gftvhe angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a bxf/)ncw yl) .2lp5bw9hcq6lnet external force acts on thy fllqb9c5 l )ncw x2w/)b.ph6e system." This statement is

  In what circumstances can the angular velocity of system of particles change witwjcn ( sx)9cwtejk)f )ok5*k3hout any channfs ww)kc)3c ejt*(9ko jxk)5ge in the system's angular momentum?

  The Earth orbits the Sun in aj a uy-/b.dmz.n elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum j zu.y-/dmb a.about the Sun?

  The Earth moves about the Sun* 6h6tt*yvyy z in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best yv66*hz *yytt describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchp -usc 2loeo6n;l48 leo 2:hwied arms close to his body. What happens to his angular momentum about the axis ofe-o8c;2 4i upl6 o:ne w2lhlos rotation?

  An ice skater performs a pirouette (a ffn0xm,,gz59 jxrs fc2ast spin) by pulling in his outstretched arms close to his body. What happexnj5 ,sffx0zc2m 9 ,grns to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast-scrmz8wh )5w4e qi 7znw2e)nw. c)m 1ea;iu l spin) by pulling in his outstretched arms close to his body. What happens to his moment of ine1ccq7.wliewmse8 hu ne amz5n2)4wr ) z-;)wi rtia about the axis of rotation?

State the law of conservation of angu vjjsrw;;k(i,-j/bm alar momentum.

  What arc length does the Earth travel in a three month2e/m;rq y;z schvc;:g jf,n o* period in its nearly circular orbit about the Sun with a radius of *o/ r2fm;,esjvc;zg; n :ycqh$1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.sc7x0 2okke nnj,e3j.30 m. What distance does the tip of the k sej .,3jxneco02k7nsecond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolh0k)0ojim6n zty5x o f;z i3p:utions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revoloe-w,w6p wafsape7bl: c k 3-c*+tr 1eutions in 4.0 s. What is the *we3-1wfe-b ap6tpoe:rwc+l s7, ackfrequency of the wheel's rotation?

  A pulsar (a rotating yvh+66o 2rzm mo5z nx/neutron star) emits pulses at a frequency of 0.40 kHz. The period of itm 62hovmx/rz+oz 6n y5s rotation is

  A phonograph record rotates at 45 rpm. nl1; :dvmx+ lwsh:*9v2c ;vh6 ylnvufThrough what angle does it turn in 0.20 sxv fl ;*lv s:+nwlh;:d169vucy2m hn v?

  A wheel of diameter 26ae0i) m3*uc8p9r u3ckl s.tas cm turns at 1500 rpm. How far will a point on the outer rim move in 2.1 se 3*)t9uausi0crkpsca83 ml .?

  A bicycle wheel rotates uniformly through 2.0 revolueqc m bq30e5;j9 ,bmhptions in 4.0 s. What is the average h bej3pe9 0mq;m,5qcb angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.x;iymh wg75iz1w/f).apb;: j4z xlc g What is the linear speed of a point 0.10 m from the center of the whee ix)ab .xm1hg ;pjyzifl5ww: gz4;/7 cl?

  A cable car at a ski resort carries skiers a distance of 6.8s:eqq 9 +tj3rb km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slippage, how fast must9q:+s3rqtj be 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 ang k8t+fubut kt 146;7 sykkx9bx 0u,hpjular speed of 2.0 rad/s. What is the linear speed of kj7thxkubu9p6kx1; 4k t ub yts8 +,0fa point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengthedhr+l(a cli247,-+1vtm figj*er fk. If the motor rotates at the rate of 20 rev/s, what is the approximate lirm* 72t+d+ l1 rac-(gf4elijvhek, f inear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating p i.uf 6(wqv5iwith a constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point onf6qip( w v5u.i the wheel's rim?

  What is the centripetal accesd4 h5/xj irw9leration of a point on the perimeter of a bicycle wheel of diadhs j95/xwr4i meter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular 5el8 *thxp/sv, rotating space station (r = 1000 m) rotate to produce an artificial v5* 8tspx /helgravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of r, a)b;z yfw 7dk.zr 90wonnx4kadius 50 m with a speed of 20 m/s. The maximum centripetal force (provide d)znw07 ;r4fzy. w,kkxo 9band by static friction) 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 spee4wex*kw 1 b+vxd of 20 m/s. The maximum centripetal force (provided by static friction) is w bwvk +x1ex4*$1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.)+w-wwjb wnqwd7 .lco :s+9es n ydo)+750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is 250 N, then what maximum linear speed cq +n + sbd:nyw+7we)so cl.jw9o)wdw -an the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg and radiu ye7*ullx8)vlb q 4yy4s 9.0 cm rolls without slipping 10 m down a lane at )y8ybll4qv4 e7y l*ux4.3 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 const1ie4 /d1no5;m g debqtant 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 constant angular acceleration o2ln- d2lkom 4kf $4.5 rad/s^2$. 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 automobimc+:lhmrtv t h:0cz.- le tire rotate after starting from rest and accelerating at a constant angular acceleratio: mrh m+0l-hc:v .ttzcn of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has alb 9f wp-gtf mz40v1z;n angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s deceleesz):ol ek/3ycg 9h2 crates with a constant angular acceleration of z ch ykc/g2e93soe):l$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of8pyq+bjs)vli28 d r p, 6.0 rad/s while turning through 2.0 revolutions. Wp,j pdsb yqi2vl8) 8+rhat is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows dov(.; 27s xnoi ybx)arawn uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions th snvx;i 7rabo2).ay(x e wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/-vjv2zuu r,wmu8 d7 .zs to rest over a distamu2vr .7,d- z8ju vzwunce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68. 3uqgsm.glch 2j1vf;- 0 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to come to tlv3fu-1 sghq;cj g2.mhe stop?

  A centrifuge in a medical laboratory rotates at a rotational speed q1rin). n5)5vbw/+blbf ra fpof 3600 rev/min. When switch. +1lin)55r)a w vbnrp/bbf fqed off, it rotates 50.0 times 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 tor; :w8d8 jp-j f+(l,noeo ohsskque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the fo k, ;o+neslhfo(jdsp-j:w8 8orce required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If a 30 c cl9 j+/zne.+pvmtb/em long wrench is used, what is the magnitude of the force ree9b +.nezc/ mjv+lp t/quired when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ofhz) y;j(xq3q/piin/ f 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 modln/ p .coot, 82*hl54myifs3tzslt4qeled as follows: mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia ayt o n8fqtl4 p/co 2z4sl*s.i5l, 3mthbout the origin?

  A solid cylinder of mass 10 kg is pivoted abou,c (/rvo4 psyyt a frictionless axis thought the center O.s/orp 4 (ycv,y A rope wrapped 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) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a lrr9(husp( xn s3:j l/frictionless axis thought the cer j:hrx9n s/3lul((spnter O. A rope wrapped 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 one uuc;1 wdb/* c2f;bpnmend. 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 of p2 /fc;w*nbcdb m; 1uua rod about one end is ML2/3.)

  Consider a bicycle wheybuei,z9f-g5 5wjx7 wel to be a ring of radius 30 cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. 5j7z -ye5xi9wf,bu gw 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, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mas7it opp *ech.(pr*u(rs 7.07 kg and radius 66.0 cm. What is the angular ac(*7rorutp*iphe cp(. celeration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley of mdi(ki qa4:k 3yf:;hccbc67,ihmq/ne ass 7.07 kg and radius 66.0 cm. What is the accelerati f 4;/ mq k36byi:c7,caie(idc n:kqhhon of the mass?

  A rotating flywheel can be used to store energy. If it is requ0mex al25pz) wired 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 inertiae;yczdq am 0 *nuua3 .g47(iyu 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 mx+)ljmq;0m d radius 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 bottom of the inclined plane) ;xmdlmj+m q0?

  A solid sphere of mass 1.0 kg and radius ;n;tloj+ luy/7 ;s6qrgiopt9 lh5w 7z 0.010 m rolls with a speed of 10 m/s. How high up an inclined pla+wjo;l6png izt/ 5y7o; 9qh7tl r;uslne can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released fr7bwz grnz..)h om rest and allowed to roll down an inclined plane. How fast is it movin.wb. hz zgn7)rg after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls w/w 1e*lm xpjm,kh5 jz+*o5l q9xioi:w ithout slipping down a 35e incline that is 7.0 m long. Asome/,ipz: xjl olh+*wi k*1qmx95 5wjsume it started from rest. The moment 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 momentum changes by c a-qh 4t0cn9j$20 \; kgm^{2}/s$ 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 b3 s h tr:rbm(rq8l()gmoment 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 5.00 rad/s wit0evsjev cyd5z/i(e:u 7/1 mnnh arms extended has a moment of inertia on57/c 1nsj veyd:ie0mev z /(uf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?