Angular displacement is usually express in units of4d77w g-jrx+lme 4j pi

  Angular velocity is expressed in uni8a.k4iq- :lql 2fll kb.p -jweag/j*g ts of

  Angular acceleration is vg:u4c yro72lexpressed in units of

  A boy and a girl are riding on a merry-7 vz8gv7j cp;mgo-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the centv vmcj7z87gp ;er. Who has the greater angular displacement?

  A boy and a girl are riding on a me/nf.d4yxr g62 lxcf4s pshu66 rry-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 greats h.lxxur4 6ynpdcg f/f64s 26er angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a d34g ti mu(6du5s22zdv mzcc;constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has tduc(v6 3md s4 2;c d2migzuz5the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a coz h8xh1z)g: djt2/xconstant rate. The boy is near the ou 2xz 8gcjoxhzdh:/ t1)ter 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-rounq0 lo al5knn- mv(dg- j(2l6pbd which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who hal l6v-25-0japdng ((lqbnk o ms the greater tangential acceleration?

  Consider a rigid body that is tt,hiuc03n9 k rotating. Which of the following is an accurate state3ch nitku,0 t9ment?

  Rolling without slipping dependkae*blr 79t(n3u );d3xmc ui ks on

  Two equal forces are appev v 1fbflk3s(h/sb9a3 n7c y0lied 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 7vn9lfay 3v f( sb b0k1shc3e/applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces arepmy n96kd8wp2 applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the planedw 2pk8y6n9 pm of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to the door. 4 wel0bexp*5azypu 4e9y,0 +f.hye :jz,vets The first force is twice as large as the second force. The ratio of the tory:5.te,lje+4u 9xv pepehy 0*wa 4,0syzz ebf que of the first to the torque of the second is

  What is the quantity used to measure an object's raqz 7n hd lxmv((d-ss- m8fp)/hk5ch 8esistance to changes in rotationmz/(sal-dqcv5 xs(788ph hk df-)hmn ?

  Consider two uniform sol/-n33uff suvy-pa aue+7tb6 knlp86bid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the laf /b vbuauk763 un3-p8lt 6esynp-fa+ rger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but onej , vm y3s*4klg5i4mn y3-yqlv has twice the radius of the other,v-gs*y3y3lq5n yimjmk44l v . The ratio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres jz,/ir;d :lhz where one has twice the mass and twice the diameter of the other. The ratir/jz hz:l;di, o of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are incr ;ymv3swg3w+ eeased to 2M and 3R, what happens to the sphere's moment of inertia abou;wy3+wvm e3sg t a central axis?

  If a constant net torque is applied to an object, that objej.0xdm v* 1muhct will

  The moment of inertia of a solid cylindextwz*nlju-ae55xyu h: c4 0u2r about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy i jzu0w2 yu:4 u*5c5nxae tx-lhs

  Consider a motorcyclm6s4+6qcm7pv 1l7cw3e9 joo e0wcd pde of mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cw6od 47cjeml91wpp+70 c 6dmvc se 3oqm. 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 withoff5 :45 +a0rfe vaj1tv5qmj nput slipping down an inclined plane startinga+v 1aq0vt5j fr5p ef4nfm5:j 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 slibe8 f*:7jex iapping down an inclined p7ei e: *ajbf8xlane 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 net extew vwld ,u/p0yp8h6te.rnal foruhp./6p ,we l8y0wdt vce acts on the system." This statement is

  In what circumstances can the angular velocity of system of particles change wx,s h;y0cr)8dfj;rraithout any change in jh;rxcs r,f;0ad )8ry the system's angular momentum?

  The Earth orbits the Susj 7 52smf zf,kgubm6+k99bf dq 6xx.8k7xcmrn in an elliptical orbit. Ignore any friction which may be present. What happens over tcmm25b,8fdgus k6k 969z f7mxxk7jr+x qsfb . ime to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ells) *dwvs(h hhyi6a0 g4cqcg5 1iptical orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth about the Su60 shg 1gwahy5qics(d h)cv4* n?

  An ice skater performs a pirouett1fxx:lg .w s,ue (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis ofs :.l,fxguwx 1 rotation?

  An ice skater performs a pirouette (a fast spin) by dmj5qiu7u+ea. 76 7cd0klfj9b p)brj pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotationjmj j7 q7 k95uecfabrl.+ di d0u6)bp7?

  An ice skater performs a pirouette (a fast spin),br)9(h j l) wg/wauxz by pulling in his outstretched a wh 9gw(,l)zx)/urajbrms close to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conservation/rn( xcix0 1s(xgatf(k ef-imwe.6h6 of angular momentum.

  What arc length does the Earth travel ino 8cnxdj6va); a three month period in its nearly circular orbit about the Sun with a radius6d) a n8xjc;vo of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance zn7.gx+ekpyovno/ww m4t 2 t9( fd7r*does the tip of the second hand sweep through in 3 minutes and 45 se4/dg(wpvx *yo.f7 ntz 7ewn 9tk2 +mroconds?

  How many rad/s is 25 revolutions per minute equivale0*vz 3gea m 9d7kh;gtcnt to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. What is the+.o voa a3c)y/3toohgm c2d4 z frehy ov3amcz3cg/ )d oo+oa24t.quency of the wheel's rotation?

  A pulsar (a rotating neutron(wyyg v 1s1w. ,mhoiy, star) emits pulses at a frequency of 0.40 kHz. The period of its rotatiwhy1s,,1.mv oiy( wgyon is

  A phonograph record rotates at 45 rpm. Thrv .keer56 oe:j;pgjn7ough what angle does it turn in 0.20 s?r v.:kegpj6 joe57en;

  A wheel of diameter 26 cm turns at ir7r c3vywch6 b8*ar/ui) j c41500 rpm. How far will a point on the outer rim mai8*vr)bcw 7 4ry3 r6cui/j hcove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. l xqb (akb86*p What is the average an6*x lakb( 8pbqgular speed of the wheel?

  A bicycle wheel rotat(vqd7q:y vwk6 es uniformly through 2.0 revolutions in 4.0 s. What is the linear speedw( vqd6:7vykq of a point 0.10 m from the center of the wheel?

  A cable car at a ski resort carries skiers a distance c0-mzoo a/w3nqky6,so; s*6log is9iof 6.8 km. The cable which moves the car is ciokmsiszsyga,6o 0/wn 96 oqo ;3l*- 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 with a c+jj8ax m +e12sne(c yod9f*3u p+ybokonstant angular speed of 2.0 rad/s. What is the2c*jueo+s3p8 bam yj (ko1n9y+ xf+ed 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 thq),zggksxc; ( f(0l wxe motor rotates at the rate of 20 rev/s, what is the approximate linear speed of w g,;q(gx0( sxkc)flz the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular speed of 2.0 rad/s.(sue f8*k4 hpk cc sz*tq48y2n What is the centripetal acceleration of a point4k4 u82scez (qp ns f8y*c*kht on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of :cgkpxck 3 x61kf92umdbd9 ; z*rt. kua bicycle wheel of diameter 70.0 cm when the bike is mkbz6muc gk91x.p 2f k u9*d3 :;rcdtkxoving 8.00 m/s?

  How many revolutionsdt8e )3oyogh* per minute (rpm) must a circular, rotating space station (r = 1000 m) rotate to produce an artificial grat*deo 3goh8) yvity of $9.80 \; m/s^2$?

  A car is negotiating a flat ci vs1kfow-sx*+wn z .v*rcular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by staw+vx. s-wk1z* f* svnotic friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating3mutl 5 pp-+2y20d9cp qtzcom a flat circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force p35 cm- c zt2uy9op+p02ltmqd(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 0.7j*.hzz4 nlx/g,t(if gphu 2ph2 0hk9t50-m string, is whirled around in a smooth level table. If the maximum tensit lhkjztu2zfgh9p ./h(g*p,h2x0i4 n on 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 k4wy6r z hg/s -y7la.z9:s:mz1ys fkimg and radius 9.0 cm rolls without slipping 10 m down a lane at 4.3 m/sy6l zsm9w/m4s-gshy1:7iaz:yrf k. z.
(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 accele.yh98lt(ocs pration 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 xl +a1mubra +*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 h;ejh ;fab p --+/ux jms78n-co5w hr pib3g0gautomobile tire rotate after starting from rest and accelerating at a constant angular apoajh7--np/- rh xb 8b wu;ei hm3f 0c+gs5jg;cceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular acceleration of +oux,o:n* oc d$4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates wit k/ab ,5sqkm7 4+0tz oi8fvaqrh a constant angular acceleration of q zr7mb /aaf,+50 tskqvo48ik$-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest ax1h g791qa hiond reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. h7xog1 19aqih What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows19:ze:do4ry1mw a19dqf n rac down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolu1cze1wamn1:yda r4:9q 9odrftions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to re s+u 8.iwbm/npst over a distance of 115 m. What is the anguls/8+b.u pnmw iar acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 mrrs n* *zfk6v0/s to rest over a distance of 115 m. How long does it take for the wheel to cz0 **rk nrsvf6ome to the stop?

  A centrifuge in a medical laboratory rotates at a rdggz ** z8efyps9w h(8otational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration before coming to *pz88h(degy*f9 swgz 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 requi0 km,tz3eze: fre 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 forczm ,z0ke:etf 3e is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of -stzypfp/. z3s*/kbv 90 Nm. If a 30 cm long wrench issz3 . bp/s*ytv/zkfp- used, what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of z/swc- 6 (w+rzzohztjxsm/xk s).t23 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: mass m i)a ;n wgjli*+8,paizs5n qkw;s at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about the origin?;n+a ij 5lknas i *p8,w)z;qgw

  A solid cylinder of mass 10 kg is pivoted about a9bcdx-w: o o+dft8gb4 frictionless axis thought the center wtc8xbdd- g9fb4: o+o 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 radius 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 p+6 h0ew 5k0 ammyz9pdfivoted about a frictionless axis thought the center O. A rope w a0z em5ph9dm60+yfkwrapped 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 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 at one end. The rod is initially x1m 3ftvuf ca4x.d9;rheld 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/u 1ca93tmd . xfvx;rf43.)

  Consider a bicycle wheel to be a ring of radius 30 c,f9dwa(bfu,0,acq z7m5zkx mm and mass 1.5 kg. Neglect the mass of the axle and sprocket.d,9amc7qx( ufmza, k5bz, f0w 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 wr90 xhmz8zv/ owapped around a frictionless disk pulley of mass 7.07 kg andmozh80v/ w9 xz radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped a /kq6ftcsov(*6veve j. shq8 w 2l+v,sround a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the accelerate8t /v6s os evsl f,hvkc+2vq6(.*qwjion of the mass?

  A rotating flywheel can be used to store energy. dq ;q8fshvgnbxad n7o82r +35If 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 invkp07na-w u5uertia 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 mgx1 )3nvvas 1e)rp m6kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high incline6n1 vmgr ma)e1s)v x3pd 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 0.01hk r9: f(bq)7x8 simmo0 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to rex 98fbh sqmo)ki(m r:7st?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released f7w0iao 3h0i6 k)3bb9qdawe virom rest and allowed to roll down a)v 7bk3ohd aiw90qi 3wba 06ein 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 r:jp mrfw429p 8kzh;) p wa5ls15 cm rolls without slipping down a 35e i2p:;frl )mzrw4skjhpw59 a8p ncline that is 7.0 m long. Assume 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 momentu2, dttd9,tuztf h 4) tz0xj+fqm 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 inerfe k n:;ep4hc)z1 fm0otia 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 aty pt 4+ecld)-c-j7zop 5.00 rad/s with arms extended has a moment of inertia o +jzel-cp t7do yp-4)cf
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?