Imagine you have a grandfather clock on the moon. On earth the Pendulum swings in a regular motion to keep accurate time. What is the period of the swing on the earth and what is it on the moon?
Grandfather Clocks on the Moon
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Imagine you have a grandfather clock on the moon. On earth the Pendulum swings in a regular motion to keep accurate time. What is the period of the swing on the earth and what is it on the moon?
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In solving this problem we must make several major assumptions. First we assume that the pendulum is massless except for the bob, that it rotates through a frictionless point. Because the angle of rotation is so small we also assume simple harmonic motion.
The period of a pendulum is dependent on gravity on the earth and the length of the rod. The period of a mass undergoing simple harmonic motion is:
T = 2(Pi)((L/g)^1/2)
T = 2(3.14)((1/9.8)^1/2)
T = 2 seconds
On the moon the period is much different:
T = 2(3.14)((1/1.6)^1/2)
T = 4.97 seconds
On the moon the clock would not keep accurate time because the period is much longer for a simple pendulum in lower gravity.