# Angular forms of acceleration, velocity and displacement

1. Jul 5, 2011

### scotty_le_b

I have been going through my equations and writing them up on the computer so I can refer to that when needed and have go to angular acceleration, velocity and displacement equations yet I dont have very many equations for those topics and I wondered if anyone had some equations for finding those values. I seemed to have more for acceleration, velocity and displacement in their linear forms, could I just changed the variables in those equations to their angular counterparts?
Thanks

2. Jul 6, 2011

### tiny-tim

hi scotty_le_b!
the popular ones, yes

for example, from the pf library on https://www.physicsforums.com/library.php?do=view_item&itemid=204" …​

In the direction of constant acceleration:

$$v\ =\ u\ +\ at$$
$$v^2\ =\ u^2\ +\ 2as$$
$$s\ =\ ut\ +\ \frac{1}{2}at^2$$

Perpendicular to the direction of constant acceleration:

$$v\ =\ u$$
$$s\ =\ ut$$

For circular motion, with angular displacement $\theta$, angular velocity $\omega$, and angular acceleration $\alpha$:

$$\omega_f\ =\ \omega_i\ +\ \alpha t$$
$$\omega_f ^2\ =\ \omega_i^2\ +\ 2\alpha\theta$$
$$\theta\ =\ \omega_it\ +\ \frac{1}{2}\alpha t^2$$

Last edited by a moderator: Apr 26, 2017