Newton's law (A-level only) — AQA A-Level Physics

Newton's laws of motion are three fundamental principles that describe the relationship between the motion of an object and the forces acting on it. They are essential for understanding dynamics, from simple collisions to rocket propulsion, and form the basis for analysing systems in equilibrium and non-equilibrium. At A-level, you must apply these laws quantitatively using F = ma and F = dp/dt, and qualitatively to explain phenomena such as terminal velocity and weightlessness.

This topic is crucial because it underpins nearly all of mechanics, including momentum, circular motion, and oscillations. It also develops your ability to draw free-body diagrams, resolve forces, and handle variable mass problems. Mastery of Newton's laws is essential for tackling synoptic questions and practical applications in AQA A-level Physics.

• →Newton's first law: An object remains at rest or moves with constant velocity unless acted upon by a resultant force. This introduces the concept of inertia and inertial frames.
• →Newton's second law: The resultant force on an object is directly proportional to the rate of change of momentum, and acts in the same direction. For constant mass, F = ma; for variable mass, F = dp/dt.
• →Newton's third law: If object A exerts a force on object B, then B exerts an equal and opposite force on A. These forces are of the same type, act on different bodies, and do not cancel.
• →Free-body diagrams: Represent all forces acting on a single object as arrows from a point, showing direction and relative magnitude. Essential for resolving forces and applying F = ma.
• →Equilibrium: When the resultant force and resultant moment on an object are zero, it is in equilibrium (either at rest or moving with constant velocity).

• State that gravity acts between any two masses and is always attractive.
• Use Newton's law of gravitation F = Gm₁m₂/r² to calculate the force between two point masses or uniform spheres.
• Explain that the force acts along the line joining the centres of mass and is an example of an inverse-square law.
• Recognise that the force on each mass is equal in magnitude and opposite in direction, consistent with Newton's third law.
• Apply the law to astronomical situations, such as calculating the force between a planet and its moon, using consistent SI units.

• 💡Write the equation F = Gm₁m₂/r² before substituting values, and show the square of the distance explicitly.
• 💡Check that masses are in kg and distance in m; convert km to m by multiplying by 10³.
• 💡When comparing gravitational forces, calculate both values and state the ratio or difference clearly.
• 💡Always draw a clear free-body diagram before attempting calculations. Label all forces and choose a positive direction. This helps avoid sign errors and ensures you include all forces.
• 💡When explaining Newton's third law, explicitly state that the forces act on different bodies and are of the same type. Use the phrasing 'the force of A on B' and 'the force of B on A'.
• 💡For variable mass problems, use F = dp/dt rather than F = ma. Remember that momentum p = mv, so dp/dt = m(dv/dt) + v(dm/dt). This is common in rocket propulsion questions.

• Treating gravity as a contact force or as acting only near large planets; correction: gravity acts at a distance between all masses, however small.
• Using the distance between surfaces rather than between centres of mass; correction: for uniform spheres, r is the centre-to-centre distance.
• Forgetting to square r or using r in km without converting to m; correction: use r² in metres and keep all quantities in SI units.
• Students often think that a constant force is required to keep an object moving at constant speed. In reality, a resultant force causes acceleration; constant velocity requires zero resultant force.
• Many believe that action and reaction forces cancel out. They do not, because they act on different objects. Only forces on the same object can be summed to find the resultant.
• Students sometimes assume that mass and weight are the same. Mass is a scalar measure of inertia (kg), while weight is a force (N) due to gravity, W = mg.

1. 1Day 1-2: Review the three laws and their definitions. Learn the precise statements and be able to give examples. Practice drawing free-body diagrams for various scenarios (e.g., object on incline, lift, connected masses).
2. 2Day 3-4: Master Newton's second law in both forms: F = ma and F = dp/dt. Solve problems involving constant mass (e.g., car accelerating, lift moving) and variable mass (e.g., rocket, conveyor belt).
3. 3Day 5-6: Focus on Newton's third law and equilibrium. Practice identifying third law pairs and distinguishing them from balanced forces. Solve equilibrium problems using resolving forces.
4. 4Day 7-8: Attempt exam-style questions, especially those involving multiple concepts (e.g., momentum and Newton's laws). Review mark schemes to understand what examiners expect.
5. 5Day 9-10: Consolidate with a mixed problem set. Create a summary sheet of key formulas and common pitfalls. Test yourself with active recall questions.

• 📋Calculation of resultant force or acceleration using F = ma: Often involves resolving forces or dealing with connected masses. Advice: draw a diagram, resolve forces, and apply F = ma to the whole system or individual masses.
• 📋Explanation of Newton's third law in a given context: e.g., explain the forces between a rocket and its exhaust gases. Advice: name the two bodies, state the type of force, and emphasise they act on different bodies.
• 📋Variable mass problems: e.g., rocket propulsion or fuel consumption. Advice: use F = dp/dt, and remember to include the rate of change of mass.
• 📋Equilibrium problems: e.g., a sign hanging from two cables. Advice: resolve forces horizontally and vertically, set resultant to zero, and solve simultaneous equations.