# Acceleration in circular motion

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1. Oct 30, 2016

### ashraful

1. The problem statement, all variables and given/known data
In the case of circular motion,the direction of the velocity is changing in every moment.So,there is a angular accelleration here.What is the direction of this accelleration?

2. Relevant equations

3. The attempt at a solution

2. Oct 31, 2016

### cnh1995

That is not angular acceleration. It's called 'centripetal' acceleration. Angular acceleration is present when angular velocity is changing w.r.t. time, which is zero in case of uniform circular motion.

3. Oct 31, 2016

### Buffu

There are three accelerations.
Centripetal acceleration ($a_c$) - towards center.
Linear acceleration($a$) - tangential to radius vector at an instant.
Angular acceleration($\alpha$) - The direction is given by right-hand thumb rule. If motion is clockwise then direction is $-\hat{k}$ else $\hat{k}$.
Note : here i assumed the motion to be horizontal in x-y plane, Direction of angular acceleration will vary if that is not the case.

The direction of angular acceleration does not change at every instant, that of course if particle does not switch between clockwise rotation and anti-clockwise rotation.

Last edited: Oct 31, 2016
4. Oct 31, 2016

### haruspex

The question only predicates acceleration implied by the circular motion. There may be other acceleration components, but not necessarily.
At any instant, a particle has one acceleration vector. You may choose to resolve it into a component in the direction of the velocity and a component normal to it. If there is a normal component then there is, instantaneously, a centre of arc. So these two components can be described as tangential and radial components respectively.
I suppose you could think of the tangential acceleration divided by the radius as an angular acceleration, but it doesn't gain anything. It is not a separate acceleration.
Angular acceleration is a more useful concept in the case of something larger, where the mass centre may be accelerating in whatever way, but the body is also rotating at a changing rate.

5. Oct 31, 2016

### Buffu

$$\alpha = {d\omega \over dt}$$
So angular acceleration is there in circular motion.

For the rest you are correct. But as OP asked the direction of $\alpha$, I pointed it out.

6. Oct 31, 2016

### haruspex

Note the word "implied". I.e., that acceleration which is necessarily present, given that motion is circular. Angular acceleration may be present, but it is not implied.
Yes, that was fine.