Determine the dimensions of angular acceleration α . Some of the...

From the given equations, the angular velocity $\omega$ is given by $\omega = \dfrac{\theta_2 - \theta_1}{t_2 - t_1}$.

Since angular displacement $\theta$ is a dimensionless quantity, its dimensions are $[M^0 L^0 T^0]$.

The dimensions of time $t$ are $[T]$.

Thus, the dimensions of angular velocity $\omega$ are $\dfrac{[M^0 L^0 T^0]}{[T]} = [T^{-1}]$.

The angular acceleration $\alpha$ is given by $\alpha = \dfrac{\omega_2 - \omega_1}{t_2 - t_1}$.

Substituting the dimensions of $\omega$ and $t$, the dimensions of $\alpha$ are $\dfrac{[T^{-1}]}{[T]} = [T^{-2}]$.