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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 ?

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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.

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  • $\begingroup$ 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 ? $\endgroup$ Nov 19, 2015 at 17:52
  • $\begingroup$ @IshitaGupta: angular and linear velocity are also related, by $v = r\omega$. $\endgroup$ Nov 19, 2015 at 17:55
  • $\begingroup$ yep they're related but they're still different vectors with different meanings so they aren't the same $\endgroup$ Nov 21, 2015 at 16:39
  • $\begingroup$ @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 $|v| = |r|\,|\omega|$. $\endgroup$ Nov 21, 2015 at 16:49
  • $\begingroup$ 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? $\endgroup$ Nov 26, 2015 at 6:37
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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.

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  • $\begingroup$ 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. $\endgroup$ Dec 1, 2015 at 12:41
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I think we include angular acceleration also We can observe two types of motion simultaneously in circular motion, namely linear and angular. Both motions occur simultaneously and are related or connected to each other by some relation. For example, F=ma. However, if I only mention F or state that I applied a force F to an object, then that object starts moving. Doesn't this imply the existence of acceleration as well? I mean, when we say there is 'a,' it also includes F through a relation like a=F/m (let's say). Or if we say a car is moving because of an applied force F, it also involves 'a' through a relation F=ma. Now, in non-uniform circular motion, a_net=√(ac²+at²), but we know at=rα (where α is angular acceleration). So, we also include angular acceleration because at and angular acceleration are connected by a relation, i.e., at=rα. Therefore, we can replace at with rα, i.e., a_net =√(ac²+(rα)²). Additionally, we can substitute v (in ac) with rω. So, it depends on the question's demand; whether it wants an answer in angular or linear motion. Both angular and linear motion in circular motion are connected by some relation. We actually include α but in terms of at=rα.

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