# Angular Displacement

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Angular displacement, abbreviated as $$\theta$$ (Greek symbol theta), is the angle through which a body moves in a circular path.

## Angular displacement from the radius formula

$$\large{ \theta_d = \frac{s}{r} }$$
Symbol English Metric
$$\large{ \theta_d }$$  (Greek symbol theta) = angular displacement  $$\large{deg}$$ $$\large{rad}$$
$$\large{ s }$$ = distance covered by the object on the circular path $$\large{ft}$$ $$\large{m}$$
$$\large{ r }$$ = radius of circular path $$\large{ft}$$ $$\large{m}$$

## Angular displacement from Angular Velocity formula

$$\large{ \theta_d = \omega \; t }$$
Symbol English Metric
$$\large{ \theta_d }$$  (Greek symbol theta) = angular displacement  $$\large{deg}$$ $$\large{rad}$$
$$\large{ \omega }$$   (Greek symbol omega) = angular velocity $$\large{\frac{deg}{sec}}$$ $$\large{\frac{rad}{s}}$$
$$\large{ t }$$  = time $$\large{sec}$$ $$\large{s}$$

## Angular displacement from angular Acceleration formula

$$\large{ \theta_d = \omega\; t + \frac{1}{2} \; a \; t^2 }$$
Symbol English Metric
$$\large{ \theta_d }$$  (Greek symbol theta) = angular displacement  $$\large{deg}$$ $$\large{rad}$$
$$\large{ a }$$  = acceleration $$\large{\frac{ft}{sec^2}}$$ $$\large{\frac{m}{s^2}}$$
$$\large{ r }$$ = radius of circular path $$\large{ft}$$ $$\large{m}$$
$$\large{ t }$$  = time $$\large{sec}$$ $$\large{s}$$ 