# Relative circular motion

1. Feb 25, 2006

### Trooko

• Two cyclists( A, B) traveling with the same constant speed, v,
• in a circular track.
• They start at the same point on the circle.
• cyclist B travel through the diameter of the circle, assume the x-axis on a xy
• Cyclist A travel on the circumference of the circle

• Find speed of A with respect to B.

Given: the constant speed, radius, angle between A and the x-axis through the centre, angle between A and B.

am I suppose to do something with the acceleration (normal/centripedal) and the two angles given.

thank you

2. Feb 26, 2006

### Astronuc

Staff Emeritus
It has to do with the velocity of each, and the velocity of A with respect to B is dependent on the angles between the velocity vectors.

When A and B start, A is moving away from B, and only starts moving toward B after A passes the quarter arc.

At time t = v/D = v/2R, B moves outside A's circular trajectory.

$\vec_B$ is always v$\,\hat{x}$, whereas

$\vec_A$ is always v$$\,\hat{\theta}$$ where $$\hat{\theta}$$ is the unit vector in the azimuthal direction (tangent to circumference of circle). As xB gets very large, the angle between A and B gets very small.

The 'speed' would be the magnitude of the velocity vector given by $\vec_A$ - $\vec_B$

3. Feb 27, 2006

### Trooko

Thanks for the reply. It really does look a lot simpler now.

But when you wrote t= V/D, did you mean t = D/V?

4. Mar 1, 2006

### Astronuc

Staff Emeritus
Yes, t = D/V. My mistake.