Physics Course/Motion/Periodic Motion/Circular Motion

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 $$\vec{r}$$ be the position vector of the object with the center of the path as the and $$\hat{r}$$ 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)
 * $$s = 2 \pi R$$

The speed (or linear velocity) is then given by
 * $$v = \frac{s}{T} = \frac{2 \pi R}{T} = 2 \pi fR\qquad\qquad\ldots\left(f=\frac{1}{T}\,=\textrm{frequency}\right)$$

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
 * $$\vec{\omega} = \frac{\vec{r}\times\vec{v}}{\left|\vec{r}\right|^2}$$

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

With circle of radius R = 1
 * $$\omega = 2 \pi f $$