9.4:
Impulse-Momentum Theorem
Consider the mathematical expression of Newton’s second law in terms of momentum. If the net force remains constant, then the change in momentum is equal to the product of force and the time interval over which the force is applied, which is nothing but the impulse. This is the impulse-momentum theorem.
The greater the time interval over which the force is acting, the greater will be the change in momentum.
For example, when a gymnast lands after a vault jump, the landing material is made of a soft cushion to prolong the time interval over which the force is acting to decrease the momentum to zero. This ensures a safe landing as compared to landing on a hard surface.
9.4:
Impulse-Momentum Theorem
The total change in the motion of an object is proportional to the total force vector acting on it and the time over which it acts. This product is called impulse, a vector quantity with the same direction as the total force acting on the object.
By writing Newton's second law of motion in terms of the momentum of an object and the external force acting on it, and simultaneously using the definition of the impulse vector, it can be shown that the total impulse on an object is equal to its net change in momentum. This mathematical relationship is called the impulse-momentum theorem, and it is true even if the force acting on the object varies with time.
For instance, in ice hockey, the puck experiences a significant impulse during a slap shot. A considerable force acts on the puck for less than a second, causing a change in the ball's velocity and hence its momentum. The difference in momentum is added to the initial momentum to calculate the final momentum. According to the theorem, the change in momentum of the puck is equal to the impulse experienced by the puck.
It is essential to note that an impulse does not cause momentum; instead, it causes a change in the momentum of an object.
This text is adapted from Openstax, University Physics Volume 1, Section 9.2: Impulse and Collisions.