Newton's First Law of Motion

Goals

  1. Describe Newton’s First Law of Motion.

  2. Skillfully apply this law.

Statement of the Law

The first law of motion is a fact that can also be classified a scientific law.

Here are multiple ways of saying this fact.

  1. An object stays at rest, or keeps moving in a straight line at the same speed if and only if the sum of the forces acting on it are zero.

  2. \(\Sigma \mathbf{F} = \mathbf{0}\) ⇔ A body will remain at rest or moving with constant velocity; that is, it will not accelerate.

  3. \(\Sigma \mathbf{F} = \mathbf{0}\) ⇔ \(mathbf{a} =mathbf{0}\)

  4. The following two facts are true.

    1. If a body is at rest or moving with constant velocity, then the sum of forces acting on the body must be zero (\(\Sigma \mathbf{F} = \mathbf{0}\) ) .
    2. If the sum of forces on a body are zero, then the body must be at rest or moving with constant velocity.

Essential Details

  1. The first law applies to a particle, which is an object that is modeled as if all its mass is concentrated as the center of mass and its size and shape don’t matter.

  2. The first law ((\(\Sigma \mathbf{F} = \mathbf{0}\) ) ) applies to a moving particle if the velocity is constant. Since velocity is a vector, the speed must be constant and the direction of travel must be a straight line. If a particle is traveling on curve path, then it is accelerating (change of direction) and it must be true that Newton’s Second Law of Motion (\(\Sigma \mathbf{F} = m\mathbf{a}\) ) is satisfied.

  3. It can be proven (omitted here) that the first law of motion applies to a rigid body or any other object if the center-mass of this system is stationary or moving with constant velocity

  4. As is often the case with engineering topics, there are multiple details and nuances about the first law that one naturally picks up through years of experiences and immersion. Be patient. 😊

  5. Newton’s Three Laws of Motion (Summary)

    1. \(\Sigma \mathbf{F} = \mathbf{0}\) ⇔ \(\mathbf{a} =\mathbf{0}\)
    2. \(\Sigma \mathbf{F} = m\mathbf{a}\)
    3. Forces always occur in pairs, equal in magnitude, opposite in direction and co-linear.

Examples of the First Law

If we model a jet like the Airbus A380, as a particle and it