what is the relationship between cetripetal force and the frequency of revolution of a body (fixed radius)?

Answer 1

If the radius is R and the period of 1 revolution is T, the centripital acceleration is given by
a = 4π²R/T and the centripital force F actimg on a mass m is
F = ma

HTH ☺

Doug

Answer 2

I'm sorry, but 'doug_donaghue' is WRONG. His expression for the centripetal acceleration is DIMENSIONALLY INCORRECT.

Any acceleration must have dimensions [L/T^2]; his expression, a = 4π²R/T, lacks one necessary power of ' T.'

The CORRECT expression for centripetal acceleration in terms of ' R ' and ' T ' is:

a = 4π²R/T^2 .

The "angular frequency" w = (2 π / T), so that this can also be written as:

a = w^2 R.

The centripetal force which creates the necessary centripetal acceleration for circular motion by an object of mass m is then given by

F = ma = m [4π²R/T^2] = m w^2 R,

where ' F ' is directed towards the centre of the circle, of course.

For a fixed value of the radius, it's simply proportional to w^2, or the square of the angular frequency.

Live long and prosper.

Answer 3

Proportional to the square of the frequency.