Sample The second law states that the net force on an object is equal to the rate of change (that is, the derivative) of its linear momentum p in an inertial reference frame: [pick] The second law can also be stated in terms of an object’s acceleration. Since the law is valid only for constant-mass the mass can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus, where F is the net force applied, m is the mass of the body, and a is the body’s acceleration.

Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it. Consistent with the first law, the time derivative of the momentum is non-zero when the momentum changes direction, even if there is no change in its magnitude; such is the case with uniform circular motion. The relationship also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum.

Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below). Newton’s second law requires modification if the effects of special relativity are to be taken into account, because at high speeds the approximation that momentum is the product of rest mass and velocity is not accurate. Newton’s second law states that an object will change acceleration if pushed or pulled upon.

An example would be pushing a ball, the velocity goes from O to how hard you push the ball. Newton’s second law also states that if it gets twice the mass it accelerates half as much. An example would be pushing a 10 lb ball as hard as you can, then pushing a 5 lb ball as hard as you can. The 10 lb ball would accelerate less than the 5 lb ball because the 10 lb ball has more mass. Newton’s second law is related to unbalanced forces. Hence they should be a net force for application of Newton’s Second Law of Motion.

If you push a ball then it will not move initially due o the force of friction. Let’s take a look at some examples to learn more about Newton’s Second Law. A truck hits a car; the car moves forward. The truck provides the force, the car is the mass, heavier the car (mass) is, the more force it takes to move it. If the car is very light, it will move forward quicker than if the car is very heavy. If you throw a 10-b. Weight and a 2-b. Weight with the same amount of force, the 2 lb. Weight will travel faster than the weight. That is because there is less mass to be moved.