A-Level mechanics connects motion, forces, energy, and momentum using a small set of powerful formulas. This cheat sheet helps students choose the right equation quickly and understand when each formula applies. It is especially useful for revision, problem solving, and checking units in exam questions.
The annotated structure keeps the most common mechanics relationships easy to compare.
Key Facts
- For constant acceleration, the SUVAT equations are , , , and .
- Newton’s second law states that resultant force is , where is in newtons, is in kilograms, and is in .
- Weight is the gravitational force on a mass and is given by , where near Earth’s surface.
- Momentum is , and conservation of momentum means when no external resultant force acts.
- Impulse equals change in momentum, so for a constant force.
- Work done by a constant force is , and kinetic energy is .
- For circular motion at constant speed, centripetal acceleration is and centripetal force is .
- The moment of a force about a pivot is , where is the perpendicular distance from the pivot to the line of action of the force.
Vocabulary
- Displacement
- Displacement is the vector distance from an object’s starting position to its final position.
- Acceleration
- Acceleration is the rate of change of velocity, given by .
- Resultant Force
- Resultant force is the single overall force that has the same effect as all forces acting together.
- Momentum
- Momentum is the product of mass and velocity, given by .
- Impulse
- Impulse is the product of force and time and equals the change in momentum, .
- Moment
- A moment is the turning effect of a force about a pivot, calculated using .
Common Mistakes to Avoid
- Using SUVAT when acceleration is not constant is wrong because equations such as assume a fixed value of throughout the motion.
- Treating velocity and speed as the same quantity is wrong because velocity has direction, so signs such as can change the answer.
- Forgetting to resolve forces into components is wrong because Newton’s law must be applied along a chosen direction, such as or .
- Using mass instead of weight in force diagrams is wrong because mass is measured in kilograms but weight is a force given by in newtons.
- Calculating a moment with the wrong distance is wrong because uses the perpendicular distance from the pivot to the force’s line of action.
Practice Questions
- 1 A car accelerates uniformly from to in . Find its acceleration and displacement.
- 2 A object is pulled by a horizontal resultant force of . Find its acceleration using .
- 3 A ball moving at is brought to rest in . Find the average force on the ball.
- 4 Explain why momentum is conserved in a collision only when the total external resultant force on the system is zero.
Understanding A-Level Mechanics Formula Sheet Annotated
Most mechanics errors begin before any calculation. Start by choosing a positive direction and keep it throughout the question. A velocity can be negative because it has direction.
A speed cannot be negative. Displacement is the change in position, while distance is the total path length. The same distinction matters for acceleration and deceleration.
Draw a simple motion sketch and label the known quantities with units. SUVAT only works when acceleration stays constant. It is not suitable for a car moving through changing traffic or an object falling with significant air resistance.
For force problems, draw a free body diagram for one object at a time. Include only forces acting on that object. Common forces are weight, normal contact force, tension, friction, drag, thrust, and lift.
Weight always acts vertically downward near Earth. The normal contact force acts at right angles to a surface, not necessarily vertically upward. Resolve forces into directions parallel and perpendicular to a slope before using Newton’s second law.
A stationary object has zero resultant force, but individual forces may still be large. This is why a book can rest on a table without moving.
Energy methods can simplify a problem when the route taken does not matter. A falling object loses gravitational potential energy and gains kinetic energy. If air resistance acts, some energy becomes internal energy in the air and object.
Energy is still conserved overall, though not all of it remains useful mechanical energy. Power describes how quickly energy is transferred. This matters for electric motors, cyclists climbing hills, and cranes lifting loads.
Check whether a force acts in the same direction as motion. Only the component along the displacement does work. A force at right angles to the motion transfers no energy through work.
Momentum is especially useful in short collisions and explosions. Treat the interacting objects as one system, then identify external forces. During a brief impact, external impulses are often small enough to ignore.
Momentum can then be conserved even when kinetic energy is not. This explains why vehicles can crumple in a crash. Increasing the stopping time reduces the average force for the same change in momentum.
In circular motion, the inward resultant force changes direction continuously. It is not an extra force added to the diagram. It may be supplied by friction on a bend, tension in a string, gravity in an orbit, or a normal contact force.
For moments, use the shortest perpendicular distance to the force’s line of action. A long lever can produce a large turning effect with a modest force, which is the principle behind spanners, door handles, and balanced beams.