# Tension in Conical Pendulum

*Most recent answer: 08/22/2015*

Q:

In a conical pendulum, the bob is rotated with different angular velocities (horizontally) and tension in the string is calculated for different values of omega. What is the correct graph between T & omega?

- Sameem Ali (age 18+)

Kolkata, West Bengal, India

- Sameem Ali (age 18+)

Kolkata, West Bengal, India

A:

I think the given data are not sufficient to find a one to one relation (mass, rope length and radius needed), but maybe we can follow the experimental approach. Tension (T) will be balancing two forces: the gravity of the bob (mg) downwards and centrifugal force radially outwards (mw^{2}r). As both components are always perpendicular, T^{2} = m^{2}g^{2} + m^{2}r^{2}w^{4}. So that means, if you draw T^{2} with respect to w^{4}, you would ideally have a line (y = a + bx). Knowing the universal constant g, you can compute the mass of the bob from y Ä±ntercept (a). From the slope (b) you can now also find the radius of the circle traced by the bob.

Tunc

*(published on 08/22/2015)*