Simple Centripetal Force Question

[chrisdapos]

Hello, I know that there are two possible formulas to solve for radius. You can use (mv^2)/r ,or, (m4pir^2)/T^2. Now, the question is asking when the radius is trippled, the centripetal force is...?

Using the first equation, I come out with 1/3. Using the second equation, I come out with 9.

That confuses me enough, but when I looked back on a quiz we had (sometimes I get solutions from quizs), I found that my teacher asked when radius is tripled, centripetal acceleration is...? The answer was 3. Can anyone provide some insight into what I am doing wrong and what equation i should use to get my answer. Thank you in advance!

 

[Doc Al]

Hello, I know that there are two possible formulas to solve for radius. You can use (mv^2)/r ,or, (m4pir^2)/T^2. Now, the question is asking when the radius is trippled, the centripetal force is...?

First off, there's another useful formula for centripetal force, which I show below. Realize that they are all equivalent; the only thing that changes are is variable of choice: linear speed, angular speed, period.

There's really not enough information given to give a sensible answer. It depends on what is being held constant. Can you give the exact question including any relevant context?

For example: If the problem stated something like "A car races on a circular track. If the speed stays the same, what happens to the centripetal force if the radius triples?" In that case, the relevant formula is the one containing v & r ($F_c = m v^2 /r$) and the answer is 1/3.

But what if it said "If the angular speed stays the same, what happens to the centripetal force if the radius triples?" In that case, the relevant formula is the one containing $\omega$ & r ($F_c = m \omega^2 r$) and the answer is that the force triples.

 

[chrisdapos]

The question reads exactly, if the radius were tripled, what would happen to the centripetal force? The preceeding question is describe the relationship between Centripetal Force and: v, v^2, T and M. I don't think the preceeding question holds any context though. Thank you for your help!

 

[andrewchang]

First off, there's another useful formula for centripetal acceleration, which I show below. Realize that they are all equivalent; the only thing that changes are is variable of choice: linear speed, angular speed, period.

There's really not enough information given to give a sensible answer. It depends on what is being held constant. Can you give the exact question including any relevant context?

For example: If the problem stated something like "A car races on a circular track. If the speed stays the same, what happens to the centripetal force if the radius triples?" In that case, the relevant formula is the one containing v & r ($a_c = m v^2 /r$) and the answer is 1/3.

But what if it said "If the angular speed stays the same, what happens to the centripetal force if the radius triples?" In that case, the relevant formula is the one containing $\omega$ & r ($a_c = m \omega^2 r$) and the answer is that the force triples.

isn't $a_c = \frac{v^2}{r}$ and $F = \frac{mv^2}{r}$?

 

[Doc Al]

isn't $a_c = \frac{v^2}{r}$ and $F = \frac{mv^2}{r}$?

Of course. Oops! I'll fix my post. (Thanks.)