Hacker News Reader

Comment by CiaranMcNulty | Hacker News Reader

I don't believe a pendulum's period is affected by its momentum at any point in its arc, just the length and its mass.

The "length of the pendulum" (for the purposes of calculating its period) is specifically the distance between the the pivot and the pendulum's centre of mass. Adding coins to the pendulum moves the centre of mass ever so slightly!

The pendulum's period isn't affected by its bob mass at all, in the simple models of a pendulum, only length from axle to center of mass of the bob.

I invite an armchair physics teacher to explain why this is different. Probably something to do with shifting the center of mass closer to the axle.

Yeah. They're actually putting them on a shelf a fair way up the pendulum itself, so I imagine that adding them shifts the center of mass noticeably. (Though we're talking single-digit parts per million corrections here, so they don't need to shift it by a huge amount.)

Just the length, rather. The mass has no effect on the period.

So how does adding a coin change the clock's speed? The extra mass can't be changing the period of its pendulum, right? This is the bit of the article I didn't understand.

The "length" that's important will be the distance to the centre of mass of the pendulum. By adding weights part-way along the pendulum, you move the centre of mass just like if you'd found a good way of adjusting the length.

For a frictionless pendulum in a vacuum this is certainly true.

The article repeatedly says they add weights to the pendulum though, which makes me wonder whether either (a) it's some connected mechanism they add weights to, or (b) this is somewhere reality diverges from the simple model.

https://youtu.be/5qEPDXDVxvw?t=169

They're added directly to the 'pendulum shelf' which looks like it's right at the top of the pendulum. That would adjust the length up (shorter) by a tiny amount by shifting the center of mass of the pendulum up. This squares with the simple model of a pendulum.

It's true the weight and shape of the bob will have an effect on the air friction applied to the system, but for a pendulum of this scale, the effect of adding a coin or two will be a negligible change in drag compared to the relatively significant change in the pendulum's center of mass.

The coins aren't being added at the centre of mass, so it kind of is changing the length?

Reply on news.ycombinator.com