The expansion of the centrifugal force formula, $F_c=m \omega \times(\omega \times x )$, relies on the vector triple product identity: $A \times( B \times C )= B ( A \cdot C )- C ( A \cdot B )$. Applying this identity with $A = \omega , B = \omega$, and $C = x$ allows the centrifugal force to be ultimately expressed in the form $F_c=m\left[\omega(\omega \cdot x )-\omega^2 x \right]$, where $\omega=|\omega|$ is the magnitude of the angular velocity.

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1. What is the vector identity used to expand the centrifugal force formula?
2. How can the centrifugal force be expressed using the angular velocity and the position vector after expanding the vector triple product? </aside>