Is the force for centripetal acceleration inversely proportional to the radius?

[avito009]

Since F=mv²/r. Does that mean the force required for centripetal acceleration is inversely proportional to the radius? If radius is more the lesser centripetal force is required, is this correct?

 

[Bystander]

F=mv²/r

What's "v²?"

 

[Suraj M]

radius is more the lesser centripetal force is required, is this correct?

That's if v is constant,
In most situations, $\omega$(angular velocity) is constant, so try expressing centripetal force in terms of $\omega$

 

[avito009]

Now there are 2 formulas for centripetal acceleration. 1. F= mv²/r. So in this formula we know that as radius increases the speed or velocity increases. So the term v²/r remains constant. So how can we prove from this formula that the Centripetal force is more if the radius is more.

But if we take the formula 2. F=mω²r. we can easily prove that as the radius increases the Centripetal force required increases. But this inference can't be derived from the first formula.

 

[Bystander]

v²/r remains constant

Think again. What is "v?"

 

[Suraj M]

F= mv2/r. So in this formula we know that as radius increases the speed or velocity increases

That would be if F is a constant.
Can you specify a situation!

 

[avito009]

Think again. What is "v?"

V is the velocity. But I didnt understand your point.

 

[Bystander]

What is "v" in terms of "r?"

 

[avito009]

What is "v" in terms of "r?"

V is velocity which is distance/time. So you mean to say that the distance or the radius in this case is more so the velocity is more at the edge. So the Centripetal Force is more. Is this what you meant to tell me?

 

[Bystander]

In your original question, you've ignored the fact that v equals omega times r and when looking at the dependence of centripetal acceleration on r.

mv2/r

inversely proportional to the radius?

 

[Pierce610]

Now there are 2 formulas for centripetal acceleration. 1. F= mv²/r. So in this formula we know that as radius increases the speed or velocity increases. So the term v²/r remains constant. So how can we prove from this formula that the Centripetal force is more if the radius is more.

But if we take the formula 2. F=mω²r. we can easily prove that as the radius increases the Centripetal force required increases. But this inference can't be derived from the first formula.

I'm tryng to interpret the law: in the first equation the force, that deviate the particle along the orbit, increases together with the speed if we fix the radius, and it decreases together with the radius if we fix the speed.
In the second equation the force increases togheter with the radius, because fixing the angolar speed and increasing the radius, the speed (not explicit here) must increase and then also the force.

 

[Pierce610]

I said badly "it decreases together with the radius" but I would say "the force decreases when the radius increases in the first equation" (if we fix the speed).

I hope that I can convince you there isn't a paradox about the force vs radius that sometime it increases, and sometime it decreases: it's enough that you fix one of the indipendent variabiles and then you'll se how the force changes when at the same time also the other variabile changes.

In other words, if we fix the angular speed, we know that the periferic speed increases when the radius increases and so the force. But if we fix the periferic speed, the angular speed decreases if the radius increases and then the force decreases.

I'm italian and I don't use to write in english but if I see anything that it's named physics it may be that I could try to speak japanese too.