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# Confustion about circular motion Watch

1. the formula F=m x omega^2 r shows that with greater radius the centripetal force is more

but F=v^2 x M/r shows that its inversely proportional?

so which one is it and what am I missing
2. Sorry you've not had any responses about this. Are you sure you've posted in the right place? Here's a link to our subject forum which should help get you more responses if you post there.

Just quoting in Danny Dorito so she can move the thread if needed
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(Original post by Danny Dorito)
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3. Joinedup mik1a perhaps one of yous can help.
the formula F=m x omega^2 r shows that with greater radius the centripetal force is more

but F=v^2 x M/r shows that its inversely proportional?

so which one is it and what am I missing
They're the same. Omega is v/r. If you increase the radius, at the same speed, omega will decrease with radius, leading its square to decrease the acceleration overall.
5. both formulae are valid. i personally prefer the one without omega
the formula F=m x omega^2 r shows that with greater radius the centripetal force is more

but F=v^2 x M/r shows that its inversely proportional?

so which one is it and what am I missing
When you say that F = mrw^2 shows that a greater r means a greater F, I assume that you mean for a constant w.

But v = rw, so if you have a bigger r and a constant w, you also get a bigger v. When you look again at F = mv^2/r, the v is squared, so the bigger v has a much bigger effect than the bigger r, giving you a bigger F overall.

Let's look at a more specific case. If there is a force of F for a particular m, r and w, let's see what happens when we double r but keep w the same. The new force is m(2r)w^2 = 2mrw^2 = 2F, so the centripetal force has doubled.

As v = rw, doubling r will also double v, for a fixed w.

So, the new force is also m(2v)^2/2r = 4mv^2/2r = 2mv^2/r = 2F, so again, the centripetal force has doubled. You get the same answer both ways.

Replace 2r with kr, where k is any constant, and the same argument applies.
7. Both equations are still correct, but it does look confusing at first.

The key is that v = wr, so the v^2 term in the second equation is 'hiding' an r^2 term inside it (since v^2 = w^2*r^2). If you substitute v = wr into the second equation and then cancel, you'll get the first equation.
8. (Original post by the bear)
both formulae are valid. i personally prefer the one without omega
But calculating omega makes it easier for other parts of the question bear.
Just recall how many equations omega features in
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Plus omega is wonderful
9. (Original post by CheeseIsVeg)
But calculating omega makes it easier for other parts of the question bear.
Just recall how many equations omega features in
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Plus omega is wonderful
you are getting confused with omega fish oils
10. (Original post by the bear)
you are getting confused with omega fish oils
But they're so
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