You may think of inertia as a mysterious force keeping you from doing something you have to do, like your homework, but that isn't what physicists mean by the word. In physics, inertia is the tendency of an object to remain at rest or in a state of uniform motion. This tendency is dependent on mass, but it isn't exactly the same thing. You can measure an object's inertia by applying a force to change its motion. Inertia is the tendency of the object to resist the applied force.

## The Concept of Inertia Comes From Newton's First Law

Because they seem so commonsense today, it's hard to appreciate how revolutionary Newton's three Laws of Motion were to the scientific community of the time. Before Newton and Galileo, scientists had held a 2,000-year-old belief that objects had a natural tendency to come to rest if left alone. Galileo addressed this belief with an experiment involving inclined planes that faced each other. He concluded that a ball cycling up and down these planes would continue to rise to the same height forever if friction were not a factor. Newton used this result to formulate his First Law, which states:

Every object continues in its state of rest or motion in a straight line unless acted upon by an external force.

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Physicists consider this statement the formal definition of inertia.

## Inertia Varies With Mass

According to Newton's Second Law, the force (F) required to change the state of motion of an object is the product of the object's mass (m) and the acceleration produced by the force (a):

F = ma

To understand how mass is related to inertia, consider a constant force F_{c} acting on two different bodies. The first body has mass m_{1} and the second body has mass m_{2}.

When acting on m_{1}, F_{c} produces an acceleration a_{1}:

(F_{c} = m_{1}a_{1})

When acting on m_{2}, it produces an acceleration a_{2}:

(F_{c} = m_{2}a_{2})

Since F_{c} is constant and doesn't change, the following is true:

m_{1}a_{1} = m_{2}a_{2}

and

m_{1}/m_{2} = a_{2}/a_{1}

If m_{1} is bigger than m_{2}, then you know a_{2} will be bigger than a_{1} to make both equal F_{c}, and vice versa.

In other words, the mass of the object is a measure of its tendency to resist the force and continue in the same state of motion. Although mass and inertia don't mean exactly the same thing, inertia is usually measured in units of mass. In the SI system, its units are grams and kilograms, and in the British system, the units are slugs. Scientists usually don't discuss inertia in motion problems. They usually discuss mass.

## Moment of Inertia

A rotating body also has a tendency to resist forces, but because it's composed of a collection of particles that are at various distances from the center of rotation, scientists talk about its moment of inertia rather than its inertia. The inertia of a body in linear motion can be equated to its mass, but calculating the moment of inertia of a rotating body is more complicated because it depends on the shape of the body. The generalized expression for the moment of inertia (I) or a rotating body of mass m and radius r is

I = kmr^{2}

where k is a constant that depends on the shape of the body. The units of moment of inertia are (mass) • (axis-to-rotation-mass distance)^{2}.