What's the relationship between mass and inertia?

Mass is directly proportional to inertia, meaning the greater the mass of an object, the greater its inertia.

Inertia is a fundamental concept in physics, referring to the tendency of an object to resist changes in its state of motion. This resistance is directly related to the mass of the object. The more mass an object has, the more it resists changes in its motion, hence the greater its inertia. This is why it's harder to push a heavy car than a light bicycle.

The relationship between mass and inertia is governed by Newton's first law of motion, also known as the law of inertia. This law states that an object at rest tends to stay at rest, and an object in motion tends to stay in motion, unless acted upon by an external force. The 'tendency' here is the object's inertia, and it's directly proportional to its mass.

For example, consider a football and a bowling ball at rest. If you apply the same force to both, the football will move much more easily than the bowling ball. This is because the bowling ball has more mass, and therefore more inertia, so it resists the change in motion more than the football.

In summary, mass and inertia are intrinsically linked. The mass of an object determines its inertia, or its resistance to changes in motion. This relationship is a fundamental principle in physics and is key to understanding how objects move and interact.