Clock Gears
- by admin
Does the weight of the pendulum on a clock affect performance?
I want to buy a clock kit, but use a small bike gear for the pendulum (it’s going to be a bike-themed clock for my bike crazy husband). I expect that the gear will be heavier than the piece that comes with the clock, so I’m wondering if that will cause the clock to be inaccurate or the little motor to fail.
Changing the mass of the pendulum weight will have two effects.
First, assuming that the motor works harder to pump the larger mass (that is, the pendulum’s amplitude of oscillation remains as large as it was designed to be), the higher momentum of the pendulum will mean that friction in the pivot will probably have a smaller effect on the motion, so the clock may run marginally faster, but probably not enough to be noticed.
The second effect is that the pendulum is not an idealized mass at the end of a massless rod, the rod itself has mass, and by making the weight on the mass larger you are moving the centre of mass downward, effectively lengthening the pendulum. This will cause the clock to run more slowly unless you adjust the weight accordingly by moving it higher up the pendulum rod.
Really, you’re asking if the motor will fail, and if the clock will keep time. Whether or not the motor fails is a function of the design of the clock. It is possible that the motor is not sufficiently powerful to pump a heavier pendulum. If that’s the case, the pendulum will run down and the clock will stop. I don’t think this is very likely, but it is possible.
As for keeping proper time, you will have to adjust the weight by moving it up the rod, but all pendulum clocks are designed to allow such an adjustment, and it is a simple matter to adjust the pendulum. First, run the clock for exactly one day with the pendulum in a certain marked position. Measure the number of seconds which the clock loses or gains in that one day. Repeat the experiment with the pendulum in a second marked position. To a very good approximation, the speed of the clock is a linear function of the height of that weight along the pendulum, so you can easily interpolate/extrapolate the position of the weight which will run the clock with very good accuracy. Note that if the gear is 10 times as heavy as the weight supplied by the manufacturer, that does *not* mean that you will have to move the weight up to 1/10 of the former length, you are only adjusting for the shift in the centre of mass of the weight+rod system, and as the weight becomes very large the rod becomes unimportant. If the rod were truly massless, then changing the weight would have no effect on the period of the clock, and you would not have to move the weight at all.
Simplicity Wooden Gear Clock by Clayton Boyer
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