# Spinning Disk Pendulum Swinging on Top of a Rotating Table

Spinning Disk Pendulum Swinging on Top of a Rotating Table

This Demonstration shows a pendulum with a small spinning rigid cylindrical bob in which the pendulum rod (assumed to have negligible mass) swings from a frame fixed on top of a rotating table. The system has three degrees of freedom: the pendulum swing angle , the spin angle of the pendulum bob, and the rotation angle of the large table.

θ

ψ

ϕ

The angular momentum of the bob with reference to a fixed point in space and the bob's absolute rate of angular momentum change are calculated and displayed in vector form.

L

dL

dt

The instantaneous values of the system's kinetic and potential energy (red and blue bars, respectively) are shown graphically. Other options are available to help study further details of this system.

The program was constructed by finding the Lagrangian, deriving the three nonlinear equations of motion and solving them numerically.

The principal moments of inertia are used for the bob. The fixed point in space that was used to calculate is the point where the pendulum rod is attached to the frame.

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