Momentum is one of the most important concepts in physics. It is defined as the product of an object's mass and velocity, written as p equals m times v. This means that both heavy slow objects and light fast objects can have significant momentum. Let's see how different combinations of mass and velocity affect momentum.
Momentum is not just a number - it's a vector quantity, which means it has both magnitude and direction. We write it as p vector equals m times v vector. When multiple objects interact, we must add their momentum vectors using vector addition. The total momentum of a system is the vector sum of all individual momenta.
Newton's second law can be expressed in terms of momentum. Force equals the rate of change of momentum with respect to time. This is actually more fundamental than F equals ma. We can derive this by starting with F equals ma, then substituting acceleration as the derivative of velocity, giving us F equals d p d t. The graph shows how momentum changes over time, where the slope represents the applied force.
The conservation of momentum is one of the most fundamental laws in physics. When no external forces act on a system, the total momentum remains constant. This means the momentum before any interaction equals the momentum after. We can see this in collisions where two objects approach each other, collide, and then move apart, but the total momentum of the system stays the same throughout the entire process.
Let's solve a collision problem step by step. We have ball A with mass 2 kilograms moving at 3 meters per second, and ball B with mass 1 kilogram moving at negative 2 meters per second. Using conservation of momentum, we set up the equation: m1 times v1 plus m2 times v2 equals m1 times v1 prime plus m2 times v2 prime. Substituting our values gives us 4 equals 2 v1 prime plus v2 prime. The total momentum before and after collision remains 4 kilogram meters per second.