Angular displacement is usually express in u;soq.3r f+ q*x2lpvdh / (frdvnits of

  Angular velocity is expressed in o7ytnr2rm-lt1f tj5s0tqk/w2 , mk n9 units of

  Angular acceleration is expressed in units/.tqf k-sr*yk of

  A boy and a girl are riding on a merw1aqw.c ehypj 6d96, zry-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 angular displacement w1, pedqh.j cy96az6w?

  A boy and a girl are riding on a mer/;b1aa zrwnfr,h)vx4 ry-go-round which is turning at a constant rate. The boy is near the outabfh van rz)x,wr4; /1er 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-g*hlq *s*l dh;0olzf,ro-round which is turning at a constant rate. The boy is l*,h; * or0zq*fs lhldnear the outer 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 turningdefxmt) h9c68/ +;ynhyfm 4gj at a constant rate. Tjt9mxm fch;/+yde6nh gf8y4)he 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 mepy gs4t,wlf wh sl/9eq,7qh) +rry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential accelwq, s4 /lhg+y9p7te sfql,) hweration?

  Consider a rigid body that is rotatis xv8dahz87vz4wysrb qj73( : ng. Which of the following is an accurate statement?8z4z7:r3b x8w7vdajvssq y (h

  Rolling without slipping dej py-w uv;diydm gru)x sdst5,r::50(pends on

  Two equal forces are applied to a door. The first force is applied at the midp xx0fi 38q5ffeoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the efxq0i8 f3x 5fdoor. Which force exerts the greater torque?

  Two equal forces are applied to a door at the doorknob. The firstd4t 2a 1ce9dig9:yvwq force is applied c 9via1:t4d2gw9yq deperpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to wp6:h j* q9 ocih5nbc49e5wt ethe door. The first force is twice as large as the second force. The ratio of the tw :c5o5h49ie*jpcb weh qn6 9torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to chanc6bd c n38ry kqujm-243)tuil ges in rotation l4)qu cmuiy dr8n6tc3-kj 2b3?

  Consider two uniform lcd 3hcmp0;g2 (iiuu.solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia tph;3lud2cuici0( mg. o that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has twice theg m;)zflez50h47ej5qv c*uzu radius of the other. The ratio of the larger sphere's moment of inertia to that of the szqvgz; *e4u0)5 hz fjm7ue5lcmaller sphere is

  Consider two uniform solid spheres where one has twice t.:c;. ixr qxo6t+tek phe mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smaller moment of ineo6x ; e+r.qx ipc:tkt.rtia is

  A uniform solid sphere has masswngq0)4bloi 9c7c xm8 M and radius R. If these are increased to 2M and 3R, what happens to the s7 ) omb4g0xcq nciw9l8phere's moment of inertia about a central axis?

  If a constant net torque isqhh7thq 40esp - 0bc:v(q fkzd80x +do applied to an object, that object will

  The moment of inertia of a solid cylinder aba4qsdfyv72h :out 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 whicht 5la.dgtq xj1ef.r. ; has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotati1 fx;alrg5jq.t. dte. onal 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 Re uijx2nj ur 8kn k*e5fy4852n rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom j48 e 5 ufex*in5n2uk2nkrj 8yof the incline depends on

  Suppose a solid sphere of mass M and radius R rolls withou6cj.qyy0ysi +;a hlr q5 i7;er/jod+ut slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of ;q+cqy +ujay si7ojry hi/6.;re0l5 dthe incline depends on

  "The total angular momentum of a system of particles changeq 86zyuy8dpr,s when a net external force acts on tydqy prz86 8,uhe system." This statement is

  In what circumstances can the angulay:w2.ka hup2,zm jf-sr velocity of system of particles change without any change in the system's angular momez.,ys kmj:-2 aufhp2w ntum?

  The Earth orbits the Sun in an elliptical orbitvx/s 51h9ehrg be0 s;j. Ignore any friction which may be present. What happens over time to the Earth's angular momentum0xesjsr9g bh;/e v5h1 about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth movwv9 ;cin(h:ilu 7qw h,yrg6*jes close to the Sun, then which of the following best describes the orbiting speed of the Earcv7un; *hi, :yihqwwrgj(9 6lth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling indmsk :uo. l /l4p9q-iz his outstretched arms close ld:z.9 qoluk/psi 4-mto his body. What happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spina 5oye30n *zji) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about tnij35* a z0eoyhe axis of rotation?

  An ice skater perfor6qvs rmt bs438ms a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about 4sr8 s3v6 btmqthe axis of rotation?

State the law of conservation of angular momenu x s tkaqsg9*u694wd;tum.

  What arc length does wib8-s-b g,p;84o -b(yjhny+afzs grthe Earth travel in a three month period in its nearly circulizsowg b;(n-r-js p8 h-y8a4,gfb +ybar orbit about 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 distanccerq t.yp.z 53e does the tip of the second hand sweep thytp 35 zrecq..rough in 3 minutes and 45 seconds?

  How many rad/s is 25 r hm;uv;8bau;rge ozs(-/o 0kxevolutions per minute equivalent to?

  A bicycle wheel rotagg n1/ jo3b4kujxu+t2tes uniformly through 2.0 revolutions in 4.0 s. What is the frequency of tt u13+ okxj4gjn2ugb/he wheel's rotation?

  A pulsar (a rotating neutron star) q-leq 3nw)8eh og3sgql 5n4 9k g/e,ulemits pulses at a frequency of 0.40 kHz. The period of its ro3- qk /qe o ,nll53lsgg98nehw4ug)q etation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 73w0hp 4c u xfpxgjhux8( g +np85/tir0.20 s+78g(5j tg3cpxxh/n 8p4xiwr pu 0fuh?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point)/f0ky ea ods+ on the outer rim move in 2.1 s?a/fed o)+sy0k

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. 6b.imi k/9auu :j+dzrWhat is theak.mb6/ jz:ri +iu9ud average angular speed of the wheel?

  A bicycle wheel rotates uni rpux;,iby 8,lformly through 2.0 revolutions in 4.0 s. What is the linear y ip,bu,l8rx;speed of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance of ifeu*3 / vi2ghlt hq2*4f)gcjmz wb8 t*0 e6ui6.8 km. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assuming no slipui2v*c6i t f0/m*et8 ib)fz*eg 2 hjwq lh3gu4page, 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 of 2.0 rad/sxtbc4tg5) i/u ;dj.vvsg/ vt;. What is the linear speed of a point on the wheel's cib/dv ;vggt) jt;5ux.vt4s/rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m in lengthvzu;zunrl81,m n9hymhd :/y 4. If the motor rotates at the rate of 20z1hmh 8:nul, v4y9ydrmunz; / 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 speed of 2.04jsqtb8rt:p +/sbt .v rad/s. What is the centripetal acceleration of a point on the wheel'sv st:t4st.bq+ bpj/8 r rim?

  What is the centripetal acceleration of a point on gf1;b ucjj;qn1 i7xum)m5zy(the perimeter of a bicycle wheel of dia ju5xy b)1m fujziq1 ;m(7cgn;meter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) *)y4z4oug. u9diauvm must a circular, rotating space station (r = 1000 m) rotate to produce an ary*o 4gui9 vau udz).4mtificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a.s or09sh0fh 3i gt4hkytwp;9 xb.)t i speed of 20 m/s.x.t9io;yit 0sw 3 4k)brhg0pf.th9h s The maximum centripetal force (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 *tmzmi3n0//d6. ce nquf mv9om with a speed of 20 m/s. The maximum c. 9ov/ nmz3ecm m0/du*nf iqt6entripetal 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 en zw)rec8( 3a 05tpuqjfd of a 0.750-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 can the mass have if the s8f t q)j pw5raecz3u0(tring is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls without slipp c4ft1rh:atrceq09 x6 ing 10 m down a lane 0r raf xqh46t9ctc1 :eat 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 s4 )ue- n.c m0 vz.feycx g-p,wcw;ew)with 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 constant angular accelerat) ;9;dhkzk9j(j2bi8ds 8o kgwdrm cvrs8ze,0 ion 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 automobied+*k1msv1 cit yk h8ute;i:p5b tr2(le tire rotate after starting from rest and acceleratpt* ;i rkcde8h ekty5iu1 vts b+(:21ming 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 acceleri2 l/qm.ry )ntx:w 2cwation of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/z4 jx w noheh3opka553 x0i7*os decelerates with a constant angular accelerawo4* 35j5p3eh 7o h 0xxzoainktion of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad eor2 4:ht,npf9al /sh/s while turning through 2.0 revolutions. What is the average angularrn o:h9la2p se,4h/tf acceleration of the wheel?

  A wheel of diameter of 68.0 c1uwm 4d ft5sh/ yd7wr3m slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotauydh 7 4s/w3w 1frm5tdtes in coming to rest?

  A wheel of diameter of 68.0 cm slows dow,d- vnqnar /hz 6ake.7gjy *d7n uniformly from 8.40 m/s to rest over a distance of 115 m. What is the angular acceajedy7/- h,za 7kgr*.dnnv 6q leration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest over oe:h*y5r* h2kg0klas a distance of 115 m. How long does it take for the wheel to come tosh2re khy l* a5:0ko*g the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3if psqwpy2zh-)5 il9,600 rev/min. When switchesfw qly5i2)-pz 9p,hi d 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 to0w uz,kg ikx3qybj1 u5*oc*e- 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 perpendicular to the wrench?0*x yw k,i-c ob5gje*uq1u kz3

  The bolts on a car wheel require tightening to a torque oft07 :thq3 v)r*kh amd*fgpu6 9nj ;d0xmjxx3q 90 Nm. If a 30 cm long wrench is used, what is the mam3 tk fxgamd hj;h07juq*0*)3pxvt d69x qn:rgnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of ine0m) nu wsol,:g3ogy4vg/o-hj rtia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule isksr/z 1u vsw;x2ry+2dix,u. oogez97 modeled as follows: mass m is at the origin, mass 2m is at x = a, and, masx2i rr9dzugux,1v. sz2eo7os yk / ;w+s 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 frict r-)tw*4hqc km elt-,sionless axis thought the center O. A 4* cl,hr)se-t qtmkw-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 po: gijl*;6vjbg 5x0 azivoted about a frictionless axis thought the center O. A rope wrapped around the outer radiuo j g5 lxz0a:vgij;b6*s $R_1$ = 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 horizo3f yftwv8ty7 )ntal position, avt8y3tw )fyf7nd then released as the free end is allowed to fall. What is the angular acceleration 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 radyub 2eli8 u2,zius 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, assuminieu2uyl, zb2 8g it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley zjq6 ctf rni;3 .a79xoof mass 7.07 kg and radius 66.0 cm. What is the angular acceleration of the pulley? jrx a6cfq7 i;t.z3on9

  A 1.53-kg mass hangs on 1gegj; je :9.fepa ;xsa rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. s: e9j; 1 ejpaxgf.;ge What is the acceleration of the mass?

  A rotating flywheel can be used to store egpb jy s+j:v,+tpzcn.l al+6 -nergy. 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 inertia0 lz, wzc.8mb-g2 ggmw 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 ref5j :.x)siq lkst 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 thsf k.qjx: )l5ie inclined plane?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of,uh/ ,6oz8qoo z; i2kimrr5yg2lgvo : 10 m/s. vy rz,i rz/o86omo2gh5 o2 ,k;: gliquHow 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 iome;22o qpmpqumr 0,skz9+ 6b(vh(ois released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance of 3s(oz,m kqbmoip v6 ;22q mo0+ehpur9(.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without sl 9i0owq0hzyr5 ;1u xwjipping down a 35e incline that is 7.0 m long. Assume it started from 0i9oyur 5xj1z;h0wq wrest. 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 momentud vbx 6( 4-suhg-hj8y)v/c qtjm 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 inert- e+h,cidfi;a 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 u/ot7b scy a85 4zdc4cp*w rax pd,/r*at 5.00 rad/s with arms extended has a moment of inerti7 p4y4bcr*c rxt5,sa 8udadzw/p*co/ a 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?