A uniform solid disc of mass 4.0kg and radius 0.30m is mounted on a frictionless horizontal axle through its centre O. A force of magnitude 50N is applied at the rim at point P such that the line of action of the force makes an angle of 70∘ with the radius OP in the plane of the disc.
(a) Derive an expression for the torque produced by the force about the centre O in terms of the given quantities.
(b) Using the standard expression for the moment of inertia of a solid disc about its central axis, determine the resulting angular acceleration of the disc.
(c) If the force continues to act for 2.0s starting from rest, calculate the angular velocity acquired by the disc at the end of this time.