Newton's Second Law Of Motion And Momentum

Newton’s second law of motion establishes a relation between the net force acting on a body and the net acceleration of the body. The second law states that the net acceleration of a body is directly proportional to the net force acting on the body. Also, the net acceleration is inversely proportional to the mass of the body.


a ∝ F


a ∝ \( \frac 1m \)

⇒ a = \( \frac Fm \)

It means, that the more the net force acting on a body, the greater would be its acceleration. And the more the mass of the body, the less would be the acceleration. In other words, if the two objects, one heavier than the other, are pushed by same force, the acceleration produced in the heavier object would be less. The heavier is the object, the more force is required to alter its velocity. Again, if the two forces, different in magnitude are applied to the same object, the force which is greater in magnitude will create more acceleration.

The net acceleration of a body is equal to the net force acting on it divided by the mass of the body. Remember, if there are multiple forces acting on a body, we have to take the resultant force in order to calculate the net acceleration. The direction of acceleration will be the same as the direction of force.

Example: If there is a block of mass 2kg, and a force of 5N is acting on it in the positive x-direction, and a force of 3N in the negative x direction, then what would be its acceleration?

Newton's 2nd Law

To calculate its acceleration, we first have to calculate the net force acting on it.

\(F_{net}\) = 5N – 3N = 2N

Mass = 2kg

∴ Acceleration = \( \frac 22 \)  = 1 m/\(s^2\)

Newton’s second law of motion related to the linear momentum:

Linear momentum is defined as the product of mass and velocity. It is denoted by the symbol P.

P = mv

Second Law of Motion: The rate of change of linear momentum of a body is the force acting on the body.

\( \frac {dp}{dt} \) =\( \frac {d(mv)}{dt} \) =m\( \frac {dv}{dt} \)= ma = F

Newton’s second law is applied in daily life to a great extent. For instance, in formula one racing, the engineers try to keep the mass of cars as low as possible. Low mass will imply more acceleration, and the more the acceleration, the chances to win the race are higher. Below video will help you visualize the concept of Newton’s second law of motion,

Stay tuned with Byju’s to learn more about Newton’s second law of motion, types of forces and much more.

Practise This Question

A mass m is suspended from a rigid support P by means of a massless string as shown in the figure. A horizontal force F is applied at point O of the rope. The system is in equilibrium when the string makes an angle θ with the vertical. Then the relation between tension T, force F and angle θ is