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Impulse changes momentum

Impulse is the integral of resultant force over time. For a constant average force,

$\vec J=\vec F_{net}\Delta t=\Delta\vec p$

Use the momentum change

Calculate $\Delta\vec p=\vec p_f-\vec p_i$ , including direction. A rebound reverses the velocity component and can make the momentum change larger than either momentum magnitude alone.

Average force

If the force varies, $F\Delta t$ represents average resultant force over the contact interval. Use consistent units for impulse in N s or kg m s⁻¹.

Common trap

Do not use the initial momentum alone when the object rebounds or ends with a non-zero final velocity.

[ 2 ]

The ball rebounds from the ground with speed $7.8 \mathrm{~ms}^{-1}$ . The ball is in contact with the ground for a time T. The average resultant force on the ball during this time is 1.1 N .
Determine T.

Build the force model

Choose the system, draw a labelled free-body diagram, classify the interactions and resolve components. Apply Newton’s laws with the correct boundary: contact forces, field forces, friction, tension, buoyancy and restoring forces each have their own direction and conditions.

Track momentum

Use $ec p=m ec v$ , $ec J=\Delta ec p$ and momentum conservation only after checking external impulse. Distinguish elastic and inelastic collisions, explosions and energy transfer.

Track circular motion

The inward resultant provides $a_c=v^2/r=\omega^2r$ . It may come from tension, gravity, normal, friction or a field force. Angular and linear descriptions are linked by $v=\omega r=2\pi r/T$ .

Final checks

Ask: Which body is the system? Which forces are external? Is mass constant? Is acceleration uniform or radial? Is kinetic energy conserved, transferred or increased?

A.2.17—Impulse

Calculate Impulse from Force and Time

Retrieve the A.2 Forces and Momentum Model

A.2.17 Exam Analysis