Angular displacement is usually rrq,a5vqi rsavg1 l3l8 (utovv+6:b lw7k)x: express in units of

  Angular velocity is expressed in units ofjo)sc (ha;1m3wuses z3zv e *65zjli.

  Angular acceleration is expressed in u9 w6goo/1br9w y, hqwtnits of

  A boy and a girl are4x9)0jlbt9 d hq6jmuu riding on a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl is clmh9tq9 jl djuxub4)60oser to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-roundo8h tyus;7 u wg* xs2c/if6p1t which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who h8sw it/6u7*fuyhtcog sp2; 1xas the greater angular speed?

  A boy and a girl are riding on a merry-go-round which: o/a(mvrh*v3zo)e yoy (o7pm is turning at a constant rate. The boy is near the outer edge, and the girl is cloveh p() oy3o7a/o rvoyz(:m m*ser to the center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turningf.lq yxv tl2l(5 aa/fbu5.tn,* x9mzh at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who hm lq*t..ynxtb2xzl9/ f5 5a( ha,u vflas the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant raio5 9a4 fj5fjjte. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tfj5 if95j j4oaangential acceleration?

  Consider a rigid body that is rotating. Which of the following v/3;6c7x em 4rjggoh uis an accurate staj 7xuoc/m eg6;4h gvr3tement?

  Rolling without slipping depends bz :k.zwov2v 7on

  Two equal forces are applied to a door. The first force is applied at th*hun 83 zpuf:hl4 f9nhe midpoint of the door; the second force is applied at the doorknob. Both forces arzp*hfl :4839huuf nnhe applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The first force is a3;s sh.bt mk+z8-tzf tpplied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts t+f;tb . 8sstthmzkz3 -he greater torque?

  Two forces are applied to a doorknob, perpendicuh:r onnti d-(,lar to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of theho: ntn ,di(r- second is

  What is the quantity used to measure an object's resistance to changes7hg j+ ajo ac4 ,s6gwbwy +e2gsn6b-w8 in rotatihgb+s84w62 +,a6 njeyag c-bjsw wog7on?

  Consider two uniform solid spheres where both have the same di*t;rg9t v ,oaaameter, but one has twice the mass of the other. The o t*r;g aa,tv9ratio 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 radius of th6qe9 t9jsmr0up- spnzyd2 ; 2mkcex.*e other. The ratio of the larger sppxuspq 2e9*-stymezdm 2;096c . jkrnhere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twib0os qqw* gcyp,:i 9.xce the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of inerti s*9yg .wpqqi0,xoc b:a is

  A uniform solid sphere has mass M and radiq5jt1ho ks.g, 31cjb1e yxap+e bn2q) us R. If these are increased to 2M and 3R, wh )+bx3cb52yg,a.11k qjopejshqt en1at happens to the sphere's moment of inertia about a central axis?

  If a constant net torque is applied to an -dq(d sfm5q duhx8 (+mobject, that object will

  The moment of inertia of a solid cyl7vozq:p 3 d +sl/66)1whhiclhzmry,einder 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 1okw** a;s;ej iw65 arw50 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 translatws 6waai*e;5wr;oj *k ional kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolln;dhbu*f2o * a+ a/m 6mrf(vjls without slipping down an inclined plane starting from rest. am2v (+;* ud a6bf/lrn*fohmj The linear velocity of the sphere at the bottom of the incline depends on

  Suppose a solid sphepmy3ysr 1y sc:wo s1*.q4 pgz6re of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom o.gywyyqrms16ps3c o41 :* zp sf the incline depends on

  "The total angular momentum of a system of par z4f+n6m - kez: i;xnzgg9i;b:o/yvmoticles changes when a net external force acts on the syof:y+z9bmox ;i4v/g;gme k:- i zn6nzstem." This statement is

  In what circumstances can the angular vel56chbyw f:gut lr 6-0xsaff( 9 iw3b2tocity of system of particles change without any change in the system(96hyxb5tff0i62f3 s glwt rucw- ab: 's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any frc c9c:qg9b r4sg/4knq iction which may be present. What happens over time to the rk cqs94n:/q g4b gc9cEarth's angular momentum about the Sun?

  The Earth moves about th 02n2t jfknu(d9,bg 2ropcvocbu6 b23e Sun in an elliptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speedd0cu( cfb 6v9njo2b kn3b2t ,p2rgo 2u of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretc:7so.f .pyy (i zpa gz(uf2z9khed arms close to his body. What happens to his angular momentum about the ax oup y(fza2s7.9pzkzi(:y f.g is of rotation?

  An ice skater performs a pirouette (a fast y ,g6jft04iwe spin) by pulling in his outstretched arms close to his body. Whg t4yf,6jw i0eat happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (aen18 03/q e,c c 2dx6ghk rhtn7gxs*kbqa)xn6 fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis ogxqheh2enbsxq3c a 6*t07kxc, gr1d 8/ kn6)nf rotation?

State the law of conservation of angulsh5urs - y*ecdim; *7)t6ehp j+omj0xar momentum.

  What arc length does the Earth travel in a three montmv9 xtp;aolz; .g16z8 xaikl;h period in its nearly circular or;mtzp; ial;.v9loz61 8xakx g bit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length up cj z8)ejm:;/fl,tgpuo +2x of 0.30 m. What distance does the tip of the second hand sweep througpe ul;82fzpoc ug ,t/m:+ )xjjh in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent toz7a:p7( ftnkcju 73l o?

  A bicycle wheel rotates uniformly through 2.0 revolutions i)p* 12maki nxe7jf ;ssn 4.0 s. What is the frequency;fx)7ka me 1jsnps*i2 of the wheel's rotation?

  A pulsar (a rotating neutronu+i,gu4z/,m js(t 3zvjyh mx; star) emits pulses at a frequency of 0.40 kHz. The period of its rotation ymjhjx4vz3u(is+; g/u ,, tzmis

  A phonograph record rot *o wy6b0vgdyb mg123rates at 45 rpm. Through what angle does it turn in 0.20 0my 1rovg 6yw3*bdbg2 s?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on teg4y d nz:by 2 )ui,2k mtvlji.t419krhe outer rim move in 2.1 s?j.m9y kne:bktl 2v44ztug ,)1di2yr i

  A bicycle wheel rotates uniformly through4/ahpu.uu2a3fv uug6mn;r p 3 2.0 revolutions in 4.0 s. What is the aver6 pg3na;uu pumua2u43f/rh v. age angular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is thf7zlcd a--sn-ak-e e 23sxbks 2jnw) .e linear speed of a point 0.10 m from the center of the-zlw- 7.dsk-ace kn )fesnsx a-b32j2 wheel?

  A cable car at a ski resort carries sk:e -p)j8hi kioiers a distance of 6.8 km. The cable which ikj oie -:ph)8moves 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 minutes?

  A wheel of radius 1.0 m is rotating ixw agsp9 nu7*bbkwdv:u8:z l *.q:8wwith a constant angular speed of 2.0 rad/s. What is the linear speed of a pointi:wu wda:79 zw8sp*.l xk *8uv:bgqbn on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in length. If the moj q v1z)gwv1p.tor rotates at the rate of 20 rev/s, what is the a 1zj)vg 1wqv.ppproximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating wi9 mopapbf a905th a constant angular speed of 2.0 rad/s. What is the op59a fbmp09a centripetal acceleration of a point on the wheel's rim?

  What is the centripe pvpw- v83p up.zb4s*ital acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm whenz.usw83-4ppvbip * p v the bike is moving 8.00 m/s?

  How many revolutions per minute (rk-vn gt6qx.;4 tcbv3f pm) must a circular, rotating space station (r = 1000 mxvvgnt kc-qbf 63 ;.t4) rotate 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 speed ofei d zo/ )h 26fy27pn/xii7hse 20 m/s. The maximum centripetal for pihfde/ s6/ix ez2n27oh7)i yce (provided 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 speed ofg czq rx2fhxib7usl,aq; 95-/ 20 m/s. 2-x9lz;agr uhx,5qfis c7/bq 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 twk c,s1/t1;o / o oknz1(swy8e;xxzhuo the end of a 0.750-m string, is whirled around in a smooth level table. Iny;s s/x( k;o/x8kec 1wt1uz o,wh1ozf the maximum tension 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 slipp+p0as- +zvgd)u5l ois0kc :e ting 10 m down a lane at 4.3 m/au5 :+stg0+ zop-s 0v)eklcdis.
(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 wit90aadu b5 lcz7h 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 co/qgdr xq2 e f cy5c3xui8*u0g)nstant 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 stav,z1.c- lz ih2tl zog*rting from 2ozgvtl- z* ,i 1hc.zlrest 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 acceleratirt;tj 7c3loz +gt3nqb0p 06skon 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 constanw 0eizqyc9e- +7yv 0cxt angular acceleration qcyx-cez+ 0iyw0 v97e of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reachex7u 2hnt- n5jks an angular speed of 6.0 rad/s while turning through 2.0 revolutions. What in thn5j 27-kuxs the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm sn 8cn k*7inx.xlows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutionkx7nnic *x.n8s the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from lxy8)v jl28xc8.40 m/s to rest over a distance of 115 j8lvlx c 2)8yxm. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformd ;ht-m5 uojtkrx(.;yly from 8.40 m/s to rest over a distance of 115 m. How long do;-drt (.mxy5jk uh;toes it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotatescgcim0 x:2 3gi9cfw8-ut (y fr2y/ nwps4pdx5 at a rotational speed of 3600 rev/min. When switchedfm 4iw ycfgxcsrx8(cptu 9-wn d5g0p232i : y/ 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 tightz6i/emj+z cjs-b.s2 pening 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 is pc +/2i.meb6pszs j jz-erpendicular to the wrench?

  The bolts on a car wheel require tightening 2)jjtw 8+z: w4brxi dbq1hfq)to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force requi itwj8+rb4xbh1j: )dq)wzqf2 red when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment 8,l k+l+-sa (59 .gg6jcccxahujy /3if lg bdsof 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: sz s*jgfa6a,wi8n/ n) mass m is at the origin, mass 2m is at a g) i6*,zn/nssjfa w8x = 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 abouhamz gl h82+ru5p e nsw8o92b6t a frictionless axis thought the center O. A rope wrapped around the ophw9 l6egrb8 hmno8as+2 z25uuter 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 frictionless ax.xr+:s/ii w jtis thought the center O. A rope wrapped around the outer rr+ isj:x w/t.iadius $R_1$ = 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 end. The rod is initially held in the - f)wazjheka:3w x c::d ndbktp.7,3h horizontal position, and then released as the free end is allowed to fall. What is the angular acceleratio3 :bp:da .) e3hftcj wkwx:zdnh-a,k7n as it is released? (The moment of inertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be-ozzz17t m; we a ring 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 for 4.1 s, what linear speed does the wheel achitmo7- z z1w;zeeve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fricdhoe,nc: (n3 ctionless disk pulley of mass 7.07 hdec c,:(no n3kg 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 puy2mh4/ofn4t r/(zq o ldr(iq )vq*es2lley of mass 7.07 kg and radius 66.0 cm. What is the acceleraqoyd2 /n )r2mlhv(zi efrq/4q(os4t *tion of the mass?

  A rotating flywheel can be used t hlekh9dxf.sdt );p :,)x1wdm o 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 e-r+u;kxy1su 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 a(ze *u(kila*gmj ph:se j 7 dg2i6o5l.nd rolls without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when it reaches the b5zlea. 2mks*i j :g6jo*e7gip (( hudlottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m 5n7be h,r2annu3 h-*9jsh6ia i te 0nfrolls with a speed of 10 m/s. How high u,jhhe r90innb ntn- a6753heafs i*2up an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.2x o1phu 3dmu6(0 kg is released from rest and allowed to roll down an inclined plane. Ho( xo6dh 1mu3puw fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 2zn*csf yk6z2ju; )rx 1.5 kg and radius 15 cm rolls without 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 f*r ) ;u62szj2n zcxkyby $I = (2/5)MR^2$.
(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 chan ci5-ppwf;l) jges 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 inertia ofnd 6vw.8n5b1rvt 5xag $5.0 \; kgm^{2}$ 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/suzt*1ewi mmd18 xd-hg6mx -w) with arms extended has a moment of inertia m6t)zu-ww e-d8i1 mm*d1 gxhxof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?