Tension in Conical Pendulum

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

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 (mw²r). As both components are always perpendicular, T² = m²g² + m²r²w⁴. So that means, if you draw T² with respect to w⁴, you would ideally have a line (y = a + bx). Knowing the universal constant g, you can compute the mass of the bob from y ıntercept (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)