# Why don't we include angular acceleration while calculating net acceleration for a particle moving in a circle ?

When we calculate net acceleration of a particle It is the vector sum of the centripetal acceleration and the tangential acceleration (if any) however why don't we also consider adding angular acceleration to this ?

The tangential acceleration $a_t$ and the angular acceleration $\dot{\omega}$ are basically the same thing. They are related by:

$$a_t = r\dot{\omega}$$

So we don't include both of them because that would be counting the same thing twice.

• But aren't they completely different vectors with different directions and meanings ? ( angluar acc. Is the rate of change of angular velocity and tangential is for linear velocity ) isn't that a bit like saying angular and linear velocity would be the same ? – Ishita Gupta Nov 19 '15 at 17:52
• @IshitaGupta: angular and linear velocity are also related, by $v = r\omega$. – John Rennie Nov 19 '15 at 17:55
• yep they're related but they're still different vectors with different meanings so they aren't the same – Ishita Gupta Nov 21 '15 at 16:39
• @IshitaGupta: $\vec{v} = \vec{r} \times \vec{\omega}$ where $\vec{v}$ is the tangential velocity and $\times$ is the vector cros product. Since the angle between $\vec{r}$ and $\vec{\omega}$ is always $\pi/2$ it's also true that $|v| = |r|\,|\omega|$. – John Rennie Nov 21 '15 at 16:49
• I understand that there is an equation which relates them but isn't that like saying that force and acceleration are the same due the Newton's 2nd law and F=MA? – Ishita Gupta Nov 26 '15 at 6:37

angular acc due to centripetal acc is zero. thats why no need to use net acc for finding angular acc. this can be find only by tangential acc.

• Hello, and welcome to Stack Exchange. It's hard to understand what you mean due to the abbreviations, over-conciseness, and lack of formatting. You may want to edit your question to fill it out and make it more comprehensible. – Daniel Griscom Dec 1 '15 at 12:41