MCAT topics → Translational Motion, Forces, Work, and Energy → Linear Momentum and Impulse

Linear Momentum and Impulse

MCAT trap: Confuses impulse with force magnitude, ignoring the time component. Impulse equals force multiplied by the time interval (J = FΔt), so a smaller force over a longer time can produce the same impulse.

Linear momentum is the product of mass and velocity (p = mv), and on the MCAT the most important insight is this: impulse (the change in momentum) is fixed by the crash physics — an airbag cannot reduce it. What an airbag does is extend the time over which that impulse is delivered, which reduces average force. If you confuse impulse with force, you will get every safety-device passage question wrong. Impulse and momentum are tied by J = FΔt = Δp, and the exam tests this relationship from straightforward calculation to passage-based engineering scenarios.

What makes this concept trip students up isn't the math — it's the conceptual layer underneath. Momentum is a vector, which means direction matters in a way that mass or speed alone doesn't capture. Two objects with equal mass and speed moving toward each other have momenta that cancel, not add. Conservation of momentum also has a condition students frequently forget: net external force must be zero. Internal forces between colliding objects don't count — only forces from outside the system can change total momentum.

The airbag question type is a classic MCAT trap. Students instinctively think airbags 'absorb' the impact and reduce what the passenger feels in some total sense. The real insight is subtler: the total change in momentum (impulse) is fixed by the collision physics — airbags can't change that. What they do is extend the time over which that impulse is delivered, which reduces the average force. If you confuse impulse with force, you'll get these passage questions wrong every time.

Common misconceptions

Common mistake
Wrong: Impulse is determined solely by the magnitude of the force applied.
Right: Impulse equals force multiplied by the time interval (J = FΔt), so a smaller force over a longer time can produce the same impulse.
Impulse depends on both the force AND how long it acts: J = FΔt. A large force applied for a tiny instant can produce less impulse than a gentle force applied over a long time. When the MCAT asks why a follow-through in sports or a padded surface is effective, the answer is always about extending Δt — not increasing or decreasing the force in isolation.
Common mistake
Wrong: Momentum is a scalar quantity with only magnitude.
Right: Momentum is a vector quantity (p = mv) with both magnitude and direction, so opposite-direction momenta can cancel.
Momentum is a vector, and this changes everything in collision problems. An object moving right with momentum +10 kg·m/s and an equal-mass object moving left with momentum −10 kg·m/s have a combined system momentum of zero, not 20. Always assign signs (or vector directions) to momentum before adding or comparing — treating it like a scalar will give you wrong totals whenever objects move in opposite directions.
Common mistake
Wrong: Momentum is conserved in all situations regardless of external forces.
Right: Momentum is conserved only when the net external force on the system is zero; internal forces do not change total momentum.
Conservation of momentum is conditional, not universal. It applies only when the net external force on the system is zero over the relevant time interval. Two hockey pucks colliding on frictionless ice? Conserved. A car braking to a stop? Not conserved — friction from the road is an external force acting on the car-Earth system boundary you've drawn. Always ask: what external forces act on my defined system before invoking conservation.
Common mistake
Wrong: Airbags reduce the total impulse experienced by a passenger during a collision.
Right: Airbags extend the collision time (Δt), reducing average force while the total impulse (Δp) remains the same.
The impulse a passenger experiences in a crash equals their change in momentum — from traveling at car speed to rest. That Δp is determined entirely by the initial and final velocities, not by the airbag. The airbag cannot reduce this impulse. What it does is increase the time Δt over which the force acts, so the average force F = J/Δt is smaller. The impulse stays the same; the peak force drops. This is the key insight the MCAT tests in every safety-device passage.
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What the exam tests

  1. Identify momentum as a vector quantity defined by p = mv, and recognize that impulse J equals both FΔt and the change in momentum Δp.
  2. Apply conservation of momentum correctly by first verifying that the net external force on the system is zero — internal forces alone cannot change total momentum.
  3. Calculate impulse from a force-time graph (impulse = area under the F-t curve) or from a known change in momentum, and use these interchangeably.
  4. Interpret real-world safety devices like airbags and crumple zones using the impulse-momentum theorem: extending collision time reduces average force while keeping total impulse constant.

Can you avoid these mistakes?

A 60 kg runner moving at 4 m/s east collides head-on with a 60 kg runner moving at 4 m/s west. What is the total momentum of the two-runner system just before the collision, and what does this tell you about what happens when they grab onto each other?
A force-time graph shows a triangular pulse: force rises linearly from 0 to 300 N over 0.2 s, then drops back to 0. What is the impulse delivered to the object, and by how much does the object's momentum change?
A soccer ball is kicked and its momentum changes from −5 kg·m/s to +15 kg·m/s. If the foot is in contact with the ball for 0.05 s, what average force did the foot exert? Would a longer contact time (follow-through) increase or decrease the average force needed to produce the same momentum change?
In a car crash, a passenger decelerates from 25 m/s to 0. Explain why deploying an airbag does not reduce the total impulse the passenger experiences, but does reduce the likelihood of injury. What specific physical quantity does the airbag reduce?

Related topics

Newton's Three Laws of Motion One-Dimensional Kinematics Two-Dimensional Kinematics and Projectile Motion Friction (Static and Kinetic)

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