Forces and Newton’s laws

Newton’s laws connect forces and motion. In mechanics we resolve forces into components, use F = ma along each direction, and model friction, slopes, pulleys and connected particles.

Key facts

• F = ma for the resultant force.
• Resolve a force F at angle θ: F cos θ along, F sin θ across.
• On a slope at θ: weight component along the slope is mg sin θ, perpendicular mg cos θ.
• Friction F ≤ μR, where R is the normal reaction.
• Connected particles: write F = ma for each, or treat as one system.

Worked examples