Angular displacement is usually express in units o-+n g.n5gu ruj37ltxl f

  Angular velocity is expressed in un;rh -n*9mb4jk v9 yp u-y:llgvits of

  Angular acceleration is expressedc4x2 5iy5cfmm/(n 9 i)8nvyax/hef w5 qicf6x in units of

  A boy and a girl are riding on a merry-go-round which is tm*k(mpna:tke(c:dih : vr +g6urning at a constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular displace nmc +*:m(: rh 6gpi:ekt(dvkament?

  A boy and a girl are riding on a merry-g pcis89dk) uapa5j( r0o-round which is turning at a constant rate. The boy is near the outer edge, and the girl is closer to the center.d 09iaup a k5j8)rcp(s Who has the greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turnivb.l cq4wpu93 j d5(fmng at a constant rate. The boy is near the outer edge, and the girl is closer to tlcdf 4qpjv5w ( 3u.mb9he center. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round whit6 6+e8/mx pq3xtzsb;ypuug 8 ch is turning at a constant rate. The boy is near the outer e3p86xub/gs 8 z ;p+uytmtx6qedge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are r0- ur.o 0btl,g z1c ,srhmdnd;iding 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 gred1,h;z-, sog0 rn0.mulc d trbater tangential acceleration?

  Consider a rigid body that is rotating. W) t9+y tfnxg7j5 n2tgsjp p*v 3vao3qd2rt.b/hich of the following is an accurate statement? *9s/g. aojypt5tqp3 xrgd 2 2+jvv)37bnn tft

  Rolling without slipping dependsxt1k.mjc v +kp8q g-.a on

  Two equal forces are applied to a door. The first force is applied at c p:sg1, t4drid/veb)the midpoint of the door; the second ) bvgst1di de4c/:pr,force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts the greater torque?

  Two equal forces are appliepo f30x+6stq ;gcv oj4d to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane v04g3c;ps j +of6t xoqof the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular to thnx21sp+ ps a- gem06vbe door. The first force i mbnxp60vg ss+2e 1p-as twice as large 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 object's resistance to changes inf1h*,grt k1qwt - .ej u-wbs+z rotation?-+sh1 wuq e zb-r.jf*w1ktt,g

  Consider two uniform solid spheres where both have the s 28 w,qy:adppe w9k0 pv7t5prgame diameter, but one has t,8rvd:kep w7tapp gwyq2590pwice 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 the same mass, but one has twice the radiuy;s tlik,uw07y: hh) ks of the other. The rati: siw0hh;k),yy 7tluko of the larger sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid sphere4ief1e5ee93-lpm*t 5f2mis d6 d yiyxs where one has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that of the smalle6f2 i d4ey*5ipd3m tm1 sy59i-elefxer moment of inertia is

  A uniform solid sphere has mass M and radius R. If these are increased taevoh y c s)ct(dyatn-99,p3.w w6a.u o 2M and 3R, what happens to the sphere's mompv tstd)accu o . haaw9-e6w.y3,yn 9(ent of inertia about a central axis?

  If a constant net torque is applied to an object, that object wl:*8j0m j dhphill

  The moment of inertia of a solid cylinder about its axis is gw:o3c/ i;u3, f4bl1szu ulhvo x;yf +civen by $\frac{1}{2} MR^2$. If 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 wheel of which has a mass ogayp36xqa*2i *+lgwtf 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of the wheels to the total translational kinet**l 6 a+a2gtgyxpq w3iic energy of the bike? Assume the wheels are uniform disks.

  Suppose a solid sphere of mass M and radius R rol mdmov8i9w1 2t: w-er ts3yn;( yeod7pls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on yr;d 87m9snwoovte-w2t:( m1ei3pdy

  Suppose a solid sphere of mass M and radius R rolls without slipping downd ahb 5gu3t4/nbxg/6cre 8(ey an inclined plane starting from rest. The angular velocity of the sphere at the bottom of t/gb 3h6dcga8t54nux( e bye/rhe incline depends on

  "The total angular momentum of a system of particles changes when ,zk193wp np w)p s3cmva net external force acts on the system." Thismp3zpvnwk)3scwp ,1 9 statement is

  In what circumstances can the angular velocity of systemhc/jeb-;v he( us2z,gj y+fy- of particles change without any change in the system's angular f/h 2-+jg ce jb, vhyzyu(;se-momentum?

  The Earth orbits the Sunf*ha8 0rcul c(j+sj: g in an elliptical orbit. Ignore any friction which may be present. What happens over time to the Earth's angular momentum about the Sun ag(c*l rjjc0+s f8:uh?

  The Earth moves about the Sun in an elliptidfer*wnutn.1vmid . b2r)ug s3 +y *hy;1 3qekcal orbit. As the Earth moves close to the Sun, then which of the following best describes the orbiting speed of the Earth abof*)v e13kuqrhd2+t3 gu si.wnn y1 m*dr ;by.eut the Sun?

  An ice skater performs a pirouette (a fast spin) by pulwk8 ehys7*a 2fw3qr d.jnl(w (ling in his outstretched arms close to his body. What happens to his angul7wa (8wdl j(.eq2nwy*3 hfrksar momentum about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullinn qn, u/rbfq*q686;8wuuezi bg in his outstretched arms close to his body. What happens to his rotuqzi 8/6rbqf, nwe6*u8q;nub ational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pullinzd3* 3vgdmtm8tr; 0 kvg in his outstretched arms close to his body. What happens to his 0mdm 3v*kzd8;vrtt g3 moment of inertia about the axis of rotation?

State the law of conservatioqq,(g+jklrhcn 2xecw- 3rcq(w mm;32 n of angular momentum.

  What arc length doesepyqf-h. d (ixr-o8+p the Earth travel in a three month period in its nearly circular orbit about the Sun withorf8-ppehyx(i+ d.- q a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length icq7 ho-bavfv +k0t 5+of 0.30 m. What distance does the tip of the secoicvto0 7fah5vb -+qk+nd hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutions per minute equivksj 6wmx/w:hr2;vr0r alent to?

  A bicycle wheel rotates unifo)g2ur ) j;ud;mpo0w5zc2.df (ff uiaqrmly through 2.0 revolutions in 4.0 s. What is the d u0zfm)5g 2uf jdrpa.qcofuw;i2(; ) frequency of the wheel's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 mq i(pr.e2a3oxhj3 h hrg 1b-5kHz. The period of its rotatih5qhojp (erbm13a xrg3i 2.-hon is

  A phonograph record rotates at 45 rpm. Through what angle does it turn in fi9 uenrx9okaky; *5ezq.,;k0.20 5u 9*n.y ,qf9rakokkez; iex ;s?

  A wheel of diameter 26 cm turns at 1509rz-+b oab0 cct3y9cd 0 rpm. How far will a point on the outer rim move in 2.czo-y3cc 0at b99+rdb1 s?

  A bicycle wheel rotates uniformly through 2.0 cirtcn69 :1a qrevolutions in 4.0 s. What is the average ang9ccqr6 i an1:tular speed of the wheel?

  A bicycle wheel rotates uniformly through 2.0 revolutye+9ukpp/ i1 mions in 4.0 s. What is the linear speed of a point 0.10 m from the center of t/p1eimk pyu9 +he wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 ( ;dvbqy j9 7v z53u.yc+rbtxzkm. The cable which moves the car is driven by a pulley with diameter 3.0 m. Assu vbbrc(;j7y tdz .uq+yvzx53 9ming 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 2.8ifux y:vc;o 80 rad/s. What is the lineavuf i;yc :8o8xr speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0gi5f8( 4kj j h rfm-vq.eoc3z0.16 m in length. If the motor rotates at the f0qv(8hj .z3g5c 4 kjfoe-rmi rate of 20 rev/s, what is the approximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a conhe ds; a)-s-sastant angular speed of 2.0 rad/s. What is the centripetal accelerasds-; h-s) aeation of a point on the wheel's rim?

  What is the centripetal acceleratieyqpi 3(ne:/,wm(tnd on of a point on the perimeter of a bicycle wheel of diameter 70.0 ci/t(epq w mn,ed:y3n(m when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must 1qx7 bw,ks .qx8it7pia circular, rotating space station (r = 1000 m) rota qpst,kxi qiw1787b.x te to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radius 50 m with a speed of 2i10)lbyk: sn)2 euqrg0 m/s. The maximum centripetal force (provided by static frictior))2b:1ul 0ein yqkg sn) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat g+s/xt 9 i9 7havbve/.m(iyjl circular curve of radius 50 m with a speed of 20 m/s..b/ iavvjet/7+mx(shg9 iy 9l The 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 ;ez-64jivf fk end of a 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the ste k i4vfzf6;j-ring 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 9.0 cm rolls without slippi;.fc fkctwp* 7h,go:ang 10 m down a7 ;akwcg fhf:ctp*,.o 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 withiu qi (d5wus*t22 9qe ppu,4vi 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 angulv8-mt;pn x + 00touzurar 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 rotat 7rvqe xy8/a3i, k8,dudh,qiue after starting from rest and accelerating at a c rvueyi7/ 8,,q,add3uq ikh8 xonstant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular augp9 qz i5k1c7cceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates with a constant y3mo v8k lyd+qd,: 7irlsf88dny;l,kangular accelerationn,yo8l 8d+iyrlmd;k3 ,lvsqy f8d :k7 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 speed of 6.0 rad/s while5*e.b sb vwa4f turning through 2.0 revolutions. Wh a. svw5fbe*4bat 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 rai+h:dvxt2 4f;p 9o;fuk sn6w est over a distance of 115 m. What is the total number of revol9pw;;: fnhdfxktsivu6 o+24 autions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly -j:hgx1c6qy5 26r pjs2(,eujthnlah from 8.40 m/s to rest over a distance of 115 m.-e n2lgj y,jc65pj2 h hqx6:sr (tuah1 What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8 vafmsnrt6f x .8:r/4p.40 m/s to rest over a distance of 115 m.sfrptx mn.6f4r:/v 8a How long does it take for the wheel to come to the stop?

  A centrifuge in a medical laboratory rotates at a r -as w*f. ylr7hgvp dldd-1q9-otational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelerationpgvqlwsdd-yfr *.--l1 7dah9 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 *;kqexg rmt7v xq :i6.require 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 force is perpendi7* m6rqx .ixketvg:q; cular to the wrench?

  The bolts on a car wheel require tightening to a torque of 90 Nm. If 2y6- w12lz tidcmw* bha 30 cm long wrench is used, what is the magnitude of the force required when the force applib2*hd -cy61wm2wlz t ied at $53^{\circ}$ to the wrench?

  A wheel with moment oz igw7fg- ng :z//xr-1v(hazmf 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 is at the origin, mass 2xuj: /lea c*r7d i4w:cm is at x = a, and, mass 3m is at x = 2a. What is the momc:edax/*r 47juwi :cl ent of inertia about the origin?

  A solid cylinder of mass 10 kg is pivot7 ys w/n7,dezaed about a frictionless axis thought the center O. A rope wrap77we/za snd y,ped around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought mn4m3 / wrsjy72gol :hao)jr0 the center O. A rope wrapp7n:)o42j grl3j o hm/s wm0aryed around the outer radius $R_1$ = 1.0 m, exerts a force $F_1$ = 5.0 N to the right. A second rope wrapped around another section of radius $R_2$ = 0.50 m exerts a force $F_2$ = 6.0 N downward. (figure below) 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 )lhp pi41c,87st vji bheld in the horizontal position, and then released as the free end is allowed to fall. Whash 178p,bticip 4jvl)t 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 tiehaaqn;nw4wr1(29g mgq0m 30a8ip uo be a ring of radius 30 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 achieve3mwani g 2e9pwauhr0q4 gq(m n;1a 0i8, assuming it rolls without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a frbv1w raq-avdau8 ep 5uw99ycfb;,** dictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What is the anwa vy-r bde5p8f9a,c u* q;d*1 ab9vwugular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless diskqw 2 : c9ha;ab;pho32zn9z/mne e4wyu pulley of mass 7.07 kg and radius 66.0 cm. What is the acch9 ;y; a4n/2nc23 whbpm 9zwzaequeo: eleration of the mass?

  A rotating flywheel can be used to store ene9:qcxrm-p 30l;u1hako*q cb f rgy. 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 inertia ag// 3r td(eamof $5.00 \; kgm^{2}$ 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 mcm;p2w9qq )4d cwd n8h starts from rest and rolls without slipping down a 1.0-m high inclined plane. What is the speed qpd)8qch 4c9;2wnmdw 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 with a spee t*3ifw.rh m l09 rm7a0,jv uprwuk+a7d of 10 m/s. How high up an inclined plane can it rmhjamv kipw 7w9.l7ru0f + a*r,3u t0climb before coming to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is reyvd au+f20(ac leased from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical dista+2v c0 aduyaf(nce of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35s()-se af 2;r a5mfxxue incline that is 7.0 m long.fasu;5r) xf(-xe m2as 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 momentum changes by5p8, ch:gnt9qi.xuz c $20 \; kgm^{2}/s$ 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 6t:* 1l .pwzmfa0jlsoinertia 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 rotafo (96-sitc.*sq vdcc ting at 5.00 rad/s with arms extended has a moment of inertia ofsf (.6 -vi9ccdtqo c*s
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?