A point P of mass moves in a vertical plane along a circle of radius with uniform…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A point P of mass m moves in a vertical plane along a circle of radius A with uniform angular speed ω. The point Q is the projection of P on the vertical diameter passing through the centre O.
(i) Taking downward displacement of Q from O as positive, derive an expression for the acceleration of Q in terms of its displacement y.
(ii) Hence prove that Q performs simple harmonic motion and write the expression for the restoring force acting on it.
(iii) Deduce an expression for the total mechanical energy of Q in terms of m, A, ω and y. State clearly which forms of energy are included.