Further Mechanics: Momentum

Further Mechanics: Momentum

Momentum Basics

• Momentum is a vector quantity that depends on both the mass of an object and its velocity.
• It is calculated by multiplying the mass of an object by its velocity (p = mv).
• The unit of momentum is kg m/s in the International System of Units (SI).

Conservation of Momentum

• The principle of conservation of momentum states that in an isolated or closed system with no external forces, the total momentum before an event is equal to the total momentum after the event.
• Collisions and explosions are examples of events where conservation of momentum applies.

Impulse and Change in Momentum

• Impulse is the change in momentum of an object when a force acts upon it for an interval of time. It is calculated as force multiplied by time (Impulse = Ft)
• Impulse has the same units as momentum (kg m/s) and can be thought of as the increase of momentum.
• The principle of impulse and momentum states that the impulse on an object is equal to the final momentum of the object minus its initial momentum (Impulse = Δp).

Collisions

• Collisions can be either elastic or inelastic.
• In elastic collisions, both momentum and kinetic energy are conserved.
• In inelastic collisions, momentum is conserved while kinetic energy is not.
• When two objects stick together and move with the same speed after colliding, the collision is considered perfectly inelastic.

Newton’s Second Law and Momentum

• An alternative form of Newton’s second law relates force to the rate of change of momentum. It states that the force acting on an object is equal to the rate of change of its momentum.
• This form is particularly useful when dealing with objects with varying mass, like rockets.

Calculating Momentum in Two Dimensions

• When calculating momentum in two dimensions, split the momentum into components and calculate the momentum in the horizontal and vertical directions separately.
• The principles of conservation and momentum apply in each individual direction.