S1.3.2—Vectors and diagrams

A vector needs magnitude and direction

Draw its arrow to scale when a scale diagram is required, label its magnitude, direction and point of application, and choose axes before resolving it. Scalars such as mass and energy have magnitude only; force, velocity and momentum are vectors.

V_x=V\cos\theta,\qquad V_y=V\sin\thetaR_x=\sum V_x,\qquad R_y=\sum V_y,\qquad R=\sqrt{R_x^2+R_y^2}

Worked resolution

For a $10.0\,\text{N}$ force at $30^\circ$ above the positive horizontal, $F_x=10.0\cos30^\circ=8.66\,\text{N}$ and $F_y=10.0\sin30^\circ=5.00\,\text{N}$ . The signs change if the chosen directions change; the physical vector does not.

Free-body diagram method

Choose one object, draw only forces acting on it at the required point of application or centre of mass, then add up to three coplanar vectors head-to-tail or by components. Subtraction means adding the reversed vector; multiplying by a negative scalar reverses direction.

Do not mix an interaction pair

The force exerted by the object on its surroundings belongs on the surroundings' diagram, not on the object's own free-body diagram.

How it is assessed

Questions classify scalar/vector quantities or find a new resultant after reversing and scaling forces.

Command terms

Identify

What earns marks

Identify vector quantities and carry the direction change through the component or graphical sum.

Watch for

Calling potential difference a vector or ignoring the reversed direction in a resultant.

Calculate carefully

Rearrange symbolically, resolve vectors, convert units and use proportional reasoning before substituting.

Report evidence

Propagate uncertainty with the correct operation, then use labelled graphs, error bars, gradients, intercepts and areas to test the model.

S1.3.2—Vectors and diagrams

Resolve Vectors and Diagrams

S1.3.2 Exam Analysis

Assessment in practice

Retrieve Mathematical Practice