Confustion about circular motion

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

Reply 1

TSR Jessica

Sorry you've not had any responses about this. :frown:

Are you sure you've posted in the right place? :smile:

Here's a link to our subject forum which should help get you more responses if you post there. :redface:

Just quoting in Danny Dorito so she can move the thread if needed :wizard:

Spoiler

Reply 2

username2548927

@Joinedup @mik1a perhaps one of yous can help.

Reply 3

RogerOxon

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.

Reply 4

the bear

both formulae are valid. i personally prefer the one without omega

Reply 5

Pangol

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.

Reply 6

mik1a

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.