3 forces acting on a conical pendulum
- Gravity(=mg): The force the Earth pulls.
- Tension: The force applied to both ends of the thread. Tension is always directed to the center from both ends.
- Centripetal force(Fc): The force that maintains circular motion. The centripetal force always toward the center of rotation.
ω: Angular velocity of rotational motion (rad/s)
T: period of rotational motion (seconds)
Find the period of a conical pendulum
Consider a conical pendulum with a line length ‘L’ and a rotation radius ‘r.’
Centripetal force(Fc) is the result of gravity and tension. Also, the centripetal force is perpendicular to gravity. From this, the following equation is calculated.
Substituting the definition of centripetal force comes the following equation.
Since it is , we can make it a bit simpler.
Solving the above equation for the period T, It becomes as follows.