Question

Obtain the relation between magnitude of linear acceleration and angular acceleration in circular motion.

Answer 1

we know,
angular acceleration is defined as the rate of change of angular velocity.
e.g., $\alpha=\frac{\Delta{\omega}}{\Delta{t}}$
where where Δω is the change in angular velocity and Δt is the change in time.
also, the units of angular acceleration are (rad/s)/s, or rad/s2. 

now, linear acceleration is the rate of change of linear velocity . e.g., $a=\frac{\Delta{v}}{\Delta{t}}$
we know, $v=\omega r$
so, $a=\frac{r\Delta{\omega}}{\Delta{t}}$

$a=r\frac{\Delta{\omega}}{\Delta{t}}$

$a=r\alpha$

so, the relation between angular acceleration and linear acceleration is given by $\boxed{\boxed{a=r\alpha}}$