# Decomposition of Rotation into Forward Motion and Turn Motion

1. Apr 16, 2015

### WWGD

Hi, just curious:
I was able to simulate rotation motion in Alice software , as a combination of two motions:
1)Moving forward
2)Turning left

(I can choose the rate at which each of these happens , in terms of meters and revolutions respectively.)

Done simultaneously, at just the right rate of each. I guess this shows that circular motion can be described by a combination of moving left and moving forward, where the rates of the two motions are in the right range each.
But I am trying to make this more precise :Is there an actual formula for circular motion/velocity
relating the two types of motions? I mean, if I were to move forward at, say, 2meters/sec, how fast should
I be moving left for the resulting motion to describe a rotation? I am too rusty on the formulas of angular velocity/acceleration, etc. but I don't have a clue otherwise.
Any ideas?
Thanks.

Last edited: Apr 16, 2015
2. Apr 16, 2015

### FactChecker

Unfortunately, that is the wrong relationship between the forward motion and the left motion. Suppose Vf is the forward velocity and Vl is the left velocity. Then the derivative of Vl is proportional to Vf. This is the derivative in an instantaneously fixed coordinate system. A circle would start out tangential to the velocity vector and start to accelerate to the left. If you are calculating motion with a fixed time step, then there is a fixed ratio between Vf and Vl that depends on the radius of the circle. You would need to proceed in time steps that are sufficiently small that the path of steps is close enough to a circle for your purposes.

3. Apr 16, 2015

### WWGD

Thanks, FactChecker.