The Big Think

November 28, 2005

Math Geekitude

Filed under: Science — jasony @ 11:48 am

Okay, Sean, here’s the answer to your question.

Assuming the merry-go-round in question is 8′ in diameter, a 175lb adult at the edge of the merry-go-round will feel a 1g lateral acceleration when the merry-go-round gets up to 10.93mph. The measuring of centripetal force is governed by the following formula:

CentripCalc.gif

where:
m is the mass of the object (in this case a 176lb adult)
r is the radius of the merry-go-round (I’ve used 8′), and
t is the speed of the merry-go-round expressed as rotations (back-converted into MPH)

So get that sucker up to almost 11mph and you’ll feel a lateral force of gravity equal to 1g. Of course, this formula doesn’t take into account the natural 1G that you feel from the earth. This is going to deflect the perceived lateral acceleration to a 45 degree angle. To get a pure 1G lateral acceleration in the presence of the natural 1G of the earth’s field you’re going to….. have to ask somebody else. That math is beyond me.

2 Comments »

  1. Hehe. Excellent. I had gone down this road a bit, but I found contradictory formulas, and my math wasn’t working out. Thanks for delving in!

    To get a pure 1G lateral acceleration in the presence of the normal 1G, you’d need infinite speed, I’m afraid — the combined vector will approach horizontal asymptotically, but since there’s always that downward element (however infinitesimal it may get by comparison to the outward force), it will never become purely horizontal.

    Whee! Our playground romp has now infected 3 websites. 🙂

    Comment by Sean — November 28, 2005 @ 1:27 pm

  2. Well yeah, obviously you’d need infinite speed. It really brings it home how a formula that exists in textbooks doesn’t really apply when you try and describe the real world. I wonder at what point somebody would just say “that’s close enough” and ignore the fact that, at 3000mph, the vertical deflection caused by the earth’s gravity is too small to matter. Makes my head hurt when I think how hard it must be to put a rocket into orbit.

    Comment by JasonY — November 28, 2005 @ 3:08 pm

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