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    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
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    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 :wizard:
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    Joinedup mik1a perhaps one of yous can help.
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    (Original post by NatoHeadshot)
    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.
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    both formulae are valid. i personally prefer the one without omega
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    (Original post by NatoHeadshot)
    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.
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    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.
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    (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 :love:
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    (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 :love:
    you are getting confused with omega fish oils :spank:
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    (Original post by the bear)
    you are getting confused with omega fish oils :spank:
    But they're so
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    :daydreaming:
 
 
 
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