Consider a particle which is constrained to move along the surface of the sphere of radius 5, centered at the origin.
(a) If we write r(t) for the motion, write down the condition ‘constrained to move along the surface of the sphere of radius 5 centered at the origin’ in terms of r(t). (Hint. For later use, try to get rid of square roots.)
(b) Explain why, for such a motion, we must have r 0 (t) ⊥ r(t). (Hint. Differentiate your answer from the previous part.)
(c) What can you say about the acceleration? (Hint. Differentiate your answer from the previous part. Draw a picture.)