Physics Tutorial 6.5 - Linear Momentum Revision Notes

In these revision notes for Linear Momentum, we cover the following key points:

• The definition of linear momentum
• How to find linear momentum of a moving object
• What does linear momentum represent?
• Where does the linear momentum differ from the moment of force?

Linear Momentum Revision Notes

We cannot use the energetic approach to analyse the motion of objects as kinetic energy is obtained by raising the velocity at power two and we may get lost the traces of objects direction because kinetic energy is always positive, regardless the moving direction. Therefore, it would not make any difference whether an object hits a hard wall or a thin sheet as long as the magnitudes of velocities are the same.

To avoid such problems, a new concept known as "linear momentum" or simply "momentum" is introduced. By definition,

Linear Momentum (p⃗) is the product of an object's mass (m) and its velocity (v⃗).

Mathematically, we have

Since mass is measured in kg and velocity in m/s, the unit of momentum is [kg × m/s]. Momentum is a vector quantity. In the past, momentum has been known as the "amount of motion."

Usually, we are more interested in the change in momentum than in the actual momentum itself. We write for the change in momentum

where m is the mass of the object, v⃗₁ and v⃗₂ are its initial and final velocities respectively.

When the a moving object hits a hard surface such as a wall, its motion changes drastically. Not only does the magnitude of velocity change, but also its direction as well. Therefore, a greater change in momentum (or change in the amount of motion) is produced compared to the case when it hits a thin sheet. This is because the wall offers a higher resistance than the sheet and as a result, it affects much more the motion of the object itself.

Do not confuse the terms "moment" and "momentum". They express two very different concepts. While the first refers to the turning effect of a force, the later expresses the amount of motion of an object.

If we want to calculate the change in momentum of an object or system, we must take as initial velocity the velocity of the object just before hitting the obstacle, not the very initial velocity the object may have had at the beginning of process. Likewise, the final velocity is taken just immediately after the object leaves the obstacle, not the final velocity of object's motion.

It is called "Linear Momentum" because there also exists a rotational momentum, which we will discuss later, in the Rotational Dynamics section. In linear momentum, we take the object as moving linearly or according such a path that is a combination of multiple linear segments.