Normal acceleration in a wheel

Since the angular velocity is constant and the trajectory of any point is circular we have a uniform circular motion or u.c.m.

Data

R = 1 m
T = 1.2 s

Resolution

If it takes 1.2 s for a full rotation, the disk turns with a period T=1.2 s. From this period, we can calculate the angular velocity of the disk:

$$\begin{gathered} \omega =\frac{2\pi }{T}\Rightarrow \\ \omega =\frac{2\pi }{1.2}\Rightarrow \\ \underline{\omega =1.67\pi rad/s} \end{gathered}$$

Considering the definition of normal or centripetal acceleration, we can calculate its value using the following expression:

$$\begin{gathered} a_n=\frac{v^2}{R}={\omega }^2·R \Rightarrow \\ {a}_n=(1.67\pi {)}^2·1 \Rightarrow \\ \boxed{a_n= 27.52 m/s^2} \end{gathered}$$