== Circular Motion == 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 r → {\displaystyle {\vec {r}}} be the position vector of the object with the center of the path as the and r ^ {\displaystyle {\hat {r}}} 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) s = 2 π R {\displaystyle s=2\pi R} The speed (or linear velocity) is then given by v = s T = 2 π R T = 2 π f R … ( f = 1 T = frequency ) {\displaystyle v={\frac {s}{T}}={\frac {2\pi R}{T}}=2\pi fR\qquad \qquad \ldots \left(f={\frac {1}{T}}\,={\textrm {frequency}}\right)} 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 ω → = r → × v → | r → | 2 {\displaystyle {\vec {\omega }}={\frac {{\vec {r}}\times {\vec {v}}}{\left|{\vec {r}}\right|^{2}}}} Due to the vector product, the angular velocity vector is perpendicular to the plane of motion. With circle of radius R = 1 ω = 2 π f {\displaystyle \omega =2\pi f}