AP Physics 1 Unit 4 Cheatsheet: Linear Momentum

Momentum: p = mv

• Vector quantity—same direction as velocity
• Units: kg·m/s
• Describes how hard an object is to stop

Key distinction: Momentum depends on both mass and velocity. A light object moving fast can have the same momentum as a heavy object moving slowly.

System momentum: Sum of individual momenta of all objects in the system.

Condition for conservation: Net external force on system = 0

• Total momentum before = total momentum after
• Σp_i = Σp_f

System selection matters:

• Choose system so external forces are zero or negligible
• Internal forces (between objects in system) always cancel by Newton's 3rd law
• If net external force ≠ 0, momentum changes by amount equal to impulse

Center of mass velocity:

v_cm = Σp_i / Σm_i = Σ(m_iv_i) / Σm_i

• Constant when no net external force

Before writing equations:

1. Draw diagram showing before/after states
2. Define positive direction (left/right or up/down)
3. Identify if momentum is conserved (net external force = 0?)
4. Determine collision type if relevant

For conservation problems:

1. Write: Σp_before = Σp_after
2. Substitute p = mv for each object
3. Solve for unknown

For impulse-momentum problems:

1. Calculate Δp = m(Δv) or use J = F_avgΔt
2. Check direction of impulse matches direction of force

For elastic/inelastic classification:

• Calculate total KE before and after
• If equal → elastic; if KE_f < KE_i → inelastic