# Circular Motion angle b/w acc and velocity etc.

1. Aug 11, 2014

### Sagar98

How do you find the angle b/w tangential acceleration and total acceleration vector, Or angle between velocity vector and Acceleration vector. I'm really confused about this and no one's helping.

2. Aug 11, 2014

### Lok

Hi sagar98,

So you have a circular motion of an object. I assume constant velocity. For this to happen the centripetal force (http://en.wikipedia.org/wiki/Centripetal) needs to act from the body towards the center of the rotation curve to keep the rotation going in a circle. Example a rock spinning around a pole held by a string from the pole to the rock. Here the force is the tension in the string and is orthogonal to the velocity vector, pointing towards the pole.

The centrifugal force is a fictitious force (as it is basically inertia) and completely opposes the centrifugal. It is felt by the rock. The two forces cancel each other and the rock has no acceleration and keeps a constant velocity in it's circular motion.

The angles are always 90 deg' from the velocity vector. Centripetal towards the pole, centrifugal opposite.

Have fun!

3. Aug 11, 2014

### Sagar98

Thanks and What if it's undergoing uniform tangential acceleration? Then how does the angle vary?

4. Aug 11, 2014

### sophiecentaur

I think what you are after is the resultant between the Constant Tangential Acceleration (at) and the centripetal acceleration v2/r. At time t (from rest, perhaps?), you can calculate the value of v so you will then have both acceleration vectors and can show their vector sum in Mag and Direction relative to radius (or whatever).

5. Aug 12, 2014

### Lok

In order to simplify the whole setup you could change your fixed frame of reference to the object to be accelerated with the Y axis pointing to the center of rotation. While the rest of the world spins accelerated around the center of rotation. This will eliminate the varying angle of position from your calculation.

Thus you will get your acceleration on the X axis and the centripetal on the Y. You just need to express the centripetal variance according to Time and the tangential acceleration. And the rest is simple trigonometry.