Angular displacement is f aro)+8fw9wnusually express in units of

  Angular velocity is exprmpc*z,9l; vftessed in units of

  Angular acceleration is expressed in units *owucbp4c b33vt1 9wgof

  A boy and a girl are riding on a merry-go-round which 9rxdevt5 cmqy0qae+61y8q /g is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the ce q yr8 6+1/qmg ecxat9d0eq5vynter. Who has the greater angular displacement?

  A boy and a girl are riding on a merry-go-round which is13 iusoq03,; zitg-sdi /3b xoy ;qhex turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has,hb e1i03d3oz g ysq/x-uq;i3;iso x t the greater angular speed?

  A boy and a girl are riding on a merry-go-round which iiki0psq m m9.g5tk7/)h )5 pm6snlm zys turning at a constant rate. The boy is zm56syi s5h/.km0mlq9)gnp)7tmk pinear 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 which is turninng0va axcob)es,8g3-gmm 8 y28shi+ pg at a constant rate. The boy is near the outer edge, while the girl is climg) aeghm8gvacp2xn y8+o0s8 s -, 3boser to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round w1h dji nxc0(-zhich 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 tangential acceleration(1 ihx cn0zjd-?

  Consider a rigid body that is rotating. Which of the following is an accuratkb0 k2,zbp1z ge sb0 g kz1,zpk2btatement?

  Rolling without slipping depends 06, s,p dhfav3n rqo:l.phly/on

  Two equal forces are applied to a door. The first force is applied at thekc qh syx s779.6+g;kpcwux. w midpoint of the door; the second force is appliedcqk c.xpwh7 ;wusxky7 +.gs 69 at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are applib00- w4*)7w jklqc0j r +pgprhcou l. 79qfanfed to a door at the doorknob. The first force is applied perpendicular to the door;7 q+ -0ljw9pwa 40fjqrkblh* n 7cfrc upg0o.) the second force is applied at 30e to the plane of the door. Which force exerts the greater torque?

  Two forces are applied to ae/f 8,umjh3 lv doorknob, perpendicular to the door. The first force is twice as large as the second forh83 j ef,mv/ulce. The ratio of the torque of the first to the torque of the second is

  What is the quantity5c gz2 o-:dbo:.feh pn used to measure an object's resistance to changes in rotation?5pn.g:zh2o: cd o- bef

  Consider two uniform solid spheres where both have the same diameter, butlrmb p1 8a)tg7 one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller lbt18mr7)a p gmoment of inertia is

  Two uniform solid spheres have the same mass, but one has j1ocetme+ al1s,d v)) nfu8q, twice the radius of the other. The rm)n8,ef,valte+ ) c1dsqo u1jatio of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one hzqndn 8w: . skq:+gt)kas twice the mass and twice the diameter of the other. The ratgts k dw8:n:qqnk+.z) io of the larger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere hav d j jqzv7* xhpni-s;z2y47p7s mass M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment n p 4y2vz7s;x7v7jd*ipzqjh-of inertia about a central axis?

  If a constant net torque is app6,opj3or 7r+f k hc3xqlied to an object, that object will

  The moment of inertia of a solid cyl5z jsfvjb4(6mn wi.k:inder about its axis is given by 0.5 MR2. Ifws 5.fi:zj4vb(njkm6 this 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 whe, vyn)+jp jtcdb,k9q;el of which 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 kinetic energy of the bike? Assume t q)+pny bjvt9dc,;k, jhe wheels are uniform disks.

  Suppose a solid sphere o;vx )5b.p u0v dizi2odf mass M and radius R rolls without slipping down an inclined plane startin u5op )idvxvi20dzb;. g 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 sl2; ) vmlnlmu ,l:d8nipipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the inclu); dp2nil ml:nm8, lvine depends on

  "The total angular momentum of a system ofjctg6k26 fte/;d8fxvegkg (4 particles changes when a net external force acts on the system." This g4xgdcgk kt; 6f ev6 /8j(ft2estatement is

  In what circumstances can the angular velocity of syste: 30ks2, 8gcizq5lr cbbunsl/m of particles change without any change in th0clu8q b sic sbrk3 /5zg2n:,le system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction which 2 c4esn+9 r*,z*tthhr tdy.ugx w+l 6ymay be +,62sr.t+*9ud*tyywx tnhr g4 lez hcpresent. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an : bj6f sw6o; qcch/rn+elliptical orbit. As the Earth moves close tb:6+/fojch ;c w rqs6no the Sun, then which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (w eyxx9/tp5+xa fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis /p5 +y9wxtx xeof rotation?

  An ice skater performs a pirouette (a fast sr5tt 4l z7)cqna14urqpin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of n1 qcr)tu4rta7zl q54rotation?

  An ice skater performs a pirouette (a fast l+p4ay*avxdc 1 l .t+mspin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about+t41xay alpcd l.+v*m the axis of rotation?

State the law of conservationojz b)r;q,7 8af2olb t nk wvw(4wq57s of angular momentum.

  What arc length does the Earth travel in a t9ko vv gzy*vy1qn l3r.8z*8gehree month period in its nearly circ ve y *3lqvzz *.9ygn81rkg8voular orbit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a len6do zxzby259 ugth of 0.30 m. What distance does the tip of 9b6ou xy2z5dz the second hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equa 7 612rxuajt:pr bol5ivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0jv r or62bgkq 41,qjm( s. What is the frequency of the wheel's ro k4 jvo,r q2g1(bj6mqrtation?

  A pulsar (a rotating neu;ptkhlp6yh 82.alv l:2 iu z r6ez(nb3tron star) emits pulses at a frequency of 0.40 kHz. The period of its rotati3brk:uh.6tpl i e (hzy2l ;alpn62zv 8on is

  A phonograph record rotatea u1j;y /.nxs c.h k:4t y6,cuyojp2iks at 45 rpm. Through what angle does it turn in 0.20 s?h/xks n 4o.u,uyjyi:yc2c61jt;k.ap

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a po+q):pvxz.z7hpu p4 yuint on the outer rim move in 2.4pzy pupxuz+qh:). 7v1 s?

  A bicycle wheel rotates uniformly 2pj a3nr*h d3zrjf/ ,dthrough 2.0 revolutions in 4.0 s. What is the avera 2jhrfd d*p3ja,rnz/3 ge angular speed of the wheel?

  A bicycle wheel rotate ,h.7-apbeiwadl 2xd 1s uniformly through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center oeh w.7a1 a2l-xpidd b,f the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The cab/xj-p uxtb2qb a 0no))i:.t 31tp opvjle which moves n0a)tp .qt/vjtox 3 u)-b oi1xpp:j2bthe 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 with a constad9 lrj, yh6yke:9ey;vnt angular speed of 2.0 rad/s. What i,hey;9:r6kly9yjd v es the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-i) ip p kpugwgfr8n.ep,.2l,+ powered weed cutter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is t g) epup+r..2f,in8iglpkw p, he approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a constant p)oyi5 xk-cgczg/w )5angular speed of 2.0 rad/s. What is the centripetal acceleration of a o p5/-)ycg)gz5cx ikwpoint on the wheel's rim?

  What is the centripetal accek 6;q0.ba8ni * qbfuhzleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving zk6qu nqb8*b a0f.i;h8.00 m/s?

  How many revolutions per minute (rpm) must a c0qju q741u oziircular, rotating space station (r = 1000 m) rotate to prod1u0j quoz4q7 iuce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of r cuh 2;ix*pm8d5-ayp 43midf aadius 50 m with a speed of 20 m/s. The maximum centripetal force (prod4 h;dc238-upai im5*a xmfpyvided 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 g cjd* g *vj)ngvgpttc+2)i4/ 50 m with a speed of 20 m/s. Thevc) 4c2/ggg* j* pidgtnj+)vt maximum centripetal 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 end29 lbg 49wrz(rowq6 u2g /kbna of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand2g wk(aur6brqn994b 2g/ owzl 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 9.0 cm rolls without slippinh+4xc qsah+5i +-xij ng 10 m down a lane at+ch -ah+xj+qsin4i x 5 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 wit+noc3 n1r hw;uj89ee wh 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 wrv5 /x8w oqccg z((s9u* e3umubhlw+6ith a 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 automobile tire rotayq3 wuv5 jz:sm0ob27e te after starting from rest and accelerating at a constant angular accelv2 7wy3: qu jembs05zoeration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, aocgel 62axuf1),ivu 8nd 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 with1bpzuo5:,yz8 ))2k+jiwdtop j ar6xt a constant angular acceleration of5: i ) ,1pkbypzdtz wjt6)xrj+uooa82 $-5.0 \; rad/s^2$. 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 ( oamc*b 0 i2o.gyc(ubwhile turning thro.y ubbo(c0(a c *2imogugh 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rty30fj7*jdr ghy/90ws ( lsujest over a distance of 115 m. What is the total number ofjws/t0l7fs3j(j yg0 d*9yh ru revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cn92e x; c rk8 szn:wnob5lv+m;f,l s(am slows down uniformly from 8.40 m/s to rest over a distance of 115 m. What n elrf+ss kn(nw2v;z;8b9 5lxa,cmo: is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m46xvqtqyk.dub) *is )z 7j)te/s to rest over a distance of 115 m. How long does it take for the wheel to7)uq)zqxkte) jis*y.4vd6b t come to the stop?

  A centrifuge in a medical laboratory rotm uu-ky90-w)w :v lmfeates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times a:9k) wuy 0m-v-lewufm t 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 whedr2q s+je/y(eel require tightening to a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnreq/d(+ se y2jitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. hh hhm;huumih t5 0c6 .df(lo35z 1yu,If a 30 cm long wrench is used, what is the magnitude of the force required when themh1 d5ht,uho hhmh;uu0lc3(6izf5 . y force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inertia e)(fp kfsr *ra 2fly.t6lj)o2$3.00 \; kgm^{2}$ 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 is at the origin, mass 2m,be (84:m 4,y7firmc lm hcexh is at x = a, and, mass 3m is at x = 2a. What ce,mhcrmyih b 8ef7l:(4 m4, xis the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionlge5a fna 7i4 t0o3zi3cz+8 ybdess 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 sectioa5+3 ezcnzg7bdia 84 03tfyion 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 pivote2j-od- pzvtb*)7de igd about a frictionless 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 radius R2 = 0.50 m exerts a force F2 = 6.0 N downward. How many radians does the cyliot*dg-) j7z2b ip e-vdnder rotate through in the first 5.0 seconds, if it starts from rest?

  A 4.00-m long rod is hinged at c9434uxx jen-b v: hrw4 /hvmwone 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 inv9h4um:hewv/3xc -w4 r j nx4bertia of a rod about one end is ML2/3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1j2va( o ag6r;p7. hsis.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, assuming it rolls wita p r .(o;shg6saj72vihout slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley ofv80wwc e7lb; usj/eu6-lz md v,vip9+ mass 7.07 kg a mw /zwu -;ldlbuv8,ep0+jie v9sc6v7 nd radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped ar 7/s7;ysd p6 zujwfb/mound a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. Whatz7uj6p dw7sf /mybs/; is the acceleration of the mass?

  A rotating flywheel can be used to store energy. I-9y;d 0 1mogzvocqn2 qf 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 inert(j tgrg4bbqdoyhh;c 1buxg+3 ;jsw)a/ 05 4tfia 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 mase6u3v e5zrtdv b;z4x ;s 1.0 kg and radius 0.010 m starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the 4vxe5zv6;bur ;3ztde speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.0 kg and radiush+h n:. 4.(lsxppzkfcl (czk0 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to :l..f0h(z cp kxhs4(znp lkc+rest?

  A hoop of radius 0.5 rtwl 0y-3moa3w1- -1ly;kkt )aefbix0 m and a mass of 0.20 kg is released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical distance oflb31mofr-k-y)0wta3y -itk w e1;l xa 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls withvm)9upxaj7o(4 ;ze euout slipping down a 35e incline that is 7.0 m long. Assume it started from rest. oxemau e)7zp4(j vu;9 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 changes by ut dedmj,c03) $20 \; kgm^{2}/s$ 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 o*x dnu5 y3lbd5ux)uf5vph2 +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 rad/s with m 1q epz6sfwj,6i7)ogarms extended has a moment of inertia ofizf 76e6 smgojqw),1 p
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?