Angular displacementy*fc t98k(ga ov e+*vlcb6bp/ is usually express in units of

  Angular velocity is expressed i nkb uz a-5n.)sw7d pxk4;bbe(n units of

  Angular acceleration is expressed in zp:bqxw *82z p0h(mue units of

  A boy and a girl are ridiy(y iwcyl k,p:ez/ :,di6 d3hxng 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 greatezpi ycik6ly,3 :h/ y,d:xdw(er angular displacement?

  A boy and a girl are riding on a merry-go-round which is turning at a constantk q,hthp74rpb: kr;0d rate. The boy is near the outer edge pdqr; thhb4kp07:k r,, and the girl is closer to the center. Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a constant rv.vd3/ axw)p hate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater lineadx /)pvh.aw3vr speed?

  A boy and a girl are riding a merry-go-round whi duire y*gq gx4mst8p2fs8h1/.w8 y8g4ke8 nbch is turning at a constant rate. The boy is near the outer edge, while the girl is closer to t bm4fxy q 2h*s8 .1g/4ykg 8w8ns8uprge8itedhe center. Who has the greater centripetal acceleration?

  A boy and a girl are ri ty,pek821iw6t,kcg z ding a merry-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 tan2e,cp,tk wyz t g61i8kgential acceleration?

  Consider a rigid body that is rotating. Which of the foll5jxiv9i 7gg5 vy8nj56aopi8nk8zb) mowing is an accurate stn z omgii88i5n79kv65) ja vy5 bxjpg8atement?

  Rolling without slipping depends onls.3 e)gpohrbo *xn9c)/, zth

  Two equal forces are appliedkz )rq5n)vzi o)i:*di to a door. The first force is applied at the midpoint of)dkqoi) ri vz*z in5): the 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 applied yi(7m io.abaj(1q ln1to a door at the doorknob. The first force is applied perpendicular to the door; the seco.qjiio7nya( b1a(m 1lnd force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, pa4. bk*waxnfshc5pbq1 .hh din6/( -r li)gv5erpendicular 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 of6wnq bhia4h sx15 fhca5vpg)l(-i/k..b*dn r the second is

  What is the quantity used to measure an object's resistance to changes in ro-o.si g aqlq:zs8 )8vwtation?zwi qs): 8o-vs.q8gal

  Consider two uniform )xtddx.1 sw w-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 to that of the smaller moment of inertx1w. )wds-txd ia is

  Two uniform solid spheres have the same mass, but one has twice the radius of to au36xb:h x0 ln:zhk+he other. The ratio of the larger sphere's moment of inertia to l6hx+b:h x0 z :3oanukthat of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass ax:mq9v+g ea0p nd twice the diameter of the other. The ratio of the larger moment of inertia to 0 9+ :xgevpqmathat of the smaller moment of inertia is

  A uniform solid sphere has ma .u9f)8m8,hjxltmdre,f rfo 1wx +3l jss M and radius R. If these are increased to 2M and 3R, what happens to the sphere's 8utm93+ rd1lrmo8 jxf, x fe.hj )fw,lmoment of inertia about a central axis?

  If a constant net torque is applifm y1wt.4xupp/o3; lded to an object, that object will

  The moment of inertia of a solid f-lu 0 byuf c01x;h)o 2b1skxtcylinder about its axis is given by 0.5 MR2. If this cylinder rcblkh1f0 x-o2) ;xu tu0yb1fsolls 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 whu ,tojxz(cqtilbp5ae 9 0.w5-ich has a mass of 10 kg and a radius of 30 cm. What is the ruzaoxq,5-t5 ib9cp jtl. w0e(atio 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 witho xig5r+huee(gr/f+(ld7on) y ut slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom )/7 (r+ey f ggxln(h5ue+irod of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without slippi4i ,bushu/ 4lc qk/l(ung down an inclined plane starting from rest. The angular velocity of the clhqi(/4k /lu sub, u4sphere at the bottom of the incline depends on

  "The total angular momentum of a system of particles changes when a net eqnfq2 jzd ho(nhs0 +4 aj51hv6xternal force ajn0j21hhof q z6a nhqd+v45 (scts on the system." This statement is

  In what circumstances can 7f4dqkjnt0r 6bu; *:l v0 aupithe angular velocity of system of particles change without any change in the system's a vp6 f74jul0tn *:kq0idr; uabngular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore r4pr ko+ (ku0kbiu, h0x-.yktany friction which may be present. What happens over time to the Earth's angular momentum 04ubr- uy r0i(kh,+kpxkkot .about the Sun?

  The Earth moves about the Sun in an ellgnd*a.unkq * /zid4-x iptical orbit. As the Earth moves close to the Sun, then wng.u n*zxi4q* kadd- /hich of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette ( vv9p(uh-fb5rv 3gwqgrv7 r7f :l0we8a fast spin) by pulling in his outstretched arms close to his body. Whv qgr8gr9wv7- r 5 v3 70ufv:lbhfpw(eat happens to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulli ydphlo7b -b7 ,xk gf(y8h69hrng in his outstretched arms close to his body. Wha xplhho,6f(kbhr -9dg7 byy78t happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fa .ow5-l6 p m9wgzvht-fst spin) by pulling in his outstretched arms close to his body. What hap6w f-hl-g5 v9pzm.towpens to his moment of inertia about the axis of rotation?

State the law of conservationn()i *pojh0end*m akh9ojv; 5 of angular momentum.

  What arc length does the Earth travel in a three month period in itia nk) ,y3rv9os nearly circular orbit about tyvk93ra)i,no he Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a kv/xm9.i1d uno:0gb 5hlqt,* ko vgmt;; dm)jclock has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 / dd:gmij0xt*v;95kl o;gm.q tb 1mon)uhv,k seconds?

  How many rad/s is 25 hnd:bzvhg 8c,.ygj,7 revolutions per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wh:syy/:i /4foa txu xl/at is the frequency of the wheel's rotatoyx:4 is/ l:fuay//x tion?

  A pulsar (a rotating neutron star) emits pulses at ho;4;nz- wf,0zj c jifa frequency of 0.40 kHz. The per,4;f- 0;n f hwijcjzoziod of its rotation is

  A phonograph record rotates at 45 rpm. Through what angli 0z wofdxjl.:v j:0f*e does it turn in 0.20 lwfv *zx. f0jo0ji::d s?

  A wheel of diameter 26 cm turns at 1500 rpm. How faa. 6k8 hi .,qwpfd6vmdr will a point on the outer rim moapv.d m.d, 6fw8 kiq6hve in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revotk* lo4xdv-cvd(3. zulutions in 4.0 s. What is the average angular speed of the whd(l.vz-kv t ouc*4dx3 eel?

  A bicycle wheel rotates uniformly through uu6( wp.2u;qq.jxuvv2.0 revolutions in 4.0 s. What is the linear speed of a point 0;uw x(26 uuupvvqj..q .10 m from the center of the wheel?

  A cable car at a ski2 v o62/xi uujsx,/cwy resort carries skiers a distance of 6.8 km. The cable which moves the car is driven by a pulley with diameter us 2w x/y6,u2/vijxoc3.0 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 fq4rr iie8q35is rotating with a constant angular speed of 2.0 rad/s. W i r5q3iq48rfehat is the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cuttexk2 7j -8y5)b y5bdzjpls2cwr r is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the approximate linear lzyr 8-5 k2xsb pb j5jcd)7w2yspeed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angular spp jy)+o u(m,wzlax 2d4eed of 2.0 rad/s. da4 p2,xw o(zmu)l jy+What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the p3ct(2 iy xm24+fnw,-fv if v*qqcvidn ,04ddoerimeter of a bicycle wheel of diameter 70.0 cm when the bike is movidnmwo3+ 2 f0if*4dq4,yxcc d2 vfv(it-inv,qng 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating space sta j8spt mp4ih48okf8:byh rb2(tion (r = 1000 m) rotate to produce an artificial gravity of fh4m h 2s:bkp8p tbr8o8(jy 4i$9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m wi9l ;*ykmmrrw.1n8a st th a speed of 20 m/s. The maximum centripetal force (provided by static friction* maw;k 8n1 y9stmrlr.) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flatm9xyl 8*phnh 0 circular curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by static friction) i*ml n80 yp9hxhs $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to the end of a 0.750-m string, is w0x():vctec7o vff*mmn-2 xn+ov8 ,arrcfcy 9hirled 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 fmnm92 v7v )trr 8:c*ffo o+ enxx,acc-vy0(c mass have if the string is not to break?

  A bowling ball of mass 7.7+ s/ d2*0of)o mkxqcit/rkhl o)y+ey5 kg and radius 9.0 cm rolls without slipping 10 m down a lane a*+yrykoqh tdol)+/mf)/0i2k e os7x ct 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 with*(( cr pip)iyr 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 acceleration oyu5;7bl )ls uzc hc+:8hjrk8j f $4.5 rad/s^2$. 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 rotat45 i9 h(d)/lnn:vdwswsb/dfke after starting from rest awl4hfwdvnk/n/ ds)9isd:( 5bnd 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 acceleration of ,ji (axillhu35ke10ftele 6rk 6mo/)$4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s dece cq2v pzc 91x/)xv+iwylerates with a constant angular acceleraipxvq)x+ zy w9c/1c2vtion 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 g k.4hvve5t *dnu2j,espeed of 6.0 rad/s while turning through 2.0 revolutions. What is the averaedv*2gk4 ,5. vujnht ege angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to t/dbv:vqbulm gf9c+mg47z;4 rest over a distance z m u9b7dtvg:v;/+q4g c4mlfbof 115 m. What is the total number of revolutions 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.*c o w:y 8cruwet3)wbst over a distance of 115 m. What is the angular accelu8t3w re.w) w cyobc*:eration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to reix-gb4xl0 o(pbzi t+: st over a distance of 115 m. How long does it take for the wheel tx xg+b-b 0 top4i:izl(o come to the stop?

  A centrifuge in a medical laboratory rotates at a rotational speed of 3600 u m1ago.cdou9u td, ,)rev/min. When switched off, it rotates 50.0 times at a constant angular acceleration bef)ooag.d ,9dmuu u,1ct ore 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 toa.)jw:co os+w a torque of 90 Nm. If a 30 cm long wrench is used, owa oc+j.:w s)what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightenx )f3 hw3r;inying to a torque of 90 Nm. If a 30 cm long wrench is used, what is ixhf ;)3 3nrywthe magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia inu03-sa u;gn$3.00 \; kgm^{2}$ 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 u,g 9zk x za(mgt5z2-9lqnr j*is at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is the moment of inertia about thetl q 5zx a2ggk r*mj-(u9n,zz9 origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thoughs 4;(4 k rwhfysi/cwy+t 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 sectios 4 sycyw; hi+krwf4(/n 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 pivoted about a frictionless axis thought the j o9l87y 5k8jgt(gmh fcenter O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a force F1 = 5.0 N to the right. A secj8ofg (58jml 9yh7 gktond 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 enk-q*t 5;f ly2 d -owu4fnau x6w0(xtmxd. The rod is initially held in the horizontal position, and then released as the free end is allowed to fall. Wh x2wfx 4wtnd -lfuaokm0;*q( t6xu5y-at 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 radius 30 cm andythcy*f w1v 13 mass 1.5 kg. Neglect the mass of the axle and sprocket. If af1v yw3y*c1th 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 diskkf4 mcfve5 7x9 pulley of mass 7.07 kg and radius 66.0 cm. What is the angular acceleration fkcfmv457ex 9 of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk c0ak7 zd ;fo..,xqx2g)ixgvc4x zsa,pulley of mass 7.07 kg and radius 66.0 cm. What isz)vf kg 7z0qx cs,xoxi a.x2adgc4;,. the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is required to stor10rk9l4k5h w-zsqei *v+ftgwe $1.00 \times 10^{6} \; J$ of energy when rotating at 400 rad/s, what is the moment of inertial of the wheel in $kgm^{2}$?

  A wheel of moment ofj/tum. a1rmxh),x)a k inertia 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 rke;a+ribi,c al ms3; 8adius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the s a ;lsbimi8;rkea +3,cpeed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 8b)jdjkg:h t o 2jbw5*kg and radius 0.010 m rolls with a speed of 10 m/s. How high j g:tj2k5h d jbw)8o*bup an inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a masss qi0o3av yktlf.d8,*n9. rpb of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it mov.83sio nq y90 vrdtl ,.pfabk*ing after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipptsfa-)wuscs 21ri*2uy4a / qlrcu;l (ing down a 35e incline that is 7.0 m long. Assume it started from rq2 4aufwc(ty1au2;ss * l cr/-lir s)uest. 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 momentuzypg eam,-4x15ca xy 1m 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 op++yt/ ee0ra sf 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 with arms extended has a mg-9 ie4rpiu hfve5t :2b //dhooment of inertia oe b-rh9 pt//ghid4ev52ifo: 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?