Question

How do you figure out the centripetal component of a acceleration vector when given only the acceleration vector and the unit normal vector?

Answer 1

Recall that acceleration can be decomposed into a centripetal component in the direction of the normal vector and a tangential component in the direction of the tangent vector. This means acceleration lies in the plane spanned by the tangent and normal vectors, lets call them \(\mathbf{T},\mathbf{N}\):