Derive the rotational form of Newton's second law as follows. Consider a rigid object that consists of a large number N of particles. Let Fi, mi, and ri represent the tangential component of the net force acting on the i th particle, the mass of that particle, and the particle's distance from the axis of rotation, respectively.

(a) Use Newton's second law to find a i , the particle's tangential acceleration.
(b) Find the torque acting on this particle.
(c) Replace a i with an equivalent expression in terms of the angular acceleration a.
(d) Sum the torques due to all the particles and show that

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Axis mi