Simple pendulum (with a twist) 1
The center of a wooden disk is joined to one end of a rod. The other end of the rod is fixed rigidly but free to swing.
- Case A: The disc is mounted rigidly on the rod.
- Case B: The disk is free to rotate about its central axis.
The rods are released from a horizontal position with both discs at rest. When the rod gets vertical, then where W(A) and W(B) are the angular velocities of the rods in Case A and Case B, respectively.
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1 solution
Some energy in Case:A goes in spinning of the disc (in the ground frame, of course). But in Case:B the disc possesses no energy in the form of pure rotation (in ground frame, again), so the system has higher total energy, hence higher w (omega).