Newton's second law

View of Moon limb with Earth on the horizon, Mare Smythii region. This image was taken before separation of the Lunar Module and the Command Module during the Apollo 11 mission. 20 July 1969

When a body interacts with the objects that surround it, it ceases to be a free particle. Therefore, it will no longer move with constant velocity and its linear moment will vary. The variation of the linear moment is equal to the vector sum of the forces acting on the body. The forces represent the different interactions the particle experiences (see force types).

Newton’s second law is also known as the motion equation. Once the acceleration vector is obtained, we can calculate the velocity vector and the position vector, so that the movement of the particle is fully described.

If the vector sum of the forces acting on a body is zero, the body has no acceleration and therefore will move with constant speed (law of inertia).

The force is a vector; Therefore, when working with it we must take into account its magnitude and direction. The vector sum of the forces that act on a body is the vectorial sum of the different forces that act on it.

The International System unit for a force is the Newton (N).

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Implications of Newton’s second law:
  • Newton’s second law describes the translational motion of a body.
  • Newton’s second law is a vector equation. It means that the force and the acceleration are two vectors and we will have to work with them as such. They are not scalars.
  • The acceleration vector of the particle is always parallel to the vector sum of the forces acting on it. Because the mass is positive and the product of a scalar by a vector results in a vector parallel to the vector.
  • Inertia and mass are two related concepts. The greater the mass of a body, the lesser will be its acceleration for a given force, and therefore more time will be needed to change its state of motion (velocity). And vice versa.
  • The speed of a body does not have to be parallel to its acceleration. That is, a body does not have to move parallel to its acceleration. It is only the case when a body starts from rest.
  • The forces that appear in the first member of Newton’s second law are the physical interactions that the particle experiences. Before trying to solve a problem it is necessary to identify which ones depend on the physical situation considered.
  • The acceleration does not depend on the point of application of the forces.
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