Physics Course/Motion/Periodic Motion/Circular Motion

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Circular Motion[edit | edit source]

θ = angular displacement
r = radius/position vector
P = position of the object along the path
v = linear velocity
Ω = angular velocity along axis of rotation
a = centripetal acceleration

Circular Motion is a motion of an object along a circular path. If the speed of the body remains constant throughout the motion, the object is said to perform a uniform circular motion. For an object in uniform circular motion along a circular path of radius R and be the position vector of the object with the center of the path as the and being the unit vector along it and T be the time taken to traverse the path once (period), the total linear distance covered in one period is (the circumference of the circle)

The speed (or linear velocity) is then given by

The linear velocity is a vector quantity whose direction at any given instance is tangential to the circle at that point. The angular velocity around the circle is

Due to the vector product, the angular velocity vector is perpendicular to the plane of motion.

With circle of radius R = 1