A-Level Physics: Mechanics Revision Guide with Worked Examples

Mechanics forms the foundation of A-Level Physics, introducing concepts and mathematical approaches that underpin much of the course. Understanding forces, motion, energy, and momentum thoroughly gives you a solid platform for more advanced topics. Here’s your comprehensive mechanics revision guide.

Motion and Kinematics

Kinematics describes how objects move without considering what causes the motion. Master these fundamentals first.

Displacement (s) is distance in a particular direction—a vector quantity measured in metres. Velocity (v) is the rate of change of displacement (m/s). Acceleration (a) is the rate of change of velocity (m/s²).

The SUVAT equations govern motion with constant acceleration:

• v = u + at
• s = ut + ½at²
• v² = u² + 2as
• s = ½(u + v)t

Where: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time.

Choosing the right equation depends on which quantities you know and which you’re finding. If you don’t have time (t), use v² = u² + 2as. If you don’t have final velocity (v), use s = ut + ½at².

Displacement-time graphs: The gradient gives velocity. Curved lines indicate acceleration. Horizontal lines mean stationary.

Velocity-time graphs: The gradient gives acceleration. The area under the curve gives displacement. Straight lines indicate constant acceleration.

Worked Example: Free Fall

A ball is dropped from rest from a height of 45m. Calculate: (a) the time taken to hit the ground, (b) the final velocity.

Given: u = 0 m/s (dropped from rest), s = 45m, a = 9.81 m/s² (gravity)

(a) Using s = ut + ½at²: 45 = 0 + ½(9.81)t² 45 = 4.905t² t² = 9.17 t = 3.03s

(b) Using v = u + at: v = 0 + 9.81 × 3.03 v = 29.7 m/s

Forces and Newton’s Laws

Newton’s Three Laws govern how forces affect motion.

Newton’s First Law: An object remains at rest or moves with constant velocity unless acted upon by a resultant force. This is about inertia—objects resist changes in motion.

Newton’s Second Law: F = ma (Force = mass × acceleration). The resultant force on an object equals its mass multiplied by its acceleration. Force is measured in Newtons (N).

Newton’s Third Law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. These pairs act on different objects.

Resolving Forces

When multiple forces act on an object, calculate the resultant by resolving into components.

For a force F at angle θ to the horizontal:

• Horizontal component: Fcosθ
• Vertical component: Fsinθ

If the resultant force is zero, the object is in equilibrium (stationary or moving at constant velocity).

Worked Example: Forces on a Slope

A 5kg block sits on a 30° slope. Calculate the component of weight acting down the slope and the normal reaction force. (g = 9.81 m/s²)

Weight W = mg = 5 × 9.81 = 49.05N (acting vertically downwards)

Component down slope = Wsin30° = 49.05 × 0.5 = 24.5N

Normal reaction N = Wcos30° = 49.05 × 0.866 = 42.5N

The normal reaction acts perpendicular to the slope, balancing the component of weight perpendicular to the slope.

Energy and Work

Work done (W) is energy transferred when a force moves an object: W = Fs cosθ, where F is force, s is displacement, and θ is the angle between force and displacement.

When force and displacement are parallel, W = Fs. Work is measured in Joules (J).

Kinetic energy (KE) is energy due to motion: KE = ½mv². A moving object can do work when it stops.

Gravitational potential energy (GPE) is energy due to position in a gravitational field: GPE = mgh, where h is height above a reference point.

Principle of conservation of energy: Energy cannot be created or destroyed, only transferred between forms. In mechanics, total energy (KE + PE + heat + sound) remains constant.

Worked Example: Energy Conservation

A 2kg ball is thrown upwards with initial velocity 15 m/s. Calculate the maximum height reached.

Initial KE = ½mv² = ½ × 2 × 15² = 225J

At maximum height, all KE converts to GPE (velocity = 0).

GPE = mgh 225 = 2 × 9.81 × h h = 225/(2 × 9.81) = 11.5m

Momentum

Momentum (p) is mass × velocity: p = mv. It’s a vector quantity measured in kg m/s.

Principle of conservation of momentum: In a closed system with no external forces, total momentum before an interaction equals total momentum after.

This applies to collisions and explosions. For two objects: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where u represents initial velocities and v represents final velocities.

Impulse is change in momentum: Impulse = Δp = FΔt. A force applied over time changes momentum.

Elastic vs Inelastic Collisions

Elastic collisions conserve both momentum and kinetic energy. Objects bounce apart.

Inelastic collisions conserve momentum but not kinetic energy. Some KE converts to heat/sound. Objects may stick together (perfectly inelastic).

Worked Example: Collision

A 1000kg car travelling at 20 m/s collides with a stationary 1500kg car. They stick together. Calculate their combined velocity after collision.

Before: p = m₁u₁ + m₂u₂ = (1000 × 20) + (1500 × 0) = 20000 kg m/s

After: p = (m₁ + m₂)v = 2500v

By conservation of momentum: 20000 = 2500v v = 8 m/s

Moments and Equilibrium

A moment is the turning effect of a force: Moment = Force × perpendicular distance from pivot.

Principle of moments: For an object in equilibrium, sum of clockwise moments equals sum of anticlockwise moments about any point.

A couple is a pair of equal, opposite, parallel forces producing a turning effect without translation. Torque (moment of a couple) = Force × perpendicular distance between forces.

Worked Example: Balanced Beam

A 3m uniform beam of weight 100N is supported at its centre. A 40N weight hangs 1m from the left end. Where must a 60N weight hang to balance the beam?

Taking moments about the centre:

Clockwise moments = 40 × 1 = 40 Nm

Anticlockwise moments = 60 × d (where d is distance from centre)

For equilibrium: 40 = 60d d = 0.67m from centre (to the right)

Density and Pressure

Density ρ = mass/volume (kg/m³)

Pressure P = Force/Area (Pascals or N/m²)

Pressure in fluids increases with depth: P = ρgh, where ρ is fluid density, g is gravitational field strength, h is depth.

Common Mistakes in Mechanics

Confusing mass and weight. Mass (kg) is quantity of matter. Weight (N) is gravitational force on that mass: W = mg.

Sign errors with vectors. Define a positive direction and stick to it. Motion in the opposite direction is negative.

Using the wrong SUVAT equation. Identify what you know and what you need to find, then choose appropriately.

Forgetting to resolve forces. On slopes or when forces act at angles, resolve into components.

Mixing up elastic and inelastic collisions. Remember: momentum always conserves, KE only conserves in elastic collisions.

Unit inconsistencies. Always work in SI units: metres, kilograms, seconds, Newtons. Convert before calculating.

UpGrades provides extensive mechanics practice with instant feedback on your working, helping you identify exactly where errors occur and build the problem-solving fluency A-Level Physics demands.