Angular displacement is usually express in unitsvrsnk y)6/67kidp-ypaui/b ) of

  Angular velocity is expresseddmc-aj a v1n:;0aby-nz o+ xs63yebq3 in units of

  Angular acceleration is expressed in units *5t;wh qe q;kq3)qzncof

  A boy and a girl are riding on a merry-go-round which is turning at a consg 7sy2kyl;9 ovtant rate. The boy is near the outer edge, and the gir7sovg9; l2 yykl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a conq7jzd7 q4)w6td41 q,iliqltg stant rate. The boy is near the outer edge, and the girl is closer to the4q7q zliw qdj,7d4lg1i qt) 6t center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning d 8wj:mub;.z fat a constant rate. The boy is near the outer edge, and the girl is closer to the center. :um8w jfbzd .;Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constanwbi ciod hz pr**fnb5,n44 17vt rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater centr n5dvpi*hr cb,4f7*o 4wi1bnzipetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constantkvnrl cw 5*m9o-gc +8b rate. The boy is nearowrclc 8+9 bg5* kmvn- the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotatkk r v9mg45gv9517sl py rsbk-5 tta,oing. Which of the following is an accurate statementkv5t v y9ok 9-rsr5t4p m ,gs7kgla5b1?

  Rolling without slipping depenihb1k cbv5e4* ds on

  Two equal forces are applied to a door. 9 nq0r fyqji.+-mj,wodvo y,0 The first force is applied at the midpoint of 0jy9dy+ vo0qjf,-iw o ,q.r nmthe door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are ap6qwc, q ;gvvui0:(tg aplied to a 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. Which forc,uaq6vq wc0g t( g;iv:e exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular tozoksg9p9.,s 4 pq5m*mxjxo f , the door. The first force is twice as large xjz*sq,4s9gp,kfxo 9mo5pm.as the second force. The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to c3yuk0e(wod/la b-qc a9a -2ljhanges in rotatia2co(ak-uy-3j/9e0aqll dwbon?

  Consider two uniform solid spheres where both have the same ddlsda:x25d 3 diameter, but one has twic352l:dadds xde the 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 th 3yck mawu1cdk 13zo7l, kx0(38pyaswice the radius of the other. The ratio of the larger sphelhpx0d8a 1u3 o,c1 z3ys(k k7wkam3cy re's moment of inertia to that of the smaller sphere is

  Consider two uniform solid7;wmgb-bzywu-ym v :. uwd*-w pd05wb spheres where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that o7u .bz0md *b;mbyw y5-d wvw:w-uw-gp f the smaller moment of inertia is

  A uniform solid sphere has mass M andws:jqguu)*cv5dp -7p 5rre- j radius R. If these are increased to 2M and 3R, what happens to the sphere's moment o-s:eupdrwjrjpv5 * uq57gc-)f inertia about a central axis?

  If a constant net torque is applied to an object, t xm-e*8h1w34k sq*wrudyz8pdhat object will

  The moment of inertit*,9g ezvis+ g9qwm k3a of a solid cylinder about its axis is given by 0.5 MR2. If this cylinder rolls wimg,zt iwqkg93+v *e 9sthout slipping, the ratio of its rotational kinetic energy to its translational kinetic energy is

  Consider a motorcycle of mass 150 kg, one wheel of whak;b-x-m azdrqgj +u ,+x2l- hich has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotatioq -xarma2 kgxu++zbd-j;, -hl nal 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 radiuwtbq9 2,r*my l;/r lg(gqwm/ cs R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the inclilmc,gbm9w /(/yrlq*; trwgq2 ne depends on

  Suppose a solid sphere of mass M ankzs+ -z:z)nwgd radius R rolls without slipping down an inclined plane+ swn)z k-:zzg starting from rest. The 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 netlym5 8qjyn w3q4kt31u external fonumtj3 4 qq81yk35ywl rce acts on the system." This statement is

  In what circumstances cwz6bmw)ig2k9t22 zskr t.3ww an the angular velocity of system of particles change wit22wigtb2 k zwkw6.3rzs)mwt9 hout any change in the system's angular momentum?

  The Earth orbits the Sun ino2 +2ypbb 0ek8ja b7qc an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Skbaq0p+ jb8 c22eo7 ybun?

  The Earth moves about the Sun in an ellipticaltve/ 9zm . ;mkv05vubl orbit. As the Earth moves close to the Sun, then which of the following best descr5. evvkmbvm/lu;09tz ibes the orbiting speed of the Earth about the Sun?

  An ice skater performs a piro,qge /.1wg0 eod/r ouzsrgi 58uette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular mogugd 085og .z/ irees,q /wo1rmentum about the axis of rotation?

  An ice skater performs a pirouette (a fast sit.;nah* 90nm2xxie x pin) by pulling in his outstretched arms close to his body. What happens to his rotational kinet*0 n2xen.9a i xim;htxic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by p78)+9c b 6ofot/*u qsknsltb nulling in his outstretched arms close to his body. What happens to his moment of inertia an+cktu*l9qob78to) / f n b6ssbout the axis of rotation?

State the law of conservatiox2( y8*mezu//wdtqy i n of angular momentum.

  What arc length does the Eagi ;j+8,q cadt.h9:r6)whu wct8cs nvrth travel in a three month period in its nearly circular orbit abou 8 drg;wji+ ) h,tccaw9:ncsqu6.8vtht 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 8gq ph/-a ukruu0 n,63 tnehmk(b8a g4distance does the tip of the second ha/hhk e 0u63up nu g4btq8 k-a(mng,8rand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equi bd8lzb8jya0 )h;1rt avalent to?

  A bicycle wheel rotates uniformly th qve2-9zl w6qdhnm -3erough 2.0 revolutions in 4.0 s. What is the frequency ofqn w6l-qhe -me93d 2zv the wheel's rotation?

  A pulsar (a rotating neutron ohx ab m p4lv 0/g4f0, ke+:/wwlr:rnzstar) emits pulses at a frequency of 0.40 kHz. The period of itr/few0+4:h/4vlg zx ow:pr b,0klanm s rotation is

  A phonograph record rotates at 45 7u*o1finp0 4dm)prvidyv j;/ rpm. Through what angle does it turn in 0.20 siyp di*po )/ fvdvnr0u7j14m;?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the .3qwe( yjq.cmh+ y) nfg)n*ijouter rim mhg.)ej)*q y+( n3nfjq wcmiy. ove in 2.1 s?

  A bicycle wheel rotates uniformly thy3 qjh lqi2+(zrough 2.0 revolutions in 4.0 s. What is the average angular speed l(qj3zi2 +qhyof the wheel?

  A bicycle wheel rotates uniformly through 2.0 revol( m3rwnii xx)1utions in 4.0 s. What is the linear speed of an )xxw3r1m(i i point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers apbrn x5inw hh67d6 gnkx51k) ) distance of 6.8 km. 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 xn 6w6pin5 b)rk5 gh7kd1)hnxfor the cable car to make the trip in 12 minutes?

  A wheel of radius 1.0 mils,3/fwo( w q is rotating with a constant angular speed of 2.0 rad/s. What isofli3 ,(sw q/w 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 motordb9h ps bp7i0mgo 5l1+ rotates at the rate of 20 rev/s, what is the approximate linear speed of tmbs o0i9pd5p g7blh1+he end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/sn 2:fq0-ksfu,hye+l y. What is the centripetal acceleration of a point on thefs+y,ku2fn le 0y :-hq wheel's rim?

  What is the centripetal acceleration of a point on the permsuk;u3blym .+1 c /s f9jlm*zxltc*7imeter of a bicycle wheel of diameter 70.0 cm when the bike k9by*+cmtu;3xs71c / mms.ulzlj f l* is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space station (r5f9 2tp4mwos6 wz5gn x = 1000 m) rotate to produc54osx nfzp5wm9g26 tw e an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat ck(zb7ing+wrkti 7 2m7bee v9(ircular curve of radius 50 m with a speed of 20 m/s. The maximum centr7 bn zwb2i(kveim 797+ g(tkeripetal 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 m .yw3ru+ y:nbwwith a speed of 20 m/s. The maximum centripetal fw3yw.rb+ n :yuorce (provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attac,k)owh 1nufve3 0q4rxhed to the end 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 , wxkfnour0hv)134eq 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 ssk*k 1nw2q9e)pla - qtlipping 10 m down a lane at 4.3 2- s9)*e 1kanktqlqwpm/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 con n.ck ;zrzv/q3stant 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 z o87vz6w-tyb 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 rotat 2c,eluye kzvj -u55mbpq18m2 e after starting from rest and accelqj8e m uem1 l55z uvc,b22-ypkerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, s5lt+ -m2tmbyand has an 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 decelerates with a constant and2x .g9s iajmgq(6dmjc pf83 -gular acceleratio mqs8(d-jfmax 2g6p3 cjig.d9 n 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 sp krmt,l.+l9g kpwu:;ld-mqa-eed of 6.0 rad/s while turning throw9 -.q ;ldlk,m r:kumlp+a- tgugh 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.d5xbu+r/s n-lyys/ xbbs p z6kfnv 361d7ca:4 40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel 3b5v:ssuy/16c/zx+n p- y6xsn b4k7ldb darfrotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ovesx a )hbdzu1n 0fbr-,1r a distanx0drsh ,)1naz u1b-fbce of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slo)w6w89b 4q-p mqwk vptws down uniformly from 8.40 m/s to rest over a distancqw -m wbqt84)6ppv9 wke of 115 m. How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/m( upa+c/jl2c 0tjms ,tin. When switched off, it rotates 50.0 times at a constantlc/ (tusctj2ja,0pm + 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 toz;xumkn)zj/. pl 7 1qgg9h.-6 gqcgn i a torque of 90 Nm. If a 30 cm long wrench is used, what is the -u x/zcg g.p7q)z961 nhqklg.;n igjmmagnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to 12ivtbed60 gw a torque of 90 Nm. If a 30 cm long wrench is used, what is the mat0w be 6g1vd2ignitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertispak c5pti- fj2e ,.1ea $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: bjo, rxkr x )u9l.fq3+ mass m is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is theo ,q)k r frlx.+xj39bu moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionleivib. cak1cbe 6;i7t;hez 2t1ss axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A second rope wrapped around another section of rada1;kv et 6ct2 e;1i.bz7c ibhiius R2 = 0.50 m exerts a force F2 = 6.0 N downward. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictrymvfjb)c5t5zc o 3)-ionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. ofz) j 35m-tvr5c)cyb A second rope wrapped around another section of radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. 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 at2:3h rrk i7utiw:gev up,n2k) one 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 released? (The moment of inertia of a rod about one end is ML2/tnrv:ki,) g:7erwphk 2u2ui 33.)

  Consider a bicycle wheel to be a ring of radius 30 cm and ma 4b6uhhtwg o/cs 8*j q(,d1glenmw .w)ss 1.5 kg. Neglect the mass of the axle and sprocket. If a force oc.*e/ohjmwhdun b g1() w4qlw8 6g,tsf 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 rdps. qfvhm e oe+m481a9sa: (lqf9d1zope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleratz(vq fa48.9os e9p1q m1d msal f:deh+ion of the pulley?

  A 1.53-kg mass hangs on a rope wrapped aroundaefta1.,b8a o koee -7 a frictionless disk pulley of mass 7.07 ae7, e1k.oo aba- et8fkg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can be used to store energy. Ifh c0jqe;d doj7.3 ljwg c;o;2 mnd45zy7q;jiy 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 inbzdnb-p exw x/g5w;4e w0-afv 4ue**nertia 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 rol6s b f/d;-ztpyw8c *(f qxasg*ls with-8c*qd6sgx a;yf b*(tsw z/pfout 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?

  A solid sphere of mass 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. tfoz 2a jr4l06 How high up an inclined plane can it cli4fjr26zto a0 lmb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and allowed,7 ujjmdrc w1;k4)k( s mitx6p to s p6()udxt41rj;w7mmck ,ji kroll 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 r wb i 6-mw8wl1uh9uq ;qgfig9/olls without slipping down a 35e incline that is 7.0 m long. Assum8ig/6whqiq9f- mwu gu1b ;wl9e 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 changestmmd;g r+wyw3:(v s.v 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 ofx1;af ct0ot; 8clxkg*dv b5dsn6e2)s $5.0 \; kgm^{2}$ 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/.ss09qpjy+w86 kj wt3r* qlat s with arms extended has a moment of inertia op a q tr06w sly.8+j3wk9j*qtsf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?