Angular displacement is usizl d/qmj+k - m.8qh.qually express in units of

  Angular velocity is expressed in unbk vo) gw2jk;384udbn(w1ljt0po ib-its of

  Angular acceleration iaee 3gh x+2n mnbvl.58s expressed in units of

  A boy and a girl are riding on a merry-go-round which is t*hgw qd4p,a 0lurning at a constant rate. The boy is near the outer edge, and the gpwd a 4,*lhqg0irl is closer to the center. Who has the greater angular displacement?

  A boy and a girl are we+x)jin2w x3 0 rnz*jriding 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 greater angular spe2 x3r*i)nxzn0ww e+jjed?

  A boy and a girl are riding on a merry-go-round enbwl,ul4 l7+ s0ic7xwhich is turning at a constant rate. The boyn ub e,lw7c+7li4sl0x is near 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 whin(f5n6vlve 1 pch is turning at a constant ratenf p1e5l(vn 6v. The 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 areva xf ddi6ud4a0-2d.x riding 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 t2.d60d-x fu i4avaxdd angential acceleration?

  Consider a rigid body that is rotatir9d zg 8s7y jjupptwu2),uj-1mvft* 8ng. Which of the following is an accurate statemen8 gut8y 29-uv *,7sdjjft puz m1wpj)rt?

  Rolling without slippingqx kh ro**;tp ic :niqe+2ut6: depends on

  Two equal forces are applied to a door. yntx-m y -:;b47chwqq2ks di(The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces -n 7b idyq;:xms2hwt( ky4-cqare applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applied to a do))h xrek(jx )bor at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 3xhk)x b)ej() r0e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a dfyw 1 s8ut:jl;oorknob, perpendicular to the door. The first force is twice as laj;wf1: tl8 syurge 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 spx)szr l64;mg w pi24object's resistance to changes in rotationsg4sip)l2w z 4 ;6mxrp?

  Consider two uniform 3u g1* xnce4c k2/cmppsolid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia tu 3*c4nxpe1gpm ck2/c o that of the smaller moment of inertia is

  Two uniform solid spheres hav/q cq/+yvs4k 7y yo8hme the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to y8+ ymsh4/c qv7y ko/qthat of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the d9uw24 j -vwvvd bf.hv9iameter of the other. The ratio uv.b 9vvwj4-f vwhd92 of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radigy3 urogb 2d-;us R. If these are increased to 2M and 3R, what happens to the sphere's mom rub3-o yg;dg2ent of inertia about a central axis?

  If a constant net torque is applied to an ob4p)wo/cerhxli6p x( , ject, that object will

  The moment of inertia of a solid cylinder zf d- y-qzyhf97ai(t+.vnh.s about its axis is given by 0.5 MR2. If this cylinder rollf .zhny9 d+ atv-hqs-iz (7fy.s 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 whift j 1e (ytq4ex,qtx((ch has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels txf,q4(yx (t1( e qettjo the total translational kinetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R:o wcdvdpd5a-/ ;w0 hpqxnv5+wx y+;y rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bot-; oc y++d55/0q pyxnxawwv ;h:pwdv dtom of the incline depends on

  Suppose a solid sphere of mass M and radius R rolls without sli:u1)g/k 18cbv)h0pq6hz yz e 0k.tru)wppjc hpping down an inclinh) p6w e/qg jrhu t)u0:z0y11bvpkkcch z .p)8ed plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a systemqll8gasy k0h q)-e7fr1p urm *fn6eb4 7(vvy/ of particles changes when a net external force acts on the system."vpm7e0)fy(6y7q1/q*g8lrhafl e 4s - ur kbvn This statement is

  In what circumstances can the angular velocity of system of pf :1a jj 3o8ot73o.r;wgzzj.0epy qfcarticles change without any change in the system's angular momeg;1wr 33: 0zz o.yqj afpc8fo7tejjo .ntum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which m+nv0jrx2y:3p w4+gqf ml e.jf ,0qmhbay be present. What happens over time to the Earth's a +j wx yh j3pg.m+2f0nql:,fbeqmvr04ngular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth moves j7zy*;c, rb./eoaqyz close to the Srzy, c.ob ;e*z/y7 qjaun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling in hif9smupik -7-bs outstretched arms close to his body. What happens to his 9ik bs m-upf7-angular momentum about the axis of rotation?

  An ice skater performs a pirouei )3, dy9hjnor9 xnpo*tte (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational y dp )i*9n9xr3,ohn jokinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling ymn*cf+ r 0+vqywdmno-p h4fhnn24 2 2in his outstretched arms close to his body. What happens to his moment of inertia about the ax npdh+n 0+ f2f m4qnvrohwy42y2*-cm nis of rotation?

State the law of conservation of a ,x:y7s)aa wjdngular momentum.

  What arc length does the Earth travel in a np mhk2u*kum.7 4+ hlbk/ axfh)m1v3ythree month period in its nearly circular orbimn1+2y4u)hh3 k7hbm*/f. ukmxlva p kt 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 distance does the tc,zn,4mux . elip of the second hanx,zu, m4nc e.ld sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute e- b5ynd66q1 q7pp8mp.scl aebquivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wha h78 jj+ /-ndbf7tg 6fzbr1fndim 9k7pt is the frequency of the wheel'pb7g7kf d9+76tjfn8 n1bmirdh /z- jf s rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kH o;qs oq;iek6os8tb lk2:m )(cz. The period of 8oq2o mo etskikbql()6;s:c; its rotation is

  A phonograph record rotates at 45 rpm. Through what angle does it turn vplcyx + 20:dh8kgv. 8bska4x)7 dgkz in 0.20 s:sxk7gaklcy48 ghxb2.8+dpv k z) 0vd?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a ;o0forl p.l9f point on the outer rim movepll.f;o9r0o f in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.zuo yk .um,,jctq11 0f0 s. What is the average anguy.z,o01,fj kuq tc 1mular speed of the wheel?

  A bicycle wheel rotati zl 8xdicdi/d;1m l41es uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center 1i iimlc 8l;/zdx 1dd4of the wheel?

  A cable car at a ski resort carries skiers a distance of 6.*0h9 dhnkngn .+va s l f.wxmulh;+j;78 km. The cable which mo0lh +kja.*9ns; ;xvnnhf l.7+wmguhdves 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 wix,m.xb5c-gl iu jw 9 qwhcvsz: 0n 9z*:;o0pajth a constant angular speed of 2.0 rad/s. What is the linear speed of a l,-:g :zxwq *m 0b0n.uc9w9axiho;pvzjc 5jspoint on the wheel's rim?

  The cutting cord on a gas-powered wp 1 l 0:isyy6ksb - auqg4;3ryq/f pf4qcq3mw.eed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/sgawu14c3s y3; fm/lkqsq- :0.y6yq pri4qb fp, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a consta u, 3+b/ *gnnxr-uc0ouywp2jfnt angular speed of 2.0 rad/s. o/cr g nwj0,*fn2-u x+b yu3up What is the centripetal acceleration of a point on the wheel's rim?

  What is the centripetal acceleration of a point on the perimeter of a*u e 3a)tfju(j bicycle wheel of diameter 70.0 cm when the j(ua*3fj ut e)bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotating 1blzagy3:uef esh/xoy5axxk39u + 3/ space station (r = 1000 m) rotate to produce an artif e 3sfyugx 9+abak 3xylxe/z/hu1:o 35icial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed ofing3/i56vo pz 20 m/s. The maximum centripetalz35 gno6v ipi/ 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 circula*ual0cq k6zq; r curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (lukqz ca 0;q*6provided by static friction) is $1.2 \times 10^{4} \; N$. What is the mass of the car?

  A 0.300-kg mass, attached to tdo5 qm-1u i-ughe 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 linear speed cu gmd15-uq-i oan the mass have if the string is not to break?

  A bowling ball of mass 7.5 kg7a j14mwble*s uvart2ltcd, a* )qm(* and radius 9.0 cm rolls without slipping 10 m down sdmmj*ar)q btv tu2le*1(a* , 4lc7 awa lane at 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 -p 5edzu( w f1yz sut:rqyv170with 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 7woi q8s,t)x ka constant 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 auto txa+a/duri za7/;tc9 mobile tire rotate after starting from rest and accelerating at axu/itrd;7c/aaz a+t9 constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelera.9le lbzdmc(b 06d7pknjw+ak;c 93c qtion of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates vt3vg,m2hj0xtuubo -) i) 5ta with a constant angular acceleration h tau,oi -30ju)b )g5tvm2t xvof $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an angular speed of 6.0 rad/s while turnlbf/qd)gcrn1ue 5 2sd9t7; wning through 2.0 revolutions. What is the average angular accelerguecdw n2f9)/;qtrd1 s57bl n ation of the wheel?

  A wheel of diameter of 68.26wuts ls0c7a )dq ra)skc9f80 cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the totack ad 8 wusrft20) c7)qls9sa6l number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly fro 2 *fh1ohwwd6um 8.40 m/s to rest over a distance of ofuw*2 1hw6hd 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 88eqm d;um8i1y .40 m/s to rest over a distance of 115 m. How long does it take for the wheel to comeq1mdyui8 m8; e to the stop?

  A centrifuge in a medical laboratory rotates at a rotatidu zr16+.:olhfa ( nhjonal speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angu +.hfouh16n :r(z djallar 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 to a b 1td3s)haf+j torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the s hj3)a 1f+tdbforce is perpendicular to the wrench?

  The bolts on a car wheel require tig9zo04z5hv htuhtening 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 appliet hzz 409hovu5d at $53^{\circ}$ to the wrench?

  A wheel with moment of inerti1w)t t 1asjwz5a $3.00 \; kgm^{2}$ 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 isw,ny 2ogm5m1m at the origin, mass 2m is at x = a, and, mass 3m is at x = 2a. What is th1 moy,mgw n25me moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frick3usqtily ho9bkwb( g a97-:9 tionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m, exerts a foo:s9yqka k9 bgt9wibhu7 -3l(rce 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 pivoted about a frictionless axis thougj ;rqlb46zolx8t 689xep s.ycht 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 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 startsz ;y q6ob48x6ptl el.csrxj 89 from rest?

  A 4.00-m long rod is hinged at one end. The rod is initially held in tzt cb 9kv(n,)ohe 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 M( ,bcz)vnok9tL2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm andziad)sq1- pe0) qay,v 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 qa0q1z,-vda) e)syp idoes the wheel achieve, assuming it rolls without slipping?

  A 1.53-kg mass hangs on ae(h7 n /od ms8 (+uhqy6.qouik rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. uoy hqsq8omn+76h i(du/ (ke .What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley 2,jsorw1)ruhn p:66z vyikt1 of mass 7.07 kg and radius 66.0 cm. What is the acceleration w r2:16 ri,)6jntyspvo1khzuof the mass?

  A rotating flywheel can bx 6w kgeg)s:+je used to 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 in .fj-q i /wdrl/xpx;4hertia 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 rolls:hj dn;zfe/ .w without slipping down a 1.0-m high inclined plane. What is the speed of the sphere when i/dhz.n :e fjw;t reaches the bottom of the inclined plane?

  A solid sphere of mass 1 qp3j1fom7uw 1.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up anqw 1 foj1um37p inclined plane can it climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest and a06vxxb+ a:nck;ycsg r 7(v7gn llowed to roll down an6sv7 g(cb0kycr7v x+x g;ann: 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 mh 024kw z-(sioui75gu. hmsgrolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mous u07.- m 2iowh(5zmgk4si hgment 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 chat sm1-l*9yf p5wnu0ilnges 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 x /tqx,uy:h8 rinertia 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 jhijsusleim(1(b)09moment of inertia h(bjs1 i )(ijem sl09uof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?