AP Physics C: Mechanics Unit 4 Cheatsheet: Linear Momentum

Definition: p = mv

• Vector quantity; direction matches velocity
• Units: kg·m/s

System momentum: Sum of individual momenta

• p_total = Σ(m_iv_i)
• Center-of-mass velocity: v_cm = Σp_i / Σm_i

Key insight: Momentum is conserved when net external force = 0.

Condition: Net external force on system = 0

• Total momentum is constant
• v_cm remains constant

Newton's 3rd Law connection:

• Impulse on object A = −impulse on object B
• Momentum change in A = −momentum change in B

If external force ≠ 0:

• Momentum transfers between system & environment
• ΔP_system = J_external

Solving strategy: Define system to minimize external forces.

Key: Momentum is conserved in a collision only if the system has zero net external impulse (isolated system); in brief collisions external forces like gravity or friction are usually negligible, so p_before = p_after. Only the KE behavior differs: elastic conserves KE, inelastic does not, and perfectly inelastic objects stick together with maximum KE loss.

Perfectly inelastic: v_f = (m₁v₁ᵢ + m₂v₂ᵢ)/(m₁ + m₂)