momentum impulse

Momentum is defined as the product of an object's mass and velocity, expressed as p = mv, where p is momentum (kg m s⁻¹), m is mass (kg), and v is velocity (m s⁻¹). Momentum is a vector quantity, meaning it has both magnitude and direction.

Impulse represents the change in momentum and equals the product of force and time: I = Ft = Δ(mv). Impulse is measured in newton-seconds (N s) or kilogram metres per second (kg m s⁻¹). The Impulse-Momentum Theorem states that the impulse applied to an object equals its change in momentum.

Conservation of Linear Momentum: In a closed system where no external forces act, the total momentum before collision equals total momentum after collision: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.

Key Terminology:

• Elastic collision: Both momentum and kinetic energy are conserved
• Inelastic collision: Only momentum is conserved; kinetic energy is lost
• Perfectly inelastic collision: Objects stick together after impact

Force-Time Graphs: The area under a force-time graph represents impulse. For variable forces, use integration: I = ∫F dt.

Mnemonic: MoVe Carefully - Momentum = mass × Velocity, always Conserved in isolated systems

Sign Convention: Establish a positive direction (usually right or up). Velocities in the opposite direction are negative. This is crucial for collision problems where objects move in opposite directions.

Understanding momentum helps explain everyday phenomena. When a heavy truck and small car travel at the same speed, the truck has greater momentum due to its larger mass. Stopping the truck requires more force over a longer time—this is why lorries need greater braking distances.

Airbags and Safety Features: Cars are designed to increase collision time, reducing impact force. Airbags inflate during crashes, extending the time over which momentum changes from perhaps 0.01s to 0.1s. Since F = Δp/Δt, increasing Δt decreases F by a factor of 10. Similarly, crumple zones deliberately deform, absorbing energy while extending impact duration.

Sports Applications: Cricket players "give" with the ball when catching, pulling their hands backward. This increases contact time, reducing the force on their hands. Conversely, batsmen follow through when hitting, maximizing the time force is applied, thus maximizing impulse and ball velocity.

Rocket Propulsion: Rockets work via conservation of momentum. Expelled gases gain momentum in one direction; the rocket gains equal momentum in the opposite direction. The Tsiolkovsky rocket equation extends these principles: Δv = ve ln(m₀/mf), where ve is exhaust velocity.

Real-World Analogy: Think of momentum as "quantity of motion." A rolling bowling ball has more "quantity of motion" than a tennis ball at the same speed. Stopping either requires removing this motion—either quickly (large force) or gradually (small force over longer time). The total "removal of motion" (impulse) remains constant.

Remember: Momentum depends on reference frame. Two colliding cars have zero total momentum in the Earth's frame only if their individual momenta cancel.