1.6: Newton's Second Law

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Translational Motion:

Newton's second law states that: "When a net force acts on any body with mass, it produces an acceleration of that body. The net force will be equal to the mass of the body times the acceleration of the body."

\[ \vec{F} \, = \, m \vec{a}\]

You will notice that the force and the acceleration in the equation above have an arrow above them. This means that they are vector quantities, having both a magnitude and a direction. Mass, on the other hand, is a scalar quantity having only a magnitude. Based on the above equation, you can infer that the magnitude of the net force acting on the body will be equal to the mass of the body times the magnitude of the acceleration, and that the direction of the net force on the body will be equal to the direction of the acceleration of the body.

Rotational Motion:

Newton's second law also applies to moments and rotational velocities. The revised version of the second law equation states that the net moment acting on the object will be equal to the mass moment of inertia of the body about the axis of rotation (\(I\)) times the angular acceleration of the body.

\[ \vec{M} \, = \, I * \vec{\alpha}\]

You should again notice that the moment and the angular acceleration of the body have arrows above them, indicating that they are vector quantities with both a magnitude and direction. The mass moment of inertia, on the other hand, is a scalar quantity having only a magnitude. The magnitude of the net moment will be equal to the mass moment of inertia times the magnitude of the angular acceleration, and the direction of the net moment will be equal to the direction of the angular acceleration.

Video lecture covering this section, delivered by Dr. Jacob Moore. YouTube source: https://youtu.be/3PF2uNGW7Dw.