Answer:
[tex]a = \dfrac{4\pi^2R}{T^2}[/tex]
Explanation:
The acceleration of a circular motion is given by
[tex]a = \omega^2 R[/tex]
where [tex]\omega[/tex] is the angular velocity and [tex]R[/tex] is the radius.
Angular velocity is related to the period, T, by
[tex]\omega=\dfrac{2\pi}{T}[/tex]
Substitute into the previous formula.
[tex]a = (\dfrac{2\pi}{T})^2 R[/tex]
[tex]a = \dfrac{4\pi^2R}{T^2}[/tex]
This acceleration does not depend on the linear or angular displacement. Hence, the amount of rotation does not change it.
