Angular displacement is usually express in bsxf aj8ou12-k-fz h-units of

  Angular velocity is expressed in unitszfs/0 kkly l)8 rxlf 3f8-umm( oa22vt of

  Angular acceleration is express ucu xn5,/zwpz :1+fvm9g8v gjed in units of

  A boy and a girl are riding on a merry-go-round which is turning at abtc85mta 5brq1zsp/ * 672rdfosc* zc constant rate. The boy is near the outer edge, and the girl is closer to the center. Who has the greater angular s8t6rdmbcz1racqo* 57 p/c*bzs 2 t5fdisplacement?

  A boy and a girl are ridhz si(8b7b 0o8w; cgkying 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 tib ;c70whbsk (gzy8 o8he greater angular speed?

  A boy and a girl are riding on a merry-go-round which is turning at a cnhi* wqq4 wdt4w1z m.*onstant rate. The boyn*4h1mq* i4 dwwz.wqt 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 which is turning at a cons7a* z*ymzsxjmchk2: v3bk+ k7tant rate. The boy is near the ob xm h*z+mk a:7y2z3kskcv*7juter edge, while the girl is closer to the center. Who has the greater centripetal acceleration?

  A boy and a girl are riding a merry-go-round which is turning at a constant(c)fvqww5iq9)ec/an 6 cwn1(eo)p ko rate. The boy is nec)e p ov5) w(e(c9f wqiqnw1)on/ck6aar the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

  Consider a rigid body that is rotating. Which of the xccgz/;2 /d 1kyp a7esb*o,qvfollowing is an accurate stated;*asckg /y,/pqvcoe2bx17 zment?

  Rolling without slipping depends -o8cq+ns aedh;9,j;hyn :c zyon

  Two equal forces are applied to a db *t gky/k64lfli9g0em :sr l*oor. The first force is applied at the midpoint of th0/rmt*6ll l y4kgs ebg*fik:9e door; the second 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 doomzr+zjel+m;s8au 1p g 6n) k8prknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Which force exerts the greas8+p6m8k;+ z zmaleug1n)j pr ter torque?

  Two forces are applied to a doorknob, perpendicular to the doorb hath,7: y/ief.1 enl. The first force is twice as large as the second force1 f.ihn,hye :b/e7lta . The ratio of the torque of the first to the torque of the second is

  What is the quantity used to measure 2dd5gx* pmfcns4 2wrd q(x*0t an object's resistance to changes in rotation?*n wg2 rp*xcfd5d 4ts(20qxmd

  Consider two uniform solid spheres where both have the same diameter, but one f 5hk oj,ae9nn5dof6/ has twice the mass of the other. The ratio of the larger moment of inertia to tnh6d/oej5a5 ,fko n 9fhat of the smaller moment of inertia is

  Two uniform solid spheres have the same mass, but one has t51b*jnzqs/o 0 di ,gya*;b aebwice the radius of the other. The ratio of the larger sphs *d bz 5ayebij/;ob n0,gqa*1ere's moment of inertia to that of the smaller sphere is

  Consider two uniform solid spheres where onewtc20ceinpjhiw *lag m/.)) 9 ,rg, ai has twice the mass and twice the diameter of the other. The ratio of the larger moment of inertia to that oj 9 )m pi.ctcawian) *,i2h,/leggw 0rf the smaller moment of inertia is

  A uniform solid sphere has masyz)fk1r j6k*3h4 t8 qkq1bxfj s M and radius R. If these are increased to 2M and 3R, what happens to the sphere's moment of inertia about a 68fj kyq 3k1j rhfq4 xkz)bt*1central axis?

  If a constant net torque is applied to an object, thatl 2g9cro 4b0qd object will

  The moment of inertia of a solid cylit uuc6o*-3w npd1 qft:n*gl/ ynder about its axis is given 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 :ux /o nx*jas(of 10 kg and a radius of 30 cm. Whua/o x(jn *sx:at is the ratio of the rotational kinetic energy of the 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 slipping dowy t91pmn djj;)p0)m9wu m -ghqn an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the ym9 mpjuq) ; 0)w9j-dpmn1 gthincline depends on

  Suppose a solid sphere of mass M and raog.gjf .(+c*b:hr vb nv2/wzudius R rolls without slipping down an inclined plane starting :/z2 *c gvfwuj.rhgon (b.+b vfrom rest. The angular velocity of the sphere at the bottom of the incline depends on

  "The total angular momentum of a syst3 s)e8e (g0.vsvkz0jj qmsg(v em of particles changes when a net external force acts on the systemv 0 3ev8s)msk (.(0geszqgvjj." This statement is

  In what circumstances can the angular velocity of system of particlesgl m zv a7lalw*ur8w)nf+,5 b;q0j5 tj change without anyz f+,rl gaw v lbwu*j5a5)lnq;8tm 70j change in the system's angular momentum?

  The Earth orbits the Sun5t+x9/2sj bvk1qfn ;ou r gob1 in an elliptical orbit. Ignore any friction which may be present. Whag2o 1 fn1s u5/t9rjk;vb xoq+bt happens over time to the Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an elliptical orbit. As th/r3idoc 7szqzz. z 5z;e Earth moves close to the Sun, then which of the following best describes thdoq 7szi. zzr5zz;3c/e orbiting speed of the Earth about the Sun?

  An ice skater performs a pirouette (a fast spin) by pulling e.zndidd9 +sy hd04 5rin his outstretched arms close to his body. What happens to his angular momentum about the axisnyez0hr. ddsd5id94 + of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretchedt/85 gyggy, jn arms close to his body. What happens to his rotational kinetic ety/,ny j ggg85nergy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in his outstretched.5d5d xxxss dwzpn/+ , arms close to his body. What happens to his mome sx/z5np +wdx.dx 5s,dnt of inertia about the axis of rotation?

State the law of conservation of angular nv()q.om7f-3cj* vhz*v c16m1iysqn h b8qmr momentum.

  What arc length does the Earth travel in a three month perioxt0dyp 02o;i id in its nearly circular orbit about the Sun with a r2ypxio0t; 0d iadius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length o9zu 1i hkw 3+yaw1ms+jqw 2m/xf 0.30 m. What distance does the tip of the wqmaim9wz1wx + 321u/j ks+hysecond hand sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolution fv1(c*uo;f0n z-lzdq s per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revolutio1s; ;(chzg4grvq n sfp0d +jp.ns in 4.0 s. What is the frequency of the wheel's rotatind.+ 4s grv0p;q(s1ph;g z cjfon?

  A pulsar (a rotating neutron star) emits pulses at a frequency7ob jkvl9: 0vy of 0.40 kHz. The period of its b7yjvo09kvl : rotation is

  A phonograph record rotates at 45 rs t0 to1/vlw rx+f di8tr9*(mipm. Through what angle does it turn in 0.20 8tilfr*r+tso1d9 x0 w(m/vits?

  A wheel of diameter 26 cm turns at 1500 rpm. How far will a point on the hhi;4r*y:a- ax6v8h+j i deaiouter rim xhy aa +iia e:rv4hj;6*8-idhmove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. ydb, hthoxb9/h7(3qza2yp 1x What is the average angula3xy/hd h7ayzb2 1x,qbpt(o h 9r speed of the wheel?

  A bicycle wheel rotates uniforml1vc gp:ak0bta)(kk*xiz; j l/5t.u x gy through 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of/gv( glbkpx0*i1ctt ku: j)ak;5z. ax the wheel?

  A cable car at a ski resort carries skiers a distance of 6.8 km. The c-f9 sd;rf7 :pky+uo w*(cog erable 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 trip go9odfc 7p-k+ ufr(r;:*we s yin 12 minutes?

  A wheel of radius 1.0 m is rotating with a constanttiz m2qd*h6g/ qpij14 angular speed of 2.0 rad/s. What is t hj4qqz1/*pgi 2tmid6 he linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.16 m 2:j4;eps5qu+qwzt 6mr9 f*lp4 xtirsin length. If the motor rotates at the rate of 20 rev/s, what is the approx rs *2s5mrwt:q6zqxl4 pu t+4if 9ejp;imate linear speed of the end of the cord?

  A wheel of radius 1.0 m is rotating with a -yhf k7o)*;m (fdqeejconstant angular speed of 2.0 rad/s. What is the centripetal acceleration of a point on the wheel's o7k)*med;f-jhfeq y( rim?

  What is the centripetal acceleration of a ub.n.vv ;qiispl,e77point on the perimeter of a bicycle wheel of diameter 70.0 cm when the bike is mob u7s.ei ;pi7nv,vq.lving 8.00 m/s?

  How many revolutions per minute (rpm) must 0 kbrudo4o-qw (j4-rja circular, rotating space station (r = 1000 mj(ku-0 qj ro4rw b4o-d) rotate 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 ja87yb ju67k f44ebuqof 20 m/s. The maximum centripeta 4qjab u 4j8euf6y7bk7l 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 rardwojl,elvayt:;q u+r/io20gv e l/p-n: 6 *kdius 50 m with a speed of 20 m/s. The mao:ne /wly :ldjpvor;6 e ul2-i*r,v0/+ tkqgaximum 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 end of a 0.r) 8a at,mxmk;;dcdk1 750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand is)adkrk ; ;1ta8mxdc,m 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 slipping 10 m thtat km )vb5xhm+4.+fc60 glt:t; qgdown a lane atxl .tfkb)mh6 htg:;v4qmt tt+gc0 a5+ 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 accelerat(;hcx6dbm r l-ion 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 acce -2t)tj3v)tv ;g pvwsyleration 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 automobilex4r /rgrcu;e( iu4d.q66 ziwu tire rotate after starting from rest and acce;ci. /z6rurd(44guqir xw ue 6lerating at a constant angular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelegei7c / 0zxkm*ration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotati:e1nth3k a* epng at 20 rad/s decelerates with a constant angular acceleration oe nh1 ak3p:*tef $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and res4rd1krxi:cyj4p :. aaches an angular speed of 6.0 rad/s while turning throsr1 i:c44jy ra:d.p kxugh 2.0 revolutions. What is the average angular acceleration of the wheel?

  A wheel of diameter of 68.0 cm sh45rqw*k +.d)q5ww -vngln o jlows down uniformly from 8.40 m/s to rest over a-n *dqqh 5)ljgrwwv+.won4k 5 distance of 115 m. What is the total number of revolutions the wheel rotates in coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.:5vc/lhge h 2c40 m/s to rest over a distance ofc:ce/ l 5g2hvh 115 m. What is the angular acceleration?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 )qge o02.kf*ahe u0bm m/s to rest over a distance of 115 m. How long does it tau k am0ege0.hb)2f qo*ke for the wheel to come to the stop?

  A centrifuge in a medical laboratory wnim 97zb/4m3p .ukk drotates at a rotational speed of 3600 rev/min. When switched .dz 7 kbi/mmk3 pwu9n4off, it rotates 50.0 times at 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 czzv5n7 3u; 5wz:a miuto a torque of 90 Nm. If a 30 cm long wrench is used, what is the magnitude ofziu5z3w5n:zc m 7v;a u 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. If a 30 cm lo+/dw iqj0rqjx;3kx 1-w fbp6-dyfg m *pa)f(tng wrench is used, whjp w- i+ wxk (ftmfrbdj */ 361-)dq;yfgx0qpaat is the magnitude of the force required when the force applied at $53^{\circ}$ to the wrench?

  A wheel with moment of iner)w4, ;hrbeyukb u:k*btia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as folloo0:e (2.eg2cwg cfe juws: mass m is at the origin, mass 2m is at x = a, and, mass 3gc2u oe(ef2cew.j:0g m is at x = 2a. What is the moment of inertia about the origin?

  A solid cylinder of mass 10 kg is pivoted about a frictionl)4dbz4t 7kd m ax;2wehess axis thought the center O. A rope wr4 zwkb;tedd4 m27 )haxapped 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 sp-; fhw.q*6v czz7yivv-y80s9htz. tigs6 e axis thought the center O. A rope wrapped around the outer rpgiv6 h y-9cys zi.6-h7 vw qtsf*08tes zz.;vadius $R_1$ = 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 i;zntbh ,xb2l6 nitially held in the horizontal position, and then released as the free end is allowed2 xtblh zn;,6b 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 30 cm and mass :(jh8w4od9qfwp h6xn 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20 N xj fnw w(:dqp84h9oh6is 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 frictionless disk l0 jpwakf0x0, pulley of mass 7.07 kg and radius 66.0 cm. What0x0wlpfa 0j,k is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on a rope wrapped around a frictionless disk pulley zluy4v(hz;sfe i;0d7 of mass 7.07 kg and radius 66.0 cm. What is the acceleration ofyzzl;e;(0sd uh4f 7 vi the mass?

  A rotating flywheel leu4wygqn rast (899eg q78h8can be 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 inertia ojlfxp gs9q. o;1u(h y(f $5.00 \; kgm^{2}$ 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:msot6rbn/zg ;yue5 lw+bq. 8 from rest and rolls without slipping down a 1.0-m high inclined plane. What is the spe5 e bw8.ou rq:/;s bz6lmy+tnged of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1ch2uip*rk r2)o;x *ol.0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming to r*po) ixh2 lk2rc ru;*oest?

  A hoop of radius 0.50 f 9 .*rjqyyjsv5 7cud/m and a mass of 0.20 kg is released from rest and allowed to roll down an incli.v*9y cuf/7sy5jqj r dned plane. How fast is it moving after dropping a vertical distance of 3.0 m?

A solid sphere of mass 1.5 kg andzca6 w,2pm -e7gnd,xw radius 15 cm rolls without slipping down a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is giv-e 6w ,wnzcg pm,a7d2xen 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 momentihzyp5 x-e po5;za03wum 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 of i4(mx7rkra k0rnertia 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 y ba9ue)9zm2t5.00 rad/s with arms extended has a moment of inertia 9buaet2m )zy9of
$2.25 \; kgm^{2}$. If the arms are pulled in so the moment of inertia decreases to $1.80 \; kgm^{2}$, what is the final angular speed?