# CIRCULAR AND RELATIVE MOTION

In uniform circular motion the object moves in a circle at constant speed. The SPEED at any point on the path is the same.

The centripetal acceleration (ac) can be found using our general concept for acceleration

ac = (change in velocity)/(change in time)

From the diagrams

ac = (v/R)(D s)/(D t)

ac = (v/R)(ds/dt)

ac = v2/R

If the magnitude of the velocity also changes in circular motion then we have two accelerations

1. The instantaneous centripetal acceleration is needed to change the direction of the velocity vector. This is always needed for circular motion even if the magnitude of the velocity is constant.
2. The tangential acceleration which is tangent to the circular path is needed to change the magnitude of the velocity vector which is also tangent to the circular path.
3. Since the acceleration vectors in 1 and 2 are perpendicular to each other (one is inward along a radius and the other is tangent to the circle) the resultant acceleration can be found using vector addition.

In Relative Motion we have to use vector addition so that we can correctly view motion in two different frames of reference.

V = u + V'

How are the vectors V, u, and V' defined?

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