(a) Starting from I = | r² dm, show that the moment of inertia of a uniform cylinder of mass M and radius R (spinning about its central axis) is given by I MR² 2 (b) A cart has four wheels, each a uniform disc of mass 1 kg and radius 0.5 m. The body of the cart has a mass of 6 kg. What is the total moment of inertia of the cart as it rolls down a slope? (c) The cart starts from rest and rolls down a slope a vertical distance of 5 m. How fast is it then travelling? [Ignore friction and air resistance.]

(a) Starting from I = | r² dm, show that the moment of inertia of a uniform cylinder of mass M and radius R (spinning about its central axis) is given by I MR² 2 (b) A cart has four wheels, each a uniform disc of mass 1 kg and radius 0.5 m. The body of the cart has a mass of 6 kg. What is the total moment of inertia of the cart as it rolls down a slope? (c) The cart starts from rest and rolls down a slope a vertical distance of 5 m. How fast is it then travelling? [Ignore friction and air resistance.]