Slightly confused regarding centripetal force, radius and frequency

[chris_0101]

Homework Statement

Hello everybody,

I have a question that is tied into my lab report regarding centripetal force. The question asks if the frequency of rotation were to increase how would the radius r and the centripetal force change?

Homework Equations

2$\pi$f = v/r

rearrange for r:

r = v/(2$\pi$f)

a = r(ω^2)

F_c = m*a

The Attempt at a Solution

By observing the formula rearranged for r, I believe that the radius is inversely proportional to frequency - so in this case as frequency increases, the radius will decreases.
Is this statement correct?

Since acceleration is dependent on radius and if the radius decreases so does the acceleration due to the direct proportionality between acceleration and radius. This ultimately means that the centripetal force is decreased as well when the frequency is increased
Is this statement also correct?

Your comments are greatly appreciated.

Thanks

 

[PeterO]

Homework Statement

Hello everybody,

I have a question that is tied into my lab report regarding centripetal force. The question asks if the frequency of rotation were to increase how would the radius r and the centripetal force change?

Homework Equations

2$\pi$f = v/r

rearrange for r:

r = v/(2$\pi$f)

a = r(ω^2)

F_c = m*a

The Attempt at a Solution

By observing the formula rearranged for r, I believe that the radius is inversely proportional to frequency - so in this case as frequency increases, the radius will decreases.
Is this statement correct?

Since acceleration is dependent on radius and if the radius decreases so does the acceleration due to the direct proportionality between acceleration and radius. This ultimately means that the centripetal force is decreased as well when the frequency is increased
Is this statement also correct?

Your comments are greatly appreciated.

Thanks

How is this circular motion being achieved? - what is going in a circle.

The question can be easily interpreted if it is a satellite around the Earth.

Is this the standard prac where you rotate a rubber stopper on a fishing line with a bunch of washers hanging from the fishing line?

 

[chris_0101]

I should have been more specific. Circular motion is achieved by an object spinning around an axis.

 

[PeterO]

I should have been more specific. Circular motion is achieved by an object spinning around an axis.

how is it attached to the axis? What is the object? What is it made of?

 

[asteriatic]

Hello,

Your understanding of the relationship between frequency, radius, and centripetal force is correct. As frequency increases, the radius decreases due to the inverse relationship between the two. This in turn leads to a decrease in centripetal force, as it is directly proportional to the acceleration, which is dependent on the radius. Your reasoning and use of the equations are also correct. Keep up the good work! If you have any further questions, don't hesitate to ask.