04-01-2013, 03:43 PM
Compound Pendulum
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INTRODUCTION
In this experiment measurements should be made of the oscillation period at small amplitudes
using a compound (that is a real) pendulum. The results should then be compared to the predictions
made by the theory of the dynamics of rigid bodies. In a practical application, the gravitational
acceleration will be determined using 2 methods in the beginner’s physics lab class: a) if
one knows the moment of inertia of a pendulum and b) if it is unknown.
Experiment
Carefully pay attention on the following points of the experiment:
• Observe the white mark on the pendulum with the telescope. It is sufficient to observe
the first and last oscillation of a measurement (of 50 to 100 oscillations) with the telescope.
In between the counting one rather lets the eyes relax.
• Only allow for small amplitudes of the oscillation, meaning thewhitemark at the bottom
of the pendulum rod must not leave the field of vision of the telescope.
• Required data: Physical properties of the pendulum rod
The aerostatic Reduction
Already Newton mentioned this correction and hence it is known as the Newtonian reduction.
It is based on the buoyant force created by the mass m′ of air which is displaced by the
pendulum. This force directed vertically upwards does not work on the centre of gravity but
seems to act on the geometric centre of the pendulum which is at distance s′ from the axis of
rotation of the pendulum.
The aerodynamic Reduction
It was first proposed by Bessel and used in his investigations. It accounts for a layer of air
adhering to the pendulumduring oscillations. Apparently this additional co-moving mass m′′
will increase the pendulum’s momentum of inertia roughly by cm′′ where c is an unknown
factor that has to be determined empirically.
Length reduction of the pendulum due to the blades
The blades used as axis of rotation for the pendulumare in reality not a mathematical line but
are rather cylindrical having a very small radius. Therefore the actual axis of rotation is not
the sharp edge but a certain distance below that.