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Physics Lesson 6.5.2 - Change in Momentum and its Importance in Understanding Objects' Motion
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Welcome to our Physics lesson on Change in Momentum and its Importance in Understanding Objects' Motion, this is the second lesson of our suite of physics lessons covering the topic of Linear Momentum, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Change in Momentum and its Importance in Understanding Objects' Motion
Like in Kinematics or Dynamics - in which more than in objects actual velocity we are interested in the change in velocity as this gives a better idea on the resultant force and therefore in the acceleration of the object itself - here we are more interested in the change in momentum than in the actual momentum itself. This point is explained by considering again the example provided in the Introduction paragraph.
If we take the original direction of the ball as positive, we have the following figure.
The initial momentum of the ball before the collision is
= 0.2 kg × 4 m/s
= 0.8 kg × m/s
and the final momentum is
= 0.2 kg × (-3) m/s
= -0.6 kg × m/s
If we calculate the change in momentum, i.e. p⃗1 - p⃗2 (or ∆p⃗), we obtain
= 0.8 kg × m/s - (-0.6 kg × m/s)
= 1.4 kg × m/s
On the other hand, when the ball hits the paper sheet, both velocities are positive as they are in the same direction. Therefore, we have the following figure
The initial momentum of the ball before the collision was
= 0.2 kg × 4 m/s
= 0.8 kg × m/s
and the final momentum after the collision is
= 0.2 kg × 3 m/s
= 0.6 kg × m/s
If we calculate the change in momentum, i.e. p⃗1 - p⃗2 (or ∆p⃗), we obtain
= 0.8 kg × m/s - 0.6 kg × m/s
= 0.2 kg × m/s
The interpretation of the above results is as follows:
"When the ball hits a hard surface such as the 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 ball."
Remarks!
- 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.
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