## Uniform Circular Motion and Relative Motion

• A body exhibits uniform circular motion (UCM) when it moves in a circle at a constant speed.
• The velocity of an object in UCM constantly changes, because its direction is always changing (even though its speed is constant).
• The usual equations of kinematics do not work on an object in UCM because its acceleration in each direction changes with time.
• An object in UCM must constantly accelerate towards the center of its circular motion. The magnitude of this centripetal acceleration is
v^2
a  =  -----
R

where v is the speed of the object, and R the radius of its track.
• Suppose two objects move relative to the ground (or some other reference frame). If their velocities relative to the ground are
v1(rel to ground),   v2(rel to ground)

then their velocity with respect to each other is simply the vector sum of their individual velocities:
relative v  =  v1(rel to ground) - v2(rel to ground)

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