Question

Establish a relation between linear acceleration and
angular acceleration.​

Answer 1

Linear acceleration = Rate of change of linear velocity

$\large\Longrightarrow \bf a = \frac{dv}{dt}.......(i)$

Angular acceleration = Rate of change of angular velocity

$\large\Longrightarrow \bf \alpha = \frac{d \omega}{dt} .....(ii)$

From (i) and (ii)

$\large \bf \frac{a}{ \alpha } = \frac{d v}{d \omega} = \frac{d(r \omega)}{ d \omega} \\ \\ \large \bf = r \frac{d \omega}{d \omega} \: \: \: \: \: \: (r \: is \: a \: constant) \\ \\ \huge \boxed{ \sf \orange{ a = \alpha r}}$