Pendulum

[chiddler]

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x = L*(theta); x = displacement from center along arc, L = length of pendulum.

I'd like to see proof for this equation please. Meaning why is x=L*theta?

Is theta in rad or degrees?

 

[MT Headed]

Theta is in radians, and it the displacement from vertical.

Proof: if the circle is radius R, how far do you travel if you go once around the circle? 2 pi R. Distance x = 2 pi R. 2 pi is also the number of radians it takes to go once around a circle. Well, what if you only went a quarter of the way around the circle? That's a quarter of 2 pi, or pi/2. You'd have traveled a quarter of the original distance too, or x = (pi/2) R. For travel around any circle, distance traveled is radius times radians. X = L * theta.

You can also derive v = omega * R, and acceleration = alpha * R the same way.

 

[chiddler]

Theta is in radians, and it the displacement from vertical.

Proof: if the circle is radius R, how far do you travel if you go once around the circle? 2 pi R. Distance x = 2 pi R. 2 pi is also the number of radians it takes to go once around a circle. Well, what if you only went a quarter of the way around the circle? That's a quarter of 2 pi, or pi/2. You'd have traveled a quarter of the original distance too, or x = (pi/2) R. For travel around any circle, distance traveled is radius times radians. X = L * theta.

You can also derive v = omega * R, and acceleration = alpha * R the same way.

thanks very much!