Mechanics
Understand how objects move, interact and exchange energy through the language of physics.
The Physics of Motion
Mechanics describes the motion of objects and the forces responsible for changing that motion. It forms one of the mathematical foundations of physics.
Motion is described using quantities such as displacement, velocity and acceleration, while forces explain how and why motion changes.
Scalars & Vectors
Physical quantities can be classified as scalars or vectors.
Scalars
A scalar has magnitude only.
- Mass
- Time
- Distance
- Speed
- Energy
- Temperature
Vectors
A vector has both magnitude and direction.
- Displacement
- Velocity
- Acceleration
- Force
- Momentum
Distance is scalar while displacement is vector. Speed is scalar while velocity is vector.
Motion
Displacement
Displacement is the vector change in position of an object.
Velocity
Velocity is the rate of change of displacement.
Acceleration
Acceleration is the rate of change of velocity.
Motion Graphs
- Gradient of displacement-time graph = velocity.
- Gradient of velocity-time graph = acceleration.
- Area under velocity-time graph = displacement.
A car increases its velocity from 8 m s⁻¹ to 20 m s⁻¹ in 4 seconds. Find its acceleration.
a = (20 − 8) / 4
a = 3 m s⁻²
Constant Acceleration
The SUVAT equations describe motion with constant acceleration.
u = initial velocity • v = final velocity • a = acceleration • s = displacement • t = time
Forces
A force is an interaction that can change the motion or shape of an object.
Newton's Laws
Newton's First Law states that an object remains at rest or continues moving with constant velocity unless acted upon by a resultant external force.
Newton's Second Law relates resultant force to acceleration for constant mass.
Newton's Third Law states that interacting bodies exert equal and opposite forces on each other.
Free-Body Diagrams
A free-body diagram shows the forces acting on an object. Always identify the direction and nature of each force.
Moments
The moment of a force measures its turning effect about a point or axis.
Equilibrium
A 20 N force acts perpendicular to a beam at a distance of 0.5 m from a pivot.
Moment = 20 × 0.5
Moment = 10 N m
Momentum
Momentum is a vector quantity associated with the motion of an object.
Conservation
In an isolated system, total momentum remains constant.
Work, Energy & Power
Energy cannot be created or destroyed. It can only be transferred between different forms.
Materials
Explore how matter responds to forces, deformation and energy storage.
Density
Density is the mass per unit volume of a material.
SI unit: kg m⁻³.
A material has a mass of 0.80 kg and a volume of 2.0 × 10⁻⁴ m³.
ρ = 0.80 / (2.0 × 10⁻⁴)
ρ = 4000 kg m⁻³
Deformation
When a force is applied to an object, it may change its shape.
Elastic
Elastic deformation is reversible when the deforming force is removed.
Plastic
Plastic deformation produces a permanent change in shape.
Beyond the elastic limit, removing the force does not return the material completely to its original shape.
Hooke's Law
Within the limit of proportionality, extension is proportional to applied force.
The limit of proportionality and elastic limit are different concepts and are not necessarily at the same point.
Stress, Strain & Young Modulus
Young modulus measures the stiffness of a material.
A wire has a cross-sectional area of 2.0 × 10⁻⁶ m² and experiences a force of 50 N.
Stress = 50 / (2.0 × 10⁻⁶)
Stress = 2.5 × 10⁷ Pa
Elastic Strain Energy
Work done in stretching a spring or wire can be stored as elastic strain energy.
The area under a force-extension graph represents elastic energy stored.
Practical Physics
Experimental planning, measurement, analysis and evaluation.
Free Fall
Investigate motion under gravity and determine acceleration using suitable measurements or graphs.
- Measure time and distance carefully.
- Repeat measurements.
- Consider reaction time.
- Analyse suitable graphs.
Viscosity
Investigate the motion of a sphere through a fluid and determine its behaviour at terminal velocity.
- Allow terminal velocity.
- Measure distance and time.
- Control temperature.
- Repeat measurements.
Young Modulus
Load a wire gradually while measuring extension and determine Young modulus from experimental data.
- Measure original length.
- Measure diameter at several points.
- Calculate cross-sectional area.
- Plot appropriate graphs.
When evaluating an experiment, explain precisely what a suggested improvement changes and why it improves the quality of the measurement.
Measurements & Uncertainties
Experimental measurements always contain some degree of uncertainty.
Percentage Uncertainty
Reducing Uncertainty
- Repeat measurements.
- Calculate a mean where appropriate.
- Use suitable-resolution instruments.
- Increase the measured quantity where possible.
- Control relevant variables.
Mechanics Calculation
A 2.0 kg object accelerates from rest to 6.0 m s⁻¹ in 3.0 s. Calculate the resultant force.
a = (6.0 − 0) / 3.0
a = 2.0 m s⁻²
F = ma
F = 2.0 × 2.0
F = 4.0 N
Unit 1 Practice
Activate each solution only after attempting the question.
REVEAL ANSWER
A scalar has magnitude only, whereas a vector has both magnitude and direction.
REVEAL ANSWER
a = (30 − 12) / 6
a = 3.0 m s⁻²
REVEAL ANSWER
F = ma
a = 20 / 5.0
a = 4.0 m s⁻²
REVEAL ANSWER
Moment = 15 × 0.40
Moment = 6.0 N m
REVEAL ANSWER
In an isolated system, total momentum before an interaction equals total momentum after it.
REVEAL ANSWER
ρ = m / V
ρ = 0.60 / (3.0 × 10⁻⁴)
ρ = 2.0 × 10³ kg m⁻³
REVEAL ANSWER
Within the limit of proportionality, extension is proportional to applied force.
REVEAL ANSWER
Stress = F / A
Stress = 80 / (4.0 × 10⁻⁶)
Stress = 2.0 × 10⁷ Pa
REVEAL ANSWER
Elastic deformation is reversible when the force is removed, whereas plastic deformation produces a permanent change.
REVEAL ANSWER
Repeated measurements help identify random variation and allow a mean to be calculated, improving reliability.
Unit 1 Equation Matrix
Rapid-access equation reference.