A-Level Physics — Mechanics to Particle Physics

Definitions

• Scalar: magnitude only (distance, speed, mass, energy, temperature). Vector: magnitude and direction (displacement, velocity, acceleration, force, momentum).

Adding and resolving vectors

• Add vectors tip-to-tail (scale diagram) or with components; the resultant closes the triangle.
• Resolve a vector F at angle theta into perpendicular components: horizontal = F cos(theta), vertical = F sin(theta).
• Combine perpendicular components with Pythagoras (magnitude = root(x^2 + y^2)) and the inverse tangent (direction).

Equilibrium and moments

• An object is in equilibrium when the resultant force is zero and the resultant moment is zero - the force vectors form a closed triangle.
• Moment = force x perpendicular distance from the pivot; principle of moments: sum of clockwise moments = sum of anticlockwise moments.
• Couple: two equal, opposite, parallel forces; torque = force x separation.
• Centre of mass: the point where the weight appears to act; an object topples when its line of weight falls outside its base.

Resolve forces along two perpendicular axes and set each direction's resultant to zero for equilibrium problems.

Diagram