Linear Momentum

Four topics on momentum, the quantity $\vec{p} = m\vec{v}$ that a force changes over time rather than all at once. The momentum an object carries as a vector pointing along its velocity, the impulse $\vec{J} = \int \vec{F}\,dt$ a force delivers and how it equals the change $\Delta\vec{p}$, the conservation of a system's total momentum whenever no external force acts, and finally collisions, where momentum always survives but kinetic energy need not.

Topics

4.1

Linear Momentum

Change in Momentum and Impulse

Conservation of Linear Momentum

Elastic and Inelastic Collisions

Lesson

Diag

locked

Equations For every problem in this unit

Linear momentum

$\vec{p} = m\vec{v}$

Newton's second law

$\vec{F}_{net} = \dfrac{d\vec{p}}{dt}$

Momentum and kinetic energy

$K = \dfrac{p^2}{2m}$

System momentum

$\vec{p}_{sys} = \sum m_i \vec{v}_i$

Impulse, variable force

$\vec{J} = \int \vec{F}\,dt$

Impulse, constant force

$\vec{J} = \vec{F}_{avg}\,\Delta t$

Impulse-momentum theorem

$\vec{J} = \Delta\vec{p}$

Graphical impulse

area under $F$ vs $t$

Conservation of momentum

$\sum \vec{p}_i = \sum \vec{p}_f$

Perfectly inelastic

$m_1\vec{v}_1 + m_2\vec{v}_2 = (m_1 + m_2)\vec{v}_f$

Elastic collision

$\sum K_i = \sum K_f$

Center-of-mass velocity

$\vec{v}_{cm} = \dfrac{\sum m_i \vec{v}_i}{\sum m_i}$

Unit 4 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items pulled from across all 4 topics, identifying which misconceptions still bite when the question does not tell you which topic it came from.