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Parliamentary video of the pendulum of the great clock |
The Great Clock of Parliament (Big Ben) uses a pendulum to keep time. Fine adjustment of the pendulum is accomplished by adding old (pre-decimal) pennies to the pendulum. According to the website of Parliament, each 9.4 g penny used to adjust the clock is added to the pendulum in such a way that the clock mechanism speeds up enough to gain two fifths of one second in 24 hours of operation. Further, the website reports that the pendulum rod has a mass of 321 kg and a length of 4.48 m, and the bob attached to the rod has a mass of 203 kg.
Part A
Assuming that the rod is thin and uniform and that the bob can be treated as a point particle, what is the approximate period of Big Ben's pendulum?
System: Rod and bob together as a single rigid body.
Interactions: Both components of the system are subject to external influences from the earth (gravity). The rod is also subject to an external influence from the axle of the pendulum. We will consider torques about the axle of the pendulum. Because of this choice of axis, the external force exerted by the axle on the pendulum will produce no torque, and so it is not relevant to the problem.
Model: Single-Axis Rotation of a Rigid Body and Simple Harmonic Motion.
Approach:
Diagrammatic Representation