Force Balance and Inertia Principle

Introduction

1. Define a Study Framework

a. The System

It is simply the object being studied.

b. The Reference Frame

It is an object relative to which the motion is studied.

Hereafter, we will always choose the terrestrial reference frame.

Defining a reference frame is essential when studying motion or a force.

In this configuration, is Smilu stationary?

You can answer YES or NO, actually the question is poorly framed 😁.

  • Relative to the road (reference frame: the road), Smilu is stationary.
  • Relative to the car (reference frame: the car), Smilu is in motion (the distance between Smilu and the car is decreasing).

Similarly, even if you are stationary in the terrestrial reference frame, you are in motion relative to...:

  • .... the center of the Earth which rotates: geocentric reference frame
  • .... the center of the Sun: heliocentric reference frame

That's why it's necessary to define a reference frame!

2. What is a Force Balance?

It's simply the list of all the forces exerted on the system (the object being studied).
We previously saw that each force has 4 characteristics.
Therefore, we need to specify the 4 characteristics for each force.

3. An Example... Known?

I take the example of a blue box sliding down an inclined plane (see III.Reaction).

Whether the box is stationary or not, we can list the forces:

Force Balance:

  • The weight P→, exerted by the Earth on the box.
  • The reaction R→, exerted by the contact surface on the box.
  • The reaction R→ can be decomposed:
    • R→N: the normal reaction (perpendicular)
    • R→T: the friction forces

4. Newton's First Law or the Principle of Inertia

Vocabulary reminder: the sum of the forces is called the resultant force.


If the box is stationary, we understand that the overall effect of all forces is zero.
In this case, the resultant of the forces is zero→.
But Newton goes further, if the overall effect of all forces is zero, the motion is unperturbed:
The system is stationary
or ... it has a uniform rectilinear motion (trajectory: a straight line, speed: constant).
The converse is true, if the system is stationary or has a uniform rectilinear motion, it undergoes a zero resultant force.

5. Let's Apply the Principle of Inertia

In the above example, we place a blue box on an inclined plane, either it has a uniformly accelerated motion or it is stationary.

According to the principle of inertia,

According to the principle of inertia,

we can conclude that the box is stationary.