Question 1

What is the difference between momentum and kinetic energy?

Accepted Answer

Momentum p = mv is a vector that measures quantity of motion; kinetic energy KE = ½mv² is a scalar that measures energy of motion. Both depend on mass and velocity but differently — momentum scales linearly with v, KE quadratically. In collisions, momentum is always conserved (closed system), but kinetic energy is only conserved in elastic collisions. A fast, light object and a slow, heavy object can have equal momenta but very different kinetic energies.

Question 2

What is an elastic vs inelastic collision?

Accepted Answer

In an elastic collision, both momentum and kinetic energy are conserved — no energy is lost to deformation, heat, or sound. Billiard ball collisions are approximately elastic. In an inelastic collision, momentum is conserved but kinetic energy decreases (converted to other forms). Perfectly inelastic collisions occur when the objects stick together — these have the maximum KE loss. Real-world collisions are always somewhere between elastic and perfectly inelastic.

Question 3

How does the impulse-momentum theorem explain airbag safety?

Accepted Answer

In a crash, the change in momentum Δp = m·Δv is fixed — determined by the car's mass and pre-crash velocity. The impulse-momentum theorem J = FΔt = Δp shows that this Δp can be achieved by a large force over a short time, or a small force over a longer time. Airbags increase the collision duration Δt, which reduces the peak force F on the occupant. Spreading the same impulse over 50 ms instead of 5 ms reduces peak force tenfold.

Question 4

Is momentum always conserved?

Accepted Answer

Momentum is conserved in a closed system where no external forces act. In reality, external forces like friction, gravity, and normal forces often act — so the total system must be defined to include all interacting bodies. For a collision between two objects on a frictionless surface, the system of both objects conserves momentum because the collision forces are internal. Gravity is an external force but is usually ignored for brief collisions.

Question 5

What is angular momentum?

Accepted Answer

Angular momentum L = Iω (moment of inertia × angular velocity) is the rotational analog of linear momentum. It is conserved when no external torque acts. A figure skater pulling their arms inward reduces I, so ω must increase — they spin faster. The conservation of angular momentum also explains why planets orbit faster when closer to the Sun (Kepler's second law) and why a gyroscope resists tilting.

Question 6

What are the units of momentum?

Accepted Answer

The SI unit of momentum is kilogram-metres per second (kg·m/s). Equivalently, since F = ma = Δp/Δt, the unit is also Newton-seconds (N·s): 1 N·s = 1 kg·m/s. Impulse has the same unit. There is no special named unit for momentum in SI, unlike force (Newton) or energy (Joule). In imperial units, momentum is measured in slug·ft/s or lb·s.

Formula	Description	Units
p = mv	Linear momentum	kg·m/s
J = FΔt	Impulse (= change in momentum)	N·s
J = Δp = mv_f − mv_i	Impulse-momentum theorem	kg·m/s
p_total = const	Conservation of momentum (no ext. force)	—
v_f = (m₁v₁+m₂v₂)/(m₁+m₂)	Perfectly inelastic collision	m/s
KE = ½mv² conserved	Elastic collision condition	J

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