which expression can be used to calculate centripetal acceleration?\n$\frac{2pi r}{t}$\n$\frac{4pi^{2}r}{t^{2…

Explanation:

Step1: Recall centripetal - acceleration formula

The centripetal acceleration formula in terms of radius $r$ and time - period $T$ is $a = \frac{4\pi^{2}r}{T^{2}}$. The formula is derived from the relationship between linear velocity $v=\frac{2\pi r}{T}$, and centripetal acceleration $a=\frac{v^{2}}{r}$. Substituting $v = \frac{2\pi r}{T}$ into $a=\frac{v^{2}}{r}$ gives $a=\frac{(\frac{2\pi r}{T})^{2}}{r}=\frac{4\pi^{2}r^{2}}{T^{2}r}=\frac{4\pi^{2}r}{T^{2}}$.

Answer:

$\frac{4\pi^{2}r}{T^{2}}$