R: Forces and Newton’s laws: Understand and use Newton’s second law for motion in a straight line (restricted to forces in two perpendicular directions or simple cases of forces given as 2D vectors); extend to situations where forces need to be resolved (restricted to 2 dimensions).

The idea

Newton's second law states that the resultant force on an object is equal to its mass times acceleration: F = ma. For motion in a straight line, you resolve forces along the direction of motion and perpendicular to it. In two perpendicular directions, apply F = ma independently in each direction. For example, a block on a rough horizontal surface: vertically, normal reaction balances weight; horizontally, applied force minus friction equals mass times acceleration. If forces are given as 2D vectors, add them to find the resultant, then use F = ma. When forces act at angles, resolve into components using trigonometry. Always define a positive direction, draw a free-body diagram, and check units. This law connects force, mass and acceleration and is fundamental to dynamics.

What earns the marks

• States Newton's second law as F = ma, where F is the resultant force.
• Resolves forces into two perpendicular directions, typically parallel and perpendicular to motion.
• Applies F = ma independently in each direction, recognising that acceleration perpendicular to motion may be zero.
• Adds forces given as 2D vectors to find the resultant force before using F = ma.
• Uses trigonometry to resolve forces at angles into components.
• Solves problems involving motion in a straight line with forces in two perpendicular directions.

Common mistakes and how to put them right

• Using the applied force instead of the resultant force in F = ma.

  Put it right: Calculate the vector sum of all forces first.

• Forgetting to resolve forces at angles into components.

  Put it right: Draw a diagram and use sin/cos to find horizontal and vertical components.

• Mixing up mass and weight in the equation.

  Put it right: Use mass in kilograms for m, and weight (mg) as a force if needed.

Exam tips

• Draw a clear free-body diagram with all forces labelled and a defined positive direction.
• Write down the equation F = ma for each direction separately, showing the resultant force as a sum of components.
• Check that all forces are in newtons and mass in kilograms before calculating acceleration.