15.11: Measuring Acceleration Due to Gravity
Consider a coffee mug hanging on a hook in a pantry. If the mug gets knocked, it oscillates back and forth like a pendulum until the oscillations die out.
A simple pendulum can be described as a point mass and a string. Meanwhile, a physical pendulum is any object whose oscillations are similar to a simple pendulum, but cannot be modeled as a point mass on a string because its mass is distributed over a larger area. The behavior of a physical pendulum can be modeled using the principles of rotational motion and the concept of the moment of inertia. For both a simple and a physical pendulum, the restoring force is the force of gravity. With a simple pendulum, gravity acts on the center of the pendulum bob, while in the case of a physical pendulum, the force of gravity acts on the center of mass (CM) of the object.
The period (T) of a simple pendulum depends on its length and acceleration due to gravity (g). The period is entirely independent of other factors, such as mass and maximum displacement. Given the dependence of T on g, if the length of a pendulum and the period of oscillation is precisely known, they can be used to measure the acceleration due to gravity. This method for determining gravity can be very accurate.
A physical pendulum can also be used to measure the free-fall acceleration due to gravity at a particular location on Earth's surface, thousands of measurements of which have been made during geophysical prospecting.
