Angular displacement is usually express in units a+1fao c66 lasun1m5jof

  Angular velocity is expressed h3 alt v6z-qx,in units of

  Angular acceleration is expressed in unit *hwi (/og7,bhpb cg(ls of

  A boy and a girl are riding olh(h na3 .v-pnao/qp ,n a merry-go-round which is turning at a constant rate. The boy is near the outer edge, and the girl oa p-hv,npq(/lh.n3a is closer to the center. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which isex4w0w l-jh4za 4 xih3j,x :eu turning at a constant rate. The boy is nx-lewah4 jzx3,jh4x 4: wue0iear the outer 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-go-round whichwh0:) , i )ln2wqnkjzgb,ne ,zkx1w)v is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has bike:v,nnn2z)h 1lk ,wqwz ,))0g wx jthe greater linear speed?

  A boy and a girl are riding a merry-go-r69uw4ukogb; 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 centripe ub9kwg;oru4 6tal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a con1 v/v1tk;v p(u/uagou y32oncstant rate. The boy is near the outer edge, while the girl is closer u(goova213 /vn/vtpy1u ;k cu to the center. Who has the greater tangential acceleration?

  Consider a rigid body that n7m l i;6dh 4ug8ik s8zustc;,is rotating. Which of the following is an accurate state8um4s,zunt;6; gi7ci k8 ldhsment?

  Rolling without slipping de ,ug omgc5; sx q;di,:ew2.slwq: ijc8pends on

  Two equal forces are applied to a door. The 9x6(tt ce(5xq3hwc)lt jn (jg first force is applied at the midpoint of the door; the secon)(xgtt35t(jcje (q nxl9 w6 chd 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 to a door at the doorknob. The first force is aa+ (- -s,se x,cetlpfxpplied perpendicular to the door; the second forcesc+e,f-x,sx p t(l- ae 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 the door. The first forzfj26 p muxafi3-);-tkhlv7ql kk l pq 4i*(8xce is twice as large as the second force. The ratio of th v(p-8)fjkp a i* fk2mltlkxh qq3i-zl7;x46 ue torque of the first to the torque of the second is

  What is the quantity used to measure an object's resistance to changes i1:33hokln0 rujg y, qzsn( --x; bxtl8ebj/o in rotatiole 1 n;,rsz/tyi0gh on(b8o3xj x b:-j3kq-ul n?

  Consider two uniform solid spheres where both have the sameb/2tb8pw ,nt5 w zoqq5w ye:ky9 3bvn0 diameter, but one has twic5qw/t03 z nnp,kybq:8v2tbw5 by w9eoe 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 t-/j 4uwbm;eiyhe same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the smaller sp/be 4w;im-yujhere is

  Consider two uniform solid spheres where one has twice the ma)0p .kv7/i gt5h1k-uhn ibuhm ss and twice the diameter of the other. The ratio of the largehm uv71biuk.t5- /0pghnhki)r moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radi.pah swfoe,2 ,v,/w+dgqw9pdus R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central.gq w9v,+ae/w,pdf dp,oswh2 axis?

  If a constant net torque is appliedk x/2mz t4f1(5gw yrjj to an object, that object will

  The moment of inertia of a solid cylinder about ibriu r70z9 r8 ffikmz7-(wh sie(q5chj9s:0cts axis is given by 0.5 MR2. If thrs7-fi:8(cs( 59iwf7zcmi ju qrkrz0b e 09 hhis 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 whichff (8w-kmt x8s) ze5fj has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational ki)8 j8sff5tkx( me wf-znetic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rolls without slij njjj0s5ab 8; gfvrv-ad40f/pping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends -v n;/v04jbj85a sjafrf0 djgon

  Suppose a solid sphere of mass M and radius R rolls without slipping g(nsvbykwm8 ao: 1q1:3t wjf. down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depeww .8j3:q sn1 mg:kvb(y1ot fands on

  "The total angular momentum of a system of particles chang*jllu x*zkixyj75gqd/ q) ,b8v7zt qi,y6b*res when a net external force acts ony vk6rlj ,y i )zqb 8ixt7*luqd7*gb5,qjz*/x the system." This statement is

  In what circumstances can the angn/5p9,dhesyc1gueni *e9d p0 o a2q7zj ,aye* ular velocity of system of particles change without any change ie9 n1cps 5h *za0o q7d i*ey d/jaen2e,,y9gpun the system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ign6eu/f- psxv8:ht; sxb ore any friction which may be present. What happens over time to the Earth's angular momene vfu sp:x/s68b;xh-ttum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As the Earth tm h-8xoq2 0g)ddwd/z moves close to the Sun, then which of the following besd 2w8 d)dztm/ 0xhoqg-t describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pir h6y:ogiyd8 g2eeh9 l5ouette (a fast spin) by pulling in his outstretched arms close to his body. What happens g2ld65go:9 hye yeih8to his angular momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) pu.u 62l, kktmc99 2kp1 dbdjxby pulling in his outstretched arms clok,b9dmdu 2 xlc29p j kp1t.uk6se to his body. What happens to his rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstrfh9p90wz b5fcetched arms close to his body. What happens to his moment of inertia about 5pf0hzb9 fc9wthe axis of rotation?

State the law of conservation ih4w -q5dl/ll/k)0 mr7ng qqsof angular momentum.

  What arc length does the Earth travel in a thr ujk-xqrh+i;).o vf+ -wcw1dg sp- v-gee month period in its nearly circular orbit about the Sun with a radius )f v;iwxdw+v1csug -j+-. opqhg-- rk of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30nf4s 9jei du-7 m. What distance does the tip of the secoj9- ius47nf dend hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivalent to?wr 3uq:wijr5 *

  A bicycle wheel rotates uniformly through 2.0 9 z.b3qxbv7gvrevolutions in 4.0 s. What is the frequency of the wheel's rotatio7vqvz9b 3x .bgn?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Thek*gfvi ,-2:: wua1d a86qtbz1ip dsj y period of its rotat auaz, k f -*gs idvyqtdbp:18w12:ij6ion is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in 0 m+0(0q8z5vcen0pl8o vagdyr .20 s?n85cy q +zd re0g8oavml( 0v0p

  A wheel of diameter 26 cmi0 nj+k8t**wy h-0 yae+jdedp turns at 1500 rpm. How far will a point on the outer rim move inde8dt0+p+way kj* j-h ie0y*n 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.09r o;3lazhr 0e s. What is the average angular spo3ar09 ;ezl rheed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. Wha 2xcgwvc a 1u4-9ojg1pt is the linea cop9ujc1g-aw4x2g1v r 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 6.8 km. xf.txxxb9r;td5 .p91xkb 8ul The cable which moves the car is driven by a pulley with diametex.8ut lb5xbxkx td1.fp99 r; xr 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 constant angular speed of 2.0 rad/s. ,gww4 ind8yq . What is the linear speed of a point on the d, w.ynq8wig4wheel's rim?

  The cutting cord on a gasu2 k1zkyh m9km rz;y 6hr2/3ht/h +cqw-powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the ap k //qyhk62u rm9w +k m1tzhh3yz;hc2rproximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant angulaj6 6ltpbcjrr* chbm v).6.a-rr speed of 2.0 rad/s. What is the centripetal acceleration of a pointrhpac)lj6v6cm.r6- t.j *bb r on the wheel's rim?

  What is the centripetal acceleration of a point on thh * b5a(plqid9e perimeter of a bicycle wheel of diameter 70.0 cm whp q*i(hlbd9a 5en the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rotak w3gw f y b2am+-rkvddpk410 s7-omc/ting space station (r = 1rv7o1 wpgy4/m+kb3kdwa - fkcds -02m000 m) rotate to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curveexpl 8rs f 7vzr98t/)x of radius 50 m with a speed of 20 m/s. The maximum cel9)vs8txp 87zrer xf/ntripetal 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 with a k9:fbe *ku5g j+ :9x -bsvffxnspeed of 20 m/s. The maximum centripetaxjus -b9:bk fve: *5 k+n9fgfxl 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 end of a 0.750-m string, is whirlj mwvwnc++q-62q8k,sqqsw pu) iotn a.;a,6 xed around in a smooth level table. If the maximum tenvaw+2xqws.nou 6n)s 8w,-ca6, q ;tpjmkqi+qsion 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 kg and radius 9wx8gibw /45x,ne coq pa7+li4 .0 cm rolls without slipping 10 m down a lane 7 ag5wo4 /b4w+,i i8lcxxnpqeat 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 a constant angular accelerationy0aadbpzgcucwd7, yzk3) 9/ i7h(rj , 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 ack+w5dy w.vkzc82-ne rceleration 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 rotate after starting frr mahmk ot3egd:4e x429ff2v;om rest and accelerating at a constant angular acceleration o44tme3fo;kex m:frvh9a 2d2gf $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and hae)g/lqzdcb:;5 lz+-*6aki gabj5b u ss 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 deceleratyarhhj8ac. ,qwj+55l es with a constant angular acceleratioy .+h8aqj chwa 5j5lr,n of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rew6r mso tr-6*ust and reaches an angular speed of 6.0 rad/s while turning through 2.0 revolutions. Whatr um 6o*r-6wts is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformo / 0qx2qqhay+ly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates in coming thy oxq/a 0q2q+o rest?

  A wheel of diameter of 68.0 cm slows down uniformly f c7w7j,r9g n nubf1/sqrom 8.40 m/s to rest over a distance of 115 m. What is the angular /c79j wbu7rqn1g,s nf acceleration?

  A wheel of diameter of 68.0 c/8;wfu :rwa0*t7zis gl x3pfcm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. Hxru f7* wz3i8tls0:gap/ fw;cow long does it take for the wheel to come to the stop?

  A centrifuge in a medict8pa*7ijfu d +al laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times * tij+f87dapuat 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 to a t.dl az81u-) mf:xdrq sorque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the forcemzax. :-u)lfdd18r qs is perpendicular to the wrench?

  The bolts on a car whe vxt0/3cqx 2ux) k*qqkel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the forxu*2)tvk /qqqxc kx03ce required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment ow w9,cohu1c mvh06zj6f 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 foll, (n1 oov7bqwggknx27 ows: mass m is at the origin, mass 2m is at x = a, and, mass v1kwnx(qoobgg 7 ,2n7 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 frictwl +w:l3ykk p2ionless 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 s3yw wl l:k2k+pecond 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 isswxob+(-5 +mseiij0r pivoted about a frictionless axis thought the center O. A rope wrapped s++ ( xiom s0iwb-rje5around 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.r exir;bubt28hb0 7hw32 6z jd The rod is initially held in the horizontal position, and then released aih ;r edz82x7b brut32w h0bj6s 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 radius 3qhecp,8cnm3ig8 zs 35yo6j wx d(ss6 10 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, assum ,sjs3 wsc5gc1i x8q6e hp3(o8ym6ndzing it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped )bv 362jt9zsllhjnc 8around a frictionless disk pulley of mass 7.07 kg and radius 8tlhj9v)n6ls3jzb c2 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a r*hz45f6o b;t mvw mmu6ope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Wh*w t66h4;vubmzmo fm5at is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is requijgad)4p)2yv,dd i: ii red 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 inerqz 32y mx;iicuyi2. w5tia 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 mahat(*rwj66f6 1 y svqdss 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m hrjv6t 6f wq1ady*s6(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 wio ,oe7 /,8w+ hcmpbtcs/fe b)nth a speed of 10 m/s. How high up an inclined plane can it climb before comic/+, bow, cme/ )bsof8n peh7tng to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rest andjg:c etwh0) gjpea+ vi2mj+,3 allowed to roll down an inclined plane. How fast is it moving after dropping ajt+30mcp+ji)hj2 ga,w :ev eg vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls wif/6:et0oeu9l dnc .9))y7lgub umuctthout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The mo9ef ub0ue)mlldct76t/:9cnou.yg)u ment 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 chx-f3ql1m7r2zen htpi1+kez 94fwmd , anges 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 1qc be- 3aj-t;)ys.brjfl8ev moment of 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 r o r dqbns,:14yrsvy8/ad/s with arms extended has a moment of inertir8:s ynq r1dy,o/sb4va 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?