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Constant mass

For a body of constant mass, Newton’s second law becomes

$\vec F_{net}=m\vec a$

Use the resultant force, not one arbitrarily selected force.

General momentum form

The broader statement is

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

or its instantaneous form. This is the safer form when mass changes or when momentum is the quantity given.

Check what changes

If mass is constant, $\Delta p=m\Delta v$ , so the two forms agree. If mass enters or leaves the system, include the momentum carried by that mass and define the system carefully.

Common trap

Do not double the acceleration simply because an applied force doubles when a fixed resistive force remains; calculate the new resultant force first.

[ 2 ]

Calculate the magnitude of the initial acceleration of the electron.

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.2.19—Newton’s second law forms

Choose the Momentum Form of Newton’s Second Law

Retrieve the A.2 Forces and Momentum Model

A.2.19 Exam Analysis