A particle of mass m is constrained to move on a circle of radius R. This circle also rotates in space about a fixed point (P) on the circumference of the circle. The rotation of the circle is about an axis of rotation perpendicular to the plane of the circle and tangent to the circle, at point (P); the rotation is at a constant angular speed W.

In the absence of a gravitational force, show that the particle's motion about one end of a diameter passing through the pivot point and the center of the circle, perpendicular to the axis of rotation, is the same as that of a plane pendulum in a uniform gravitational field.

Explain why this result is reasonable.