When the mass and the radius are held constant what happens to the centripetal force if the frequency of the rotation is increased?

Answer 1

One formula to calculate centripetal acceleration is:

a = omega2r, where omega is the angular velocity.

Combining this with Newton's Second Law:

F=ma

you get:

F = m omega2 r

For completeness sake, omega (in radians per second) = 2 pi f (2 x pi x the frequency,

in revolutions / second). Thus, omega and the frequency are proportional.

As you can see, the force is proportional to the square of the angular velocity.

For example, doubling the frequency would cause double the angular velocity,

which would require an increase of the force by a factor of 4.

Answer 2

If the mass and radius are held constant while the frequency of rotation is increased, the centripetal force will also increase. This is because an increase in frequency results in a higher velocity for the rotating object, which requires a greater centripetal force to maintain its circular motion according to the formula Fc = m*v^2/r.