Lesson 10: Momentum

What is linear momentum?

p = mv — A vector quantity in the direction of velocity. Units: kg·m/s

What is Newton's 2nd Law in terms of momentum?

F_net = dp/dt — Net force equals the rate of change of momentum.

What is impulse?

J = Δp = F_avg · Δt — Change in momentum equals average force times time interval. Units: N·s

What is the Impulse-Momentum Theorem?

J = Δp — Impulse equals the change in momentum of an object.

Why do airbags and padding reduce injury?

They increase collision time Δt, reducing the average force F for the same impulse (J = FΔt = Δp).

What is conservation of linear momentum?

Σp_i = Σp_f — Total momentum is conserved when the net external force on the system = 0.

What is an elastic collision?

Both momentum AND kinetic energy are conserved — objects bounce off each other.

What is a perfectly inelastic collision?

Momentum is conserved, maximum KE is lost — objects stick together after collision.

What is the final velocity formula for a perfectly inelastic collision?

(m₁+m₂)v_f = m₁v₁ᵢ + m₂v₂ᵢ → solve for v_f.

What are the final velocities in a 1D elastic collision?

v₁f = ((m₁-m₂)v₁ᵢ + 2m₂v₂ᵢ)/(m₁+m₂) and v₂f = ((m₂-m₁)v₂ᵢ + 2m₁v₁ᵢ)/(m₁+m₂).

How do you solve a 2D collision?

Apply conservation of momentum separately for x and y: Σp_x conserved AND Σp_y conserved independently.

What is the center of mass (CM)?

x_cm = Σ(mᵢxᵢ)/M — Mass-weighted average position of a system; M = total mass.

What is the velocity of the center of mass?

v_cm = Σ(mᵢvᵢ)/M = p_total/M — The CM moves as if all mass and all external forces act there.

What does F_ext = Ma_cm mean?

Only external forces accelerate the center of mass — internal forces between objects in the system have no effect on CM motion.

What is rocket thrust?

F_thrust = -v_exhaust(dm/dt) — Reaction force from expelling exhaust mass; dm/dt is negative as fuel burns.

What is the Tsiolkovsky Rocket Equation?

Δv = v_e ln(m_i/m_f) — v_e = exhaust speed, m_i = initial mass, m_f = final mass after burning fuel.

Why do rockets work in a vacuum?

They expel exhaust mass rearward by Newton's 3rd Law — no external medium is needed to push against.