Consider an inertial frame of reference and a frame of reference which is rotating with constant angular velocity relative to . Assume that the two frames have a common origin .
Let be any vector. Explain why the derivative of in frame is related to its derivative in by the following equation
[Hint: It may be useful to use Cartesian basis vectors in both frames.]
Let be the position vector of a particle, measured from . Derive the expression relating the particle's acceleration as observed in , to the acceleration observed in , written in terms of and
A small bead of mass is threaded on a smooth, rigid, circular wire of radius . At any given instant, the wire hangs in a vertical plane with respect to a downward gravitational acceleration . The wire is rotating with constant angular velocity about its vertical diameter. Let be the angle between the downward vertical and the radial line going from the centre of the hoop to the bead.
(i) Show that satisfies the following equation of motion
(ii) Find any equilibrium angles and determine their stability.
(iii) Find the force of the wire on the bead as a function of and .