R: Forces and Newton’s laws: Understand and use Newton’s third law; equilibrium of forces on a particle and motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2D vectors); application to problems involving smooth pulleys and connected particles; resolving forces in 2 dimensions; equilibrium of a particle under coplanar forces.

The idea

Newton’s third law: if A exerts a force on B, B exerts an equal and opposite force on A; these act on different bodies. For a particle in equilibrium, the resultant force is zero: resolve forces in two perpendicular directions and set sum of components to zero. For motion in a straight line, use F = ma along the direction of motion. Resolve forces into components using trigonometry (e.g., F cos θ, F sin θ). For smooth pulleys and connected particles, treat the system as a whole or separately, noting tension is the same throughout a light inextensible string over a smooth pulley. Example: two masses connected over a pulley; write equations for each mass and solve for acceleration and tension. Coplanar forces can be represented as 2D vectors; equilibrium requires vector sum zero.

What earns the marks

• State Newton’s third law correctly: forces come in pairs, equal in magnitude, opposite in direction, acting on different bodies.
• For equilibrium, resolve forces in two perpendicular directions and set the sum of components in each direction to zero.
• For motion, apply F = ma along the direction of motion; if forces are at angles, resolve first.
• For connected particles over a smooth pulley, the tension is the same on both sides of the pulley and the acceleration magnitude is the same for both particles (if string is inextensible).
• Resolve forces using F cos θ and F sin θ, where θ is the angle to the chosen axis; ensure correct signs.

Common mistakes and how to put them right

• Applying Newton’s third law to forces on the same body.

  Put it right: Third-law pairs act on different bodies; for example, weight of a book on a table and the normal force from the table on the book are not a third-law pair (they act on the same body).

• Forgetting to resolve forces when they are not along the axes.

  Put it right: Resolve into two perpendicular directions before summing.

• Assuming tension is different on each side of a smooth pulley.

  Put it right: For a light inextensible string over a smooth pulley, tension is the same throughout.

Exam tips

• Draw a clear diagram showing all forces acting on each particle; label angles and directions.
• For connected particles, write separate equations for each particle and solve simultaneously; check the direction of acceleration for each.
• When resolving, choose axes that simplify the problem (e.g., along the direction of motion and perpendicular to it).