PHSX 220 Physics I (w/ Calculus) · Unit 3: Momentum, rotation, gravitation · on Exam 3
Ch 9.1–9.3 Momentum and impulse
Study notes for Momentum and impulse in PHSX 220 Physics I (w/ Calculus) at Montana State University: the big ideas, key formulas, a worked example, common mistakes and an exam tip. The same topic has endless practice questions and flashcards in Mathub.
Big ideas
- Momentum $\vec p = m\vec v$ is a vector. Newton's second law in its general form: $\sum\vec F = d\vec p/dt$.
- Impulse–momentum theorem: $\vec J = \int\vec F\,dt = \vec F_{\text{avg}}\Delta t = \Delta\vec p$. A longer collision time means a smaller average force for the same momentum change (airbags, bending your knees).
- Conservation of momentum: if the net external force on a system is zero (or the collision is so brief that external impulses are negligible), total momentum is conserved: $\sum\vec p_i = \sum\vec p_f$, component by component.
- Recoil: a gun and bullet start at rest, so $m_g v_g = -m_b v_b$. Explosions and rockets work the same way.
Key formulas
Momentum and impulse
$$\vec p = m\vec v,\qquad \vec J = \vec F_{\text{avg}}\Delta t = \Delta\vec p$$
Conservation
$$m_1\vec v_{1i} + m_2\vec v_{2i} = m_1\vec v_{1f} + m_2\vec v_{2f}$$
Worked example
A 0.15 kg ball moving at 20 m/s hits a wall and rebounds at 20 m/s. Contact lasts 0.010 s. Find the impulse and average force.
Show the solution
Take the rebound direction positive: $\Delta p = 0.15(20) - 0.15(-20) = 6.0\ \text{kg·m/s}$. $F_{\text{avg}} = 6.0/0.010 = 600$ N, directed away from the wall.
Common mistakes
- Computing Δp = m(v_f − v_i) without signs; a reversal doubles the change.
- Applying momentum conservation while a large external force acts over the interval (e.g. gravity over a long time).
Exam tipMomentum conservation is about the system. Draw a box around the objects and ask whether anything outside the box pushes on it during the event.
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