Momentum | Physics for GCSE/IGCSE - Class 10 PDF Download

Momentum

• An object with mass that is in motion has momentum which is defined by the equation:
• Momentum is calculated using the formula: momentum = mass × velocity, represented as p = mv.
• Where:
  p = momentum in kilogram metre per second (kg m/s)
  m = mass in kilograms (kg)
  v = velocity in metres per second (m/s)
• When an object is stationary (velocity = 0), it possesses no momentum.
• Momentum is what sustains an object's motion in a consistent direction, rendering it challenging to alter the course of an object with substantial momentum.
• Due to velocity being a vector quantity, the momentum of an object is contingent upon its direction of travel.
• Consequently, momentum can exhibit both positive and negative values.
  • For instance, if an object travels to the right, it possesses positive momentum, while an object moving in the opposite direction (to the left) carries negative momentum.

• The momentum of an object undergoes alteration under the following circumstances:
  • The object experiences acceleration, resulting in an increase in speed, or deceleration, leading to a decrease in speed.
  • Changes occur in the object's direction of motion.
  • Variations arise in the object's mass.

Conservation of Momentum

• The conservation of momentum principle states that within a closed system, the combined momentum before an event equals the combined momentum after the event.
• A closed system implies constant energy within it and the absence of external forces like friction.
• In simpler terms, the total momentum before a collision equals the total momentum after the collision.
• A system can comprise one or multiple objects under consideration.
• Since momentum is a vector, if objects within a system move in opposite directions at identical speeds, their momenta cancel each other out, resulting in an overall momentum of zero.
• Momentum remains conserved over time.
• The diagram below illustrates two masses labeled m with velocity u and M at rest (i.e., zero velocity):

• Before the collision:
  • The momentum solely belongs to mass m, which is in motion.
  • Considering the right as the positive direction, the total momentum of the system is the product of mass m and velocity u.
• After the collision:
  • Mass M also acquires momentum.
  • Mass m now moves with a velocity of -v (since it travels leftward), while mass M moves with velocity V.
  • The total momentum encompasses the momentum of M plus the momentum of m.
  • This can be expressed as (M × V) + (m × -v) or equivalently, (M × V) - (m × v).