Forces and moments
Identify the forces on a body, apply Hooke's law, calculate moments and the torque of a couple, and use the two conditions for equilibrium.
Before you begin
A force can change how a body moves, and it can also turn it. The lessons start with the forces that act on a body, from fields and from contact, and the force of a stretched spring. They then turn to moments and couples, and finish with the two conditions a body needs to stay in equilibrium.
Be comfortable with: resolving vectors into components, because most equilibrium problems are solved by resolving forces.
Learning goals
- Describe the forces on a mass, a charge and a current-carrying conductor in gravitational, electric and magnetic fields.
- Describe normal, frictional, buoyant and viscous forces qualitatively.
- Apply Hooke's law within the limit of proportionality.
- Apply moments, couples and force-and-torque equilibrium using free-body diagrams and vector triangles.
- Treat the weight of a body as acting at a single point, its centre of gravity
- Apply the principle of moments to new situations and problems
- Explain inertia and momentum, then apply Newton's laws using free-body diagrams.
Syllabus statements covered
- describe the forces on a mass, charge and current-carrying conductor in gravitational, electric and magnetic fields, as appropriate
- show a qualitative understanding of forces including normal force, buoyant force (upthrust), frictional force and viscous force, e.g. air resistance. (knowledge of the concepts of coefficients of friction and viscosity is not required)
- recall and apply Hooke’s law (F = kx, where k is the force constant) to new situations or to solve related problems
- define and apply the moment of a force and the torque of a couple
- show an understanding that a couple is a pair of forces which tends to produce rotation only
- show an understanding that the weight of a body may be taken as acting at a single point known as its centre of gravity
- apply the principle of moments to new situations or to solve related problems
- show an understanding that, when there is no resultant force and no resultant torque, a system is in equilibrium
- use free-body diagrams and vector triangles to represent forces on bodies that are in rotational and translational equilibrium
Lessons
Work through them in order.
Core lessons
- Field and contact forcesDescribe the forces fields exert on mass, charge and current, and the normal force, friction, upthrust and drag on a body.
- Hooke's law and springsApply F = kx within the limit of proportionality, find k from a force–extension graph and combine springs in series and parallel.
- Moments, couples and centre of gravityDefine and calculate the moment of a force and the torque of a couple, and treat weight as acting at the centre of gravity.
- Translational and rotational equilibriumUse the two conditions for equilibrium, with moments, resolved forces and force triangles, to find unknown forces.
Beyond the syllabus
- Buoyancy calculationsCalculate upthrust with Archimedes' principle, the submerged fraction of a floating body and the reading on a support under water.Beyond the syllabus
- Centre-of-mass calculationsCalculate the centre of mass of a set of particles or of a uniform lamina with a piece cut out.Beyond the syllabus
- Stability and topplingUse the line of action of the weight to decide when a tilted body topples, and find the critical angle.Beyond the syllabus
- Coefficient of frictionUse the coefficients of static and kinetic friction, limiting friction and the angle at which a block starts to slide.Beyond the syllabus
- Variable-mass systemsFind rocket thrust and the force needed to change the momentum of a stream of mass.Beyond the syllabus
Practise and check
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Topic reference
Quick reference
| Idea | Relation | Notes |
|---|---|---|
| weight | W = mg | acts at the centre of gravity; g = 9.81 N kg⁻¹ |
| electric force | F = qE | on a charge in an electric field |
| normal force | perpendicular to the surface | not always equal to the weight |
| friction | along the surface | opposes sliding, or the tendency to slide |
| upthrust | upward, from the fluid | fluid pressure is greater on the lower surface |
| viscous force (drag) | opposite the velocity relative to the fluid | grows with speed |
| Hooke’s law | F = kx | x is the extension, not the length; only up to the limit of proportionality |
| moment of a force | F × perpendicular distance | distance from the point to the line of action |
| torque of a couple | one force × perpendicular separation | resultant force zero |
| equilibrium | ∑ F = 0 and ∑ moments = 0 | moments about any point |
Core knowledge to remember
- Forces act between two bodies. On a free-body diagram, draw only the forces on the chosen body.
- The moment of a force about a point is the force multiplied by the perpendicular distance from the point to the line of action of the force.
- A couple is a pair of equal, opposite forces whose lines of action do not coincide. Its resultant force is zero, so it produces rotation only. Its torque is one force multiplied by the perpendicular distance between the lines of action.
- The centre of gravity is the point at which the whole weight of a body may be taken to act.
- Principle of moments: for a body in rotational equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point.
- A body is in equilibrium when there is no resultant force and no resultant torque. Three forces in equilibrium form a closed triangle when drawn head to tail.
Common mistakes
- Drawing both forces of a Newton’s third law pair on the same free-body diagram.
- Using the length of a lever instead of the perpendicular distance to the line of action.
- Using the stretched length of a spring in F = kx instead of the extension.
- Checking that the forces balance but forgetting the moments.
- Accepting a support force that would need a cable to push or a support to pull.