Inertia: The "Laziness" of an Object
Inertia is often described as the laziness of an object. This may seem odd, as if it is some kind of personification gone awry. What is meant by this statement is that inertia describes an object's resistance to a change in its motion. This is related to Newton's first law of motion, which states that an object will continue to move at a constant velocity (including at rest - a velocity of 0) unless an external force is applied to an object.
Connections to Newton's First Law
Newton's first law is often colloquially known by the phrase "An object at rest tends to stay at rest and an object in motion tends to stay in motion unless acted upon by an outside force." In fact the first law is often known as the law of inertia. Essentially, this means that if the net force on an object is zero, its state of motion will remain unchanged. Since forces are needed to cause acceleration - a change in an object's state of motion - and the second law dictates that force and mass are directly related for a constant acceleration, it follows that a more sizable force will be needed to change the state of motion of a more massive object.
In Ancient Greece, Aristotle often described motion in terms of an object's desire to return to its "natural place." The idea of inertia is a significant improvement upon this idea. Aristotle would say that when a rock is thrown into the air, it returns to the ground because that is the rock's "natural place." However, utilizing the idea of inertia, the rock should continue upward indefinitely, unless its motion is impeded by some force. Typically this force is the result of either the action of gravity or friction, which in the case of free fall is noted as air resistance. In the absence of thse obstacles, an object's motion will remain unchanged forever.
The Inertial Balance
Mass, and therefore inertia, is an inherent property of all matter. An intertial balance cam be used to determine the mass of an object by taking advantage of the property of inertia. A mass can be placed in the pan of the balance and set into motion by pulling the pan to the side and releasing it. This sets the pan into a vibrating motion. The greater the mass in the pan, the longer the period of vibration. This is due to the mass's resistance to change its motion at the leftmost and rightmost points of the swing.
While the period of vibration does increase as the mass of the object increases, the two are not directly related. In fact, a graph of period vs. mass looks like a graph of y vs. √x. There is a direct relationship between period squared and mass. In fact the relationship can be summed up by the formula shown below (note that T is the variable used to represent period of vibration):
Compare the shape of the graph of period vs. mass (non-linear) to period squared vs mass (linear):