Non-uniform Circular motion

Question

This object is rotating at non-uniform circular motion. Its centripetal acceleration is a_c  = 20 m/s² and its tangential acceleration is a_t  = 13 m/s². What is the total acceleration?

What is the angle of the total acceleration as measured from the centripetal acceleration?

Answer 1

|a| = sqrt(a_C² + a_T²)

Draw the situation: a_c is in the radial direction and a_T is tangential. The angle defined with respect to the radius makes the radial direction the adjacent side or the direction of the acceleration tan^-1(a_T/a_C) or cos^-1(a_C/a)

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