Newton's three laws
Inertia, , action-reaction.
Newton's first law (inertia). A particle continues in its state of rest or uniform motion in a straight line unless acted upon by a resultant external force.
- If , then .
- Equivalent statements: 'in equilibrium' and 'moving with constant velocity' have the same force-balance.
Newton's second law. The resultant force on a particle equals its mass times its acceleration:
- Vector equation; apply COMPONENT-WISE if forces are not all collinear.
- is in the direction of .
- Units: in newtons (N), in kg, in m s. .
Newton's third law. If body exerts a force on body , then exerts an equal and opposite force on .
- Used in normal reactions: the ground pushes the box up with force ; the box pushes the ground down with force .
- Used in connected-particle systems: the string pulls toward with tension ; equally, the string pulls toward with the same .
Universal workflow for an M1 dynamics problem:
- Draw the force diagram with every force labelled.
- Choose axes (along/perpendicular to motion, or horizontal/vertical).
- Resolve each force into those axes.
- Apply along each axis.
- Solve the resulting equation(s).
- Law 1: no net force = no acceleration.
- Law 2: (vector).
- Law 3: equal and opposite reactions.
- Workflow: diagram, axes, resolve, , solve.