Mechanics: Momentum

Mechanics: Momentum

Definition of Momentum in Mechanics

  • Momentum is the quantity of motion an object has. It is a vector quantity, having both direction and magnitude.
  • The momentum of an object is equal to the mass of the object times its velocity. It is denoted by the letter ‘p’.
  • A change in momentum is known as Impulse, which is the product of the force acting on the object and the duration of time the force is applied for. It is also a vector quantity.

Mathematical Formulas

  • The formula for momentum is p = mv, where m is the mass and v is the velocity.
  • The formula for impulse (J) is J = Ft, where F is the force applied and t is the time during which the force is applied. Because Impulse equals change in momentum, we can also write J = Δp.

Types of Collisions in Terms of Momentum

  • Elastic collisions are collisions in which both momentum and kinetic energy are conserved before and after the collision.
  • Inelastic collisions are collisions in which momentum is conserved but kinetic energy is not.
  • Totally inelastic collisions are a subtype of inelastic collisions where the objects stick together and move as one after the collision.

Concepts of Momentum in Mechanics

  • Conservation of Momentum: The total momentum of a system of objects remains constant if no external forces are acting on it.
  • Impulse: It is defined as the change in momentum of an object when a force acts upon it for an interval of time.

Importance of Units

  • The unit of momentum in the International System (SI) is the kilogram metre per second (kg m/s). Impulse, having the same units, is also measured in (kg m/s).
  • Be mindful of the units used in any momentum related problems. Ignoring or incorrectly converting units can lead to wrong answers.

Momentum Problem Tips

  • When solving problems involving momentum, it can be helpful to draw a before-and-after diagram, especially in collision problems.
  • Always set up your problem with a clear definition of positive and negative directions. Be consistent in this throughout the problem.