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Harvard University has an interesting article on a rod whose end that falls faster than gravity around a pivot.

http://sciencedemonstrations.fas.harvard.edu/presentations/falling-faster-g

How did they derive this formula?

Where R is length of rod/2, or the centre of mass.

Why did they use cos instead of sin?

Also, in this formula

Why did they use Lcos instead of L/2 cos?

http://sciencedemonstrations.fas.harvard.edu/presentations/falling-faster-g

How did they derive this formula?

Why did they use cos instead of sin?

Also, in this formula

Why did they use Lcos instead of L/2 cos?