Atwood's machine was developed to observe acceleration.

Before unleashing the second law, let's make two useful observations. First, it is intuitively clear that a greater force produces a greater acceleration. For example, two pro wrestlers pushing on a stalled car will get it going sooner than just one could. Second, inertia or mass is somehow involved. Those two wrestlers would need to use more force to push a schoolbus than to push a Volkswagen bug.

In fact, Newton realized that for a given force F, the greater the mass of the object, the smaller its acceleration. Thus, Newton's second law can be expressed concisely as follows:

Newton's second lawFnet = ma or F = ma

This simple equation shows that the unit of force must be the units of mass times the units of acceleration. In SI units, it is written as kg*m/s². This combination of units is appropriately called the NEWTON (N).

Sir Isaac Newton is honored on the British pound note.

Most people are more familiar with the pound as the unit of force. In physics, however, as well as in other scientific fields such as engineering, the newton is standard. To get a feel for this unit, consider that a medium-sized apple like the one that legend says fell on Newton's head weighs about 1 newton, or .22 pounds.

In physics, the same units often appear in different relation to each other, depending on what is being "solved for" (that is, what question must be answered). For example, the second law can be written like this:

a   =  F m

Let's look at a few examples of the second law in action.

Newton's second law governs the braking distance of a vehicle.

Example 1

Suppose a rocket in space is accelerating at 4 m/s². If, at a later time, the rocket loses half its mass in fuel but triples its thrust (i.e., net propelling force), what is the new acceleration?

Consider this car (still leaking that oil) moving to the right. Is a force acting on the car? If so, what is the direction of this force relative to the velocity of the car?

Is there an unbalanced force acting?

An applied pulling force of 100 N is used to accelerate an object to the right along a rough surface that offers 40 N of frictional resistance. If the normal force is 60 N, what is the acceleration of the object?