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Oscillating Mass On Rotating Table

Nasser M. Abbasi

August 8, 2012 compiled on — Wednesday July 06, 2016 at 08:35 AM
This Demonstration describes the dynamics of a spring-mass system on a rotating disk in the horizontal plane. A mass at the end of a spring moves back and forth along the radius of a spinning disk. The spring is anchored to the center of the disk, which is the origin of an inertial coordinates system. The bob mass is considered part of the overall disk mass for purpose of calculation of the mass moment of inertia; therefore the overall mass moment of inertia around the axis of rotation changes as the bob distance relative to the disk center changes.

There is no friction between the bob and the disk and the spring mass is negligible. The spring is assumed to be infinitely rigid against rotational movement and will remain straight as it vibrates.

In this system, the overall moment of linear momentum, also called the angular momentum, is constant since no external torque and no energy dissipation is present, therefore when the bob is near the center of the disk, the angular speed of the disk increases, since the mass moment of inertia has decreased. Conversely, when the bob is close to the edge of the disk, the angular speed of the disk decreases, since the mass moment of inertia has increased. This is similar to what happens when ice skaters pull their hands closer to their body in order to increase the speed at which they are spinning.

The table has a raised edge and when the bob hits the edge, its velocity is set to zero if the edge wall is an inelastic type otherwise its velocity reverses direction if the edge is an elastic type. Pure elastic and inelastic material is assumed at the edge.