Angular displacement is usuaf 0;a;mfj7i/o5s alst3 ftt v;lly express in units of

  Angular velocity is expresse aga-l+ he1uz7lqo;is*wr:9:sdzt* nd in units of

  Angular acceleration is expressed in unitsct;hca4( 1on hux)n-w of

  A boy and a girl are riding on a merry-go-rke 9) tti+ aat1jblwqcn w-rzn ; 0xf1(4;jyj2ound 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 angular displace02e1)a9rb+jxn ; ftan ;tzjli w q(y41cw kt-jment?

  A boy and a girl are riding on a merry-go-r:htfcnw+ 8 8lbound which is turning at a constant rate. The boy is near the wcl h8f:+nb8touter 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)2hdxfcexg yp6* ol: . 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 lind* :)plf2 y.ocx6e hxgear speed?

  A boy and a girl are riding a merry-go-round which is turning at a constant.ky*v9h- o o-n90os mbbvyi/x rate. The boy is near the outer edge, while the girl is.9-yxnvk o*so0b-m/o h 9i bvy 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 8v*7dhkkjodt7k 67 em constant rate. odk etd 7m786k7 kjhv*The boy is near 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 th vcgk(dd i+2n7n3e( tde following is an accurate stadg2 v37e(n( ctdin+dktement?

  Rolling without slippi 8foc/4n9- dv kdrhqv:ng depends on

  Two equal forces are applied to a door. The first force is applied at the mi)ncald k:bj 9to h x-qdh(r08)dpoint of the door; the h :8)rx-9jb( dckn)oaht l0qdsecond 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 a3pe9 gyrb+o*, co9qq qt the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30e to the plane of the door. Wo99gb,qo3+ ecrqq y*phich force exerts the greater torque?

  Two forces are applied to a4hok br 0.3wyp doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of yhr4w3p o 0.bkthe first to the torque of the second is

  What is the quantity us 6oy3qn7 s,t6-iruzbied to measure an object's resistance to changes in rotatiiq 6yz6-r, 7 bios3utnon?

  Consider two uniform bh*c j) wd05o6+y)98pcezp rc/zhtrq solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the h/+9z5*q 8cycr h6 rpp )e)wt ocb0jdzlarger moment of inertia to that of the smaller moment of inertia is

  Two uniform solid spheres have the sam :wmwao v6ij5 x.2lxh(e mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia to that of the.6mxwx oal5i2(hwj: v smaller sphere is

  Consider two uniform solid spheres where one has twice the mass and dye;p 3snj7 d5y0sbauo8u -m2 twice the diameter of the other. The ratio of the ld0;dy2 abnss -j87p53yuo e muarger moment of inertia to that of the smaller moment of inertia is

  A uniform solid sphere has mass M and radius 0yr+b5iunxi 1bs/) mxR. If these are increased to 2M and 3R, what happens to the sphere's mo bsurb5yix1) +xi0m /nment of inertia about a central axis?

  If a constant net torqueq8kusohlj2z: -o-o*j /da t4q is applied to an object, that object will

  The moment of inertia of a solid cv*9um 1n .v*2d qhjw*hmow be h7mp6d+ylinder about its axis is given by 0.5 MR2. If this cylinder rolls without slipping, the ratio of its rotational kinetic energy to its translational kinetic energy192 *pjd w*mw.u hmbh*v q ednv76+omh is

  Consider a motorcycle of mass 150 kg, one whfec-,m. 3s1m gtzc nj80c0jcjeel of which has a mass of 10 kg and a radius of 30 cm. What is the rat8f m t,ngcejjcs1z 0j30-.ccmio 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 ro xdwwh:m)j7wyhj7.o moj36jb n j1c9* lls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends)j7whjm9:bo.jy*hj c7nwjmx1dw 3o6 on

  Suppose a solid sphere of mass M and radius R rolls without slipping downe /twy: e5le9a an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends :5ew9l/eet yaon

  "The total angular momentum of a system of particl ,dtmk wwg:l+n*z gv0d8hi50 res changes when a net external force acts on the system." This sthnm0,z*v w iwtk+g8gd0r l5d:atement is

  In what circumstances can the angular velocity of system of particles ch.1z).7 a homkgcgcoz6ange without any change in the system's angularm1o)oczg. .k7 zga 6ch momentum?

  The Earth orbits the Sun in an elliptical orbit. Ig7qu0yi oiyh/er(o/s4 tnzl07 nore any friction which may be present. What happens over time to thntls7qi 0 h (ro7ou4y/0/e iyze Earth's angular momentum about the Sun?

  The Earth moves about the Sun in an ellipticalz-wjalph 4iu ),a :)tj orbit. As the Earth moves close to the Sun, then which of the following best desw ilp:4ajzth ,)a)-ujcribes the orbiting speed of the Earth about the Sun?

  An ice skater performs a pird/4p k cb2p:irouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum ab ibpdr:/p42k cout the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling in hci0iafu m jxp97w0ajnb3,va, 6.4d gjis outstretched arms close to his body. What happens to hi.xdu0npibj,c9v0 j,6aw7f3 aag4jims rotational kinetic energy about the axis of rotation?

  An ice skater performs a pirouette (a fast spin) by pulling i+trov 9v/wt7z7n p1tbn his outstretched arms 7rtn7 pwtb/ +zt91 ovvclose to his body. What happens to his moment of inertia about the axis of rotation?

State the law of conso m1u k z7w-mk rtb;e 1nce(0q/ev8d2eervation of angular momentum.

  What arc length does thuoe+w q9diy+u1evl3 , q -.rhhe Earth travel in a three month period in its nearly circular ore+ed u voluq+1i,.y-q3h9 rhw bit about the Sun with a radius of $1.5 \times 10^{11} \; m$?

  The second hand of a clock has a length of 0.30 m. What distance doe +-mtqy 7r/uqss the tip of the second hand+yr -/7usmtq q sweep through in 3 minutes and 45 seconds?

  How many rad/s is 25 revolutiony8f+cz q2j9d ss per minute equivalent to?

  A bicycle wheel rotates uniformly through 2.0 revoluti mt4xoud u;;3nons in 4.0 s. What is the frequency of the wheel's rota3uunm ;; d4xottion?

  A pulsar (a rotating neutron star) emits pulses at a frequency of 0.40 kHz. Tv ,l8 ct1z0hddhe periv1l,d 80 cthdzod of its rotation is

  A phonograph record rotates at zakzt-dp 9 (m045 rpm. Through what angle does it turn in 0.20 sz d-9p (a0tzkm?

  A wheel of diameter 26 cm turns aty ;k1l hwd(a1eiqs;gf7q mf+7 1500 rpm. How far will a point on the outer rim dw7ms+a lqi7(;yheg1 1 kff;qmove in 2.1 s?

  A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s.8by+)ubku +g t What is the average angular sguu) t8b +yk+bpeed of the wheel?

  A bicycle wheel rotates uniformly e fgr:x, *xq/wthrough 2.0 revolutions in 4.0 s. What is the linear speed of a point 0.10 m from the center of the wh/ ,*rxf gxeq:weel?

  A cable car at a ski resort carries skiers a distance of 6p1 8kn w22li 6m,i+/ u:byvlgmqysm(v l3 vq+v.8 km. The cable which moves the car is driven by a pulley with diameter 3+p,vm2s23:wy v+1vq/uklygmib v 8 lmi6q l (n.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 ,o2 9 qxltf+syconstant angular speed of 2.0 rad/s. What is,9+y2fs x oqlt the linear speed of a point on the wheel's rim?

  The cutting cord on a gas-powered weed cutter is 0.19inu+yz j0tp+ d+6sxbdtb .w96 m in length. If the motor rotates at the rate of sy9jwx6zuti09+.p +dtbnb d+ 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 constant angu yeppz+il4.l+h v( 7qklar speed of 2.0 rad/s. What is the centripetal acceleration of q(ivek++p.z yp lh74l a point on the wheel's rim?

  What is the centripetal acceleration of a pocg 5fgkpoi:j883d /hrint on the perimeter of a bicycle wheep538i:dfhj/k8og gcr l of diameter 70.0 cm when the bike is moving 8.00 m/s?

  How many revolutions per minute (rpm) must a circular, rorxm li+ez a)m7w 0b1j/tating space station (r = 1000 m) rotate+abe7 )jwl0x1r /izm m to produce an artificial gravity of $9.80 \; m/s^2$?

  A car is negotiatingqsr 3luo /an-25s29kan n w mm0)1omhg a flat circular curve of radius 50 m with a speed of 20 m/s. The on/o-w1nrnmsh2 l29ag)qs5mmku a 30maximum centripetal 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 speed of 20 m8vgjjiy1 piiz7 (sid2 h-u9 ;s/s. The maximum centripetal force (provided by static fg iv7jj-8zphi; s i 9i12(dysuriction) 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 e:jsz)7 5 b20s(yquxbrxg k,7 e6ctfo 0.750-m string, is whirled around in a smooth level table. If the maximum tension that the string can withstand ,27 s 0f()ubseg 756qz:jyorebxkcxt 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 radiusm1 9exw) nimm7 9.0 cm rolls without slipping 10 m down a lane mmnm9x )1w7eiat 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 constr/a+-grrfs l vfzr64+ ant 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 angular acc9xv(3y8brhsdksbim c )):)zdeleration 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 stn2 p 6mkjh5j0tarting from rest and accelerating at a constant an60 knmj pht2j5gular acceleration of $2.00 \; rad/s^2$ over a 5.00-s interval?

  A wheel starts at rest, and has an angular accelipn-9 pbb+8/b p .scrneration of $4 \; rad/s^2$. Through what angle does it turn in 3.0 s?

  A Ferris wheel rotating at 20 rad/s decelerates withkdjbqo :9z,2j 4 c)mqf a constant angular accelerationbm cd,q jj:29f) 4kqoz of $-5.0 \; rad/s^2$. How many revolutions does it rotate before coming to rest?

  A wheel starts from rest and reaches an6j ;pm* jqquew p7coa/ eu4+2x angular speed of 6.0 rad/s while turning through 2.0 revolutions. What is the average angularq*pq;um6 2c pjwau/7 +eej4ox acceleration of the wheel?

  A wheel of diameter of 68.0 cm sloy40rsvg4kfa 8(mzbjdn * 2:3ekd pn3fws down uniformly from 8.40 m/s to rest over a distance of 115 m. What is the total number of revolutions the wheel rotates iv:3afb( p 3z0 ksn4jyr2ng4fedm8d *kn coming to rest?

  A wheel of diameter of 68.0 cm slows down uniformly from 8.40 m/s to rest ove+j,jcpg/yk6z r a distancey /6+j, kzcgpj of 115 m. What is the angular acceleration?

  A wheel of diameter of 68.md0 ujm-r7ca)0y )aa h0 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 tama)7hd)u-jr a00c my o come to the stop?

  A centrifuge in a medical laboratoqca zswk3(lvv )czj4o4j9h84p * xy /cry rotates at a rotational speed of 3600 rev/min. When switched off, it rotates 50.0 times at a constant angular acceleratio ahk9s j*y/c8vv4cz4l 3)q4c x(opwj zn 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 of 90 Nm. 5x ch9)9gl ir+2yaq nyIf a 30 cm long wrench is used, what is the 9i xn+hg5yy2q9)al crmagnitude of the force required when the force is perpendicular to the wrench?

  The bolts on a car wheel require tightening to a torvt8 yay:yu3r6 1n gzl.que of 90 Nm. If a 30 cm long wrench is used, what is the magnitude of the force required when the force applied g rv1:a t.3 8zyyn6luyat $53^{\circ}$ to the wrench?

  A wheel with moment of in3 ar15.vy wcdyobqm2 -4h5m zlertia $3.00 \; kgm^{2}$ has a net torque of 3.50 Nm applied to it. What angular acceleration does it experience?

  A triatomic molecule is modeled as follows: mas cs s8u;a4p)lks m is at the origin, mass 2m is at x = a, and, mass 3m is at xk c8s4;)as ulp = 2a. What is the moment of inertia about the origin?

  A solid cylinder of map +p9g(-sf5 h pkz-w7xflxz/ dss 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 x(/7- shgp p9zpd-f5lxzf+wkm, 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. (See Fig. 8-1.) What is the angular acceleration of the cylinder?

  A solid cylinder of mass 10 kg is piff uesptki8.:2e 5r.;oc .lshvoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R1 = 1.0 m fs2cfu.hl;s kp.: o8retie.5, 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. The ro)80dxf bitm n/d is initially held in the horizontal position, and then released as the free end is allowed /d m8x0f)itbnto 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 1.5 kg. Neglecynst4; 5o wtndg(r m+c4 br-9vt the mass of the axle and sprocket. If a force of 20-wcgt49rr4 v; mtsd n+b (nyo5 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 frictionless disk pulley of mas95,ucoh,owr0 wu dp m5s 7.07 ko hou5 ,5w 90wdcrmp,ug and radius 66.0 cm. What is the angular acceleration of the pulley?

  A 1.53-kg mass hangs on f(czol s:(fvs1 5hx9ha rope wrapped around a frictionless disk pulley of mass 7.07 kg and radius 66.0 cm. What fhc9s (h1zlo :s x(vf5is the acceleration of the mass?

  A rotating flywheel can be used to store energy. If it is re/ *ij* 4i zey:je*yf-ni;8,hln maq j gkx19jmquired 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 inertdhv:lrcpa 07vg f 5 udsv9wj-0q,z 4v,ia 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 startzk atjn/,yectp i4fg9rz9* ,1 0t6rc os from rest and rolls without slipping down a 1.0-m high inclined pl0,9964t,cg aprt1 o*kty/ifz je r cznane. What is the speed of the sphere when it reaches the bottom of the inclined plane?

  A solid sphere of mass 1.ozw 1q *w13rec0 kg and radius 0.010 m rolls with a speed of 10 m/s. How high up an inclined plane can it climb before coming113 qc*ore wwz to rest?

  A hoop of radius 0.50 m and a mass of 0.20 kg is released from rg7ieiq;:pi 8o,dbs ms jv 4,m)est and allowed to roll down an inclined plane. How fast is it moving after dropping a vertical dij4;:bq ),emi 8g,io vspdms7 istance of 3.0 m?

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping dowjx3 zh ;f.etl6n a 35e incline that is 7.0 m long. Assume it started from rest. The moment of inertia z3h. jet6l; fxof 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 changer*c ;uq tnf cw:;;za4ws 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 momeprei z;5ggp- pvouo+zu8s: 16nt 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 arms exgsa1j13 c ogd;tended has a moment of inerti1;dc3as1jog g a 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?