Angular displacement is usually express in unitw o4ykgmkw 1p95 9v;xts of

  Angular velocity is expresso0n m qa*i.q:qed in units of

  Angular acceleration zoo: 82 s zpv6,1ajgo9iawm9gis expressed in units of

  A boy and a girl are riding on a merry4.5 w :xts.pywv -yblkdqd )2zju* (gx-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 angul*d w y:z.j( xq 2ws4xtu. ldy)-gbpvk5ar displacement?

  A boy and a girl are riding on a merry-go-r3 )6ie s9g/+i es1 ,ermbtuctwound which is turning at a constant rate. The boy is near the outer edge, and the girl i s 9wsbmt1/ee+6, gtrc) i3ueis 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 aa.5v5ah d,phdf d xm4k: (5pmqt a constant rate. The boy is near the outer edge, and the girl is closer to the ck ,.pv4xp 5d dd5ahh(:famq 5menter. Who has the greater linear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant ratebkc/d u0 kh7umx7 5a(y. The boy ikmc7u bkhu70y a(d/5 xs near the outer edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are ridin y.94 r/jsiuagg 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 centey9 agu/ .sj4irr. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the following is an accurate sb7: gh*fgz 7w)l f(pwrl/ 0 (-apgucbatatemenbfgz ((0/l:p)blp* hwrwaa7g7guf -c t?

  Rolling without slipping d;bk 57egtr b7vepends on

  Two equal forces are applied to a door. The firstl :qw:1ux ud;n force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force exerts t wunqldu;:x1: he greater torque?

  Two equal forces are applied to a door at the doorknobp(r (*msg(jvo. The first force is applied perpendicular to the door; the second force is applied at 30e to( r omj*vg(sp( the plane of the door. Which force exerts the greater torque?

  Two forces are applied to a doorknob, perpendicular.kk0aofxn 2rv8 a.q.b8g+alh to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the t.kh.og v80l qx .ab akrnf+2a8orque of the second is

  What is the quantity use9y 2kl6: ea /fd 8,9ws wdot6/xchjvvcd to measure an object's resistance to changes in rotation? da:wx w69v8koccv yt6 sh/d 2j/le9,f

  Consider two uniform solid spheres where both have the s3;umz ig ctyr8/amb);)zmnm: ame diameter, but one has twice the mass of the other. m8ruz;y)mzmg;i :c nb 3t/a)mThe 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 radiu y xeg9 qjraibk.5-(vwqz ;0*as of the other. The ratio of the larger qw0*.k9vrxyqe a(j-5ai b ;zg sphere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and twice the dg fdg* 84+ewdkm -2fsdiameter of the other. The ratio of the larger moment of iner4+f 8-d 2*fmdgdeskgwtia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M ali7f+n py a(pd99vl(9jw9 mk rnd radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a central ax v7lld (9j9rpp9f+yn k(a i9wmis?

  If a constant net torque is applvqopd t 8mf+/yku l-4jm)6k+ kied to an object, that object will

  The moment of inertia of a solid cylinder about its axis is giv st66:2 b:tfttasnkr9k o p: ,nm3;wyqen 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 ob7 m4pep yrjq k/sd06.f mass 150 kg, one wheel of which has a mass of 10 kg and a radius of 30 cm. What is the ratio of the rotational kinetic energy of tm syqpdkr4670 .b /jpehe 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 without sl4 y wal+(nqk9( oj mb/3l)rrjaipping down an inclined plane starting f9kroa jq)y mr 4/nal3 (lb+wj(rom 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 slipping down an in7mcy*0er ka8fx ht -;dclined plane starting from rest. The angular velocity of the sphere at the bottom0rycd h- ax8f tem;7k* of the incline depends on

  "The total angular momentum of a system of particl*tpcry2 6p776vq inxt6s ; wyaes changes when a net external force acts on the systrcaiq; * tnypwx76sp26t 6 7vyem." This statement is

  In what circumstances can the angular velocity of system of particles change wi/ mz99zcb5:ixi w /wosthout any change in the/x bm 9zi5owi wcsz/:9 system's angular momentum?

  The Earth orbits the Sun in an elliptical orbit. Ignore any friction icjhnf2l/ 0 x7 7eraw.which may be/2 7ilnxh ec. a7fw0rj present. What happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticc tsgxuu,- ;1cal orbit. As the Earth moves close to the Sun, then1c-gsuctx; u , which of the following best describes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) 88cutj f.yl 2bdsl;dkq, 2oj9by pulling in his outstretched arms close to his body. What happens to his angular momentum aboulu2o 2fy,;9l 8ksd.8qtcj dbj t the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchdm3,gnqm jl 8v ,gq3d0ed arms close to his body. What happens to his rotational kinetic gq3n,dm3,qj l8v dg0m energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by p;-dwd moy;7+*v ktupme 5:awkulling in his outstretched arms close to his body. What e7 adk tdyv* ;kmou5:pm+ww -;happens to his moment of inertia about the axis of rotation?

State the law of conservation of angular val5kghx5 w59d; ix(q momentum.

  What arc length does the Earth traveam uxz.jr3g- 8l in a three month period in its nearly circular orbit about the Sun with a r.zgjra mu 8-3xadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clocir wxs6aew,,)k gix: 8k has a length of 0.30 m. What distance does the tip of the second hand sweep through in 3 minutes and 45 se,ex )sxw:wrg6 ik,a8iconds?

  How many rad/s is 25 revolutions perx25h7-/- (v6uvpr,mrtzq tan0q1ujb a6o cfp minute equivalent to?

  A bicycle wheel rotatuw0z hdf sc:w 2bs/5/30fm obxes uniformly through 2.0 revolutions in 4.0 s. What is the frequency of the wheehb omsc: w0bz0 xwd//2sf3uf 5l's rotation?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. fq- jxim2-(2 ihu0jxx The perxj0mjhf2 iu2(--ix qxiod of its rotation is

  A phonograph record rotates at 45o6 dzwac455ukm jun* 0i5s2)yuqt;r1lb k +yr rpm. Through what angle does it turn in 0.20 )su5w +knquzk4mrudry5 a0l6tbi c 5*y2jo;1 s?

  A wheel of diameter 26 cm turn/q(5x eg jc2-vw*quipm3 ez 6as at 1500 rpm. How far will a point on the outer rim move in 2.1qq*vuw5xgemej/a2(z 63c i -p s?

  A bicycle wheel rotates uniformly througad6xta n6z5+y o;11;d 1,lt jgjotn tgh 2.0 revolutions in 4.0 s. What is the average angular speed of the whea5j1d+td to;6;1glng1xn6jt,zy t oa el?

  A bicycle wheel rotates uniformly through 2.0 rehu+ z2lp k.+tat(zn*p volutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of a p.z*t2nu+p kh(z +tlthe wheel?

  A cable car at a ski resort carries skiers a 8 nhonmi(v 8uv2lrvugf )u 4e50hdh4 (distance of 6.8 km. The cable which moves 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 ti5 g nuehr0vf) luvo4h(n8udhmv (842rip in 12 minutes?

  A wheel of radius 1.0 m is rotating with a constanm7jeq h;ac j qk tuhxjt;*k;77/7be* rt angular speed of 2.0 rad/s. What ic/j ;e7qx k* ujq*m;;bhr7a 7etkt 7hjs the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutoc1piok dg 7h0d-3e2e zo.n9bter is 0.16 m in length. If the motor rotates at the rate of 20 rev/s, what is the anh20d9.7oc ob-k3oie e dpz1gpproximate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with aot2u 2c/hj 5za constant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on5ucz/ 2jho2 at the wheel's rim?

  What is the centripez( jc48vrw+9ppr : pjwtal acceleration of a point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is moving 8.00 m/spr (wrp j4z9:8vcj+pw?

  How many revolutions per minute (rpm) must a circular, rotating spacebq 6 wnagiu4) au5g:hrq.(;eo station (r = 1000 m) rotate to produce an artificial ga6g;bqwairu)u( .go:5 h 4n qeravity of $9.80 \; m/s^2$?

  A car is negotiating a flat circular curve of radx k z2e;6th ycq.1+zj-:xsggdius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by1gz tjy-:.c;q6+ge z dx2xs kh static friction) is $1.2 \times 10^{4} \; N$. What is the centripetal acceleration of the car?

  A car is negotiating a flat circular n.*gd xf1vrd8 curve of radius 50 m with a speed of 20 m/s. The maximum centripetal force (provided by d *xg8nr1vfd. 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 whir abf7dtr+s e 5r9sq96uled 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 mass have if the s f r6desq7uab9ts5 9+rtring is not to break?

  A bowling ball of mass 7.5 kg and radius 9.0 cm rolls 9c q) xdf.:h xz7po,(qf1qujlwithout slipping 10 m down a lane at 4.3 m/s.dfqq)oxpcl j (9,x z1f.qhu7:
(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 anohc2 co adse17/ co6:rgular 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 witrdd xo w4mt2-hu gv.j.34d8vnh 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 automobii kym+0uvz+auh6a- o3le tire rotate after starting from rest and accelerating at a constant angular az y m+ ha+au6v-ok30iucceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has ;.q+ infn ae9dt2 :wu+ mf2nvpan angular acceleration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 re2yzm33 v/j5fu(t vf wad/s decelerates with a constant angular acceleration oewfu/t2( 3vv3mz5 yjf f $-5.0 \; rad/s^2$. 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 turxk +6tk j0/rvrning through 2.0 rj0r6x+k rv t/kevolutions. 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 t;mb.(bx2( o*ancp:p . yx ms*uty7wzoo rest over a distance of 115 m. What is the total number of rev c.tm*zoy o p7:wb (s.a; n(mp*2xxbyuolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly fr0(qcsfqn d jvof+wxa+ t.t743 om 8.40 m/s to rest over a distance of 115tvf od7+afnx4. wc3sjq qt0 +( m. What is the angular acceleration?

  A wheel of diameter of 68.0d 1hs)w b(g+bh cm slows down uniformly from 8.40 m/s to rest over a distance of 115 m. How long does it take for the wheel to h1+ bgd)shwb(come to the stop?

  A centrifuge in a medical laboratory rota gmtv5 uk(wr ntpd-46eb f-7fodesm( n4- 1vs9tes at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular accelerwd- b4ks vv6fpm (945oedsntt(u m7gr-fe - 1nation 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 torque )h ly6n/;vkfchrj;1vcp g,/g of 90 Nm. If a 30 cm long wcv)g f j//;, phnrvhyk;c16glrench is used, what is the magnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torqulfaax,5 .n x/..dl cbhe of 90 Nm. If a 30 cm long wrench is used, .hlx/.bnd a,a cl.f5x what is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of inb jx.:arx *4plertia $3.00 \; kgm^{2}$ 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 74.d7,x9bt 3 (ujs ickxp tnyt2m is at x = a, and, mass 3m is at x = 2a. Whin73 t,xk.4dt p9 u7sjtcxby( at is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionless p8c focwi; e+(ev/n z)axis thought the center O. A rope wrapped around the outer radiunc w(v;/p i8)fcezeo+s $R_1$ = 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 axibj8 l(jpvy:9j eba g7 pisz pk12vzd1 6.9tz0es thought the center O. A rope wrapp19y1a6 8 eplg.vzdijs:92p7 kebzptv jz0jb ( ed 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 held l9q zzr*;;f y cvc.*8,fozcy3qba /b ein 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 inertia of a rod about one end is ML2/z* ,cyc zbf8fzbyr*;3/val . ;qcq9oe3.)

  Consider a bicycle wheel to be a ring of radius 30 cm and mass 1.5 kg.u sj6*f m rd z/hy wy27,blnm-5//irsk Neglect the mas*mn5ys, k blrm2sf / h6wjz/iu-/dyr7s 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 without slipping?

  A 1.53-kg mass hangs on a rope wrapped around a fp7:i rtz0+ ce2xzalt 6rictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What ic2lepi7:zr+ 60atz tx s the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless dibd+n-lrjg(p;c 3y/r h sk pulley of mass3 ydjh;cn+-p(g/lr rb 7.07 kg and radius 66.0 cm. What is the acceleration of the mass?

  A rotating flywheel can ay;+ho5 pg17 uh*umu lbe 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 ofwn (cr:21gt(d5kr qel 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 radius 0.010 m startzvru67 7 2nmzl9z3yoje;o a. ss from rest and rolls without slipping down a 1.0-m high incl69 3s7louj;y .ozn vra7 mez2zined 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 with a speed of 10 m/s.bo f.qyziqlo+ mae()hj 3x:va +6a8f3 How high up an inclined plane can it climb before coming to )o 3b(ff.qe 3m+6ov x8 zq+hail:ayja rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg m1of: . c 69zof-ei0gogbu y;eis released from rest and allowed to roll down an inclined plane. How fast is it moving after dropping a verf em:g.o0fyce i6g; 1o-z9uo btical distance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolfimsdzqof2xq f)8x f- *xi-+. ls without slipping down a 35e incline that is 7.0 m lo-.)i-8x df mxfsqzf*2xf+qoing. 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 momentuk./fbzu4yamz zz +76 fm 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 o,a9wop h;/r m h9p skb..0qdosf 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 moment pa/nwg3f 5p 4vof inertia 5fw4n3/ pap gvof
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?