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The Toy Story Theorem: Ep. 3


pegkowalski

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As I recall, in the official 1995 Pixar original film, Toy Story, after springing off the bouncy ball in his death-defying 'flight' Buzz Lightyear grabs a ceiling fan, and takes a lap, holding on.

We've established that - assuming my estimated heights are somewhat accurate - Buzz will enter this centripetal acceleration cycle at a velocity of about 2.426 m/s!

But what exactly IS his centripetal acceleration?

I think we'd be lying if we said we've never asked ourselves that question before.

Let's take a look:

F = [(m)(v^2)] / r

And:

F = ma

So, to find the acceleration we can set:

ma = [(m)(v^2)] / r

And mass cancels out, so with numbers plugged in - an average ceiling fan having about a 1.3m radius - we would see that:

a = (2.426)^2 / 1.3

a = 5.885 / 1.3

a = 4.527 m/(s^2)

I hope that answered most of your childhood questions.

I will have one more installment of this series as Buzz lets go of the fan, to free fall land back on Andy's bed, right where it all started!

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