How would you compute vertical circular motion?

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For example, what is the ratio of the tension in a string used to rotate a 5 kg mass at a length of 3m with an constant angular speed of 40m/s at the top and bottom positions of the rotations?

Vivekanand Vellanki

Lets first draw a figure:

The forces acting on the string are the weight of the mass attached to the string and the centrifugal force.

At point A, both are in the same direction; while at B they are in opposite directions.

The ratio would be \frac{\left(W-F\right)}{\left(W+F\right)}

where W=mg and


Substituting in the formula should give you the ratio.