Dynamics

This lesson covers dynamics at A-Level — the study of how forces affect the motion of objects. While statics deals with objects in equilibrium, dynamics applies Newton's second law to objects that are accelerating. This lesson brings together forces, acceleration, and the equations of motion.

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Newton's Second Law in Practice

The fundamental equation of dynamics is:

$F_{\text{net}} = ma$Fnet​=ma

where $F_{\text{net}}$Fnet​ is the resultant (net) force, $m$m is the mass, and $a$a is the acceleration. The acceleration is always in the direction of the net force.

Strategy for dynamics problems:

1. Identify all forces acting on the object.
2. Draw a clear force diagram.
3. Choose a positive direction (usually the direction of motion).
4. Apply $F_{\text{net}} = ma$Fnet​=ma in the chosen direction.
5. If necessary, resolve perpendicular to the direction of motion (often to find the normal reaction).

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Motion on a Rough Horizontal Surface

For an object of mass $m$m on a rough horizontal surface with coefficient of friction $\mu$μ, subject to a driving force $D$D and resistance $R_{\text{resist}}$Rresist​:

$D - F - R_{\text{resist}} = ma$D−F−Rresist​=ma

where $F = \mu mg$F=μmg is the friction force.