Two identical platters, like the ones used in Experiment I, are shown. In this c

Question

Two identical platters, like the ones used in Experiment I, are shown. In this case, the platters rotate about the same axis with different angular velocities as shown. The upper plate will be lowered onto the lower plate, and they will quickly rotate together with the same angular velocity.

A. Before the plate touch, what is the direction of the angular momentum of the top plate?

B. Before the plates touch, what is the direction of the angular momentum of the bottom plate?

C. After the top plate is lowered onto the bottom plate, what is the direction of the angular momentum of the combined top and bottom plate system? Explain your reasoning

D. After the top plate is lowered onto the bottom plate, what is the magnitude of the angular velocity of the combined top and bottom plate system in terms of Wo? Explain your reasoning.

E. Does the combined system afterwards have more, less or the same kinetic energy as before? Explain your reasoning.

Explanation / Answer

A.)Before the plates touch:

the angular momentum of upper plate is in upward direction(L=r x mv where r=radius and v=velocity, apply right hand thumb rule)

B.) the angular momentum of lower plate is in downward direction

C.) and D.) Here the angular momentum of the system containing both the plates is conserved because when the plates meet they exert forces (torques) on each other, which are internal forces(torques).

So if they have same moment of inertia I, then

4Iw0 - 2Iw0 = 2Iw (where upward direction is assumed positive and combined angular velocity of plates is w)

so w=w0 in upward direction.

E.) Now kinetic energy before the plates meet each other =K1

K1 = 1/2 I (4w0)^2 + 1/2 I (2w0)^2 = 10 Iw^2

Combined Kinetic energy=K2

K2 = 1/2 2I (w0)^2 = Iw^2

So K1>K2

Kinetic energy is less than before.

Kinetic energy is not conserved because some part of the kinetic energy is lost in heat (friction and other factors).

Take a note that total energy of the system is still conserved here. The exact amount of heat is produced which is lost in kinetic energy.

(That's why it doesn't matter if the plates are friction less or not, you can apply conservation of angular momentum concept anytime where the 'external' torque is absent.)

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