The relation between radius and angular velocity according to the equation, .
Therefore, from the above equation it is clear that Radius() is inversely proportional to angular velocity(), which represents the path of circular motion. So, to acquire greater angular velocity, the radius must be reduced.
The formula for the period T of a pendulum is , where is the length of the pendulum and is the acceleration due to gravity.
Therefore,
The frequency or swing rate of a pendulum is determined by its length.
The slower the pendulum swings, the longer its length.
The faster the swing rate, the shorter the pendulum.
Using this approach, we can make the pendulum swing faster by shortening the length of the wire, metal rod, or string.