A student sits on a rotating stool holding two 4.0 kg objects. When his arms are
ID: 1679616 • Letter: A
Question
A student sits on a rotating stool holding two 4.0 kg objects. When his arms are extendedhorizontally, the objects are 1.0 m from the axis of rotation, andhe rotates with an angular speed of 0.75 rad/s. The moment ofinertia of the student plus stool is 3.0kg·m2 and is assumed to be constant. Thestudent then pulls the objects horizontally to 0.40 m from the rotation axis. (a) Find the new angular speed of the student.rad/s
(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before J after J
(a) Find the new angular speed of the student.
rad/s
(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before J after J
before J after J
Explanation / Answer
Initial moment of inertia is that of the student & stoolplus the two masses: Ii = 3.0 + 4.0*1.02 + 4.0*1.02= 11.0 kgm2
Final moment of inertia is same idea, but the masses arecloser: If = 3.0 + 4.0*0.402 + 4.0*0.402
= 4.28 kgm2
Now, since angular momentum is conserved:
Ii i = If f
11.0 * 0.75 = 4.28 *
= 1.93 rad/s
initial KE = (1/2) I 2
= (1/2) * 11.0 * 0.752
= 3.09J
final KE = (1/2) I 2
= (1/2) * 4.28 * 1.932
=7.97 J Now, since angular momentum is conserved:
Ii i = If f
11.0 * 0.75 = 4.28 *
= 1.93 rad/s
initial KE = (1/2) I 2
= (1/2) * 11.0 * 0.752
= 3.09J
final KE = (1/2) I 2
= (1/2) * 4.28 * 1.932
=7.97 J
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