How Are Force And Motion Related?

Isaac Newton gave the best description of the links between force and motion in his three famous laws, and learning about them is a crucial part of learning physics. They tell you what happens when a force is applied to a mass, and also define the key concept of force. If you want to understand the relationship between force and motion, the first two of Newton's laws are the most important ones to consider, and they're easy to get to grips with. They explain that any change from moving to not moving or vice-versa requires an unbalanced force and that the amount of motion is proportional to the size of the force and inversely proportional to the mass of the object.

Newton's first law says that an object will either remain at rest (not in motion) or in motion at exactly the same speed and in exactly the same direction unless it is acted on by an "unbalanced" force. In simpler terms, it says that something only moves if something else pushes it, and that things only stop, change direction or start to move faster if something pushes it.

Understanding the meaning of "unbalanced force" clarifies this law. If two forces act on an object, one pushing it to the left and the other pushing it to the right, it will only move if one of the forces is bigger than the other. If they have exactly the same strength, the object will just stay where it is.

One way to imagine this is to think about a set of scales, with weights on either side of it. The weights are being pulled down by gravity, and the only thing that affects how much gravity pulls them is how much mass there is. If you have the same amount of mass on both sides, the scale stays still. The scale only moves if you literally make it unbalanced in terms of mass. The difference in masses means that the forces acting on both sides of the scale are unbalanced, and so the scale moves.

Imagining constant motion at the same speed is harder because you don't encounter this in day-to-day life. Think about what would happen if you had a toy car sitting on a perfectly smooth (frictionless) surface and there was no air in the room. The car would stay still unless it was pushed, as described above. But what happens after the push? There is no friction with the surface to slow it down and no air to slow it down. The surface balances the force of gravity (by something called the "normal reaction," related to Newton's third law), and there are no forces acting on it from the left or right. In this situation, the car would keep traveling at the same speed along the surface. If the surface was infinitely long, the car would keep moving at that speed forever.

Newton's second law defines the concept of force. It states that the force applied to an object is equal to its mass multiplied by the acceleration the force causes. In symbols, this is:

\(F=ma\)

The unit of force is the Newton – to acknowledge the person who defined it – which is a shorthand way of saying kilogram-meters per second squared (kg m/s²). If you have a 1 kg mass, and you want to accelerate it by 1 m/s every second, you need to apply a force of 1 N.

Writing Newton's law in the following way helps to clarify the link between force and motion:

\(a=\frac{F}{m}\)

Acceleration, on the left, tells us how much something is moving. The right-hand side shows that a bigger force leads to more motion if the mass of the object is the same. If a specific force is applied, this equation also shows that the amount of acceleration depends on the mass you're trying to move. A bigger, heavier object moves less than a smaller, lighter object subjected to the same-sized push. If you kick a soccer ball, it will move a lot more than if you kick a bowling ball with the same strength.