of fixed mass m , v v a ( . ) i.e the Second Law can also be written as F = k m a ( . ) which shows that force is proportional to the product of mass m and acceleration a . The unit of force has not been defined so far.
In fact, we use Eq. ( . ) to define the unit of force. We, therefore, have the liberty to choose any constant value for k .
For simplicity, we choose k = . The second law then is a ( . ) In SI unit force is one that causes an acceleration of m s - to a mass of kg. This unit is known as newton : N = kg m s - .
Let us note at this stage some important points about the second law : . In the second law, F = implies a = . The second law is obviously consistent with the first law. .
The second law of motion is a vector law. It is equivalent to three equations, one for each component of the vectors : ma x x x ma z z z a = d ( . ) This means that if a force is not parallel to the velocity of the body, but makes some angle with it, it changes only the component of velocity along the direction of force. The component of velocity normal to the force remains unchanged.
For example, in the motion of a projectile under the vertical gravitational force, the horizontal component of velocity remains unchanged (Fig. . ). .
The second law of motion given by Eq. ( . ) is applicable to a single point particle. The force F in the law stands for the net external force on the particle and a stands for acceleration of the particle.
It turns out, however, that the law in the same form applies to a rigid body or, even more generally, to a system of particles. In that case, F refers to the total external force on the system and a refers to the acceleration of the