# Forces, density and pressure

> CIE A-Level Physics · CIE 9702
> Source: https://www.owlsprep.com/study/cie-9702-u4-overview/
> Weight: n/a

This unit introduces core concepts of force interactions, static equilibrium, and fluid properties, forming the foundation for all subsequent mechanics topics in A-Level Physics.

**Prerequisites:** [Basic kinematics and SI unit conventions](https://www.owlsprep.com/study/cie-9702-u3-overview/)

## Learning objectives

- Identify and classify common forces acting on mechanical systems and draw accurate free-body diagrams
- Apply equilibrium conditions to solve for unknown forces in static rigid body systems
- Calculate moments and torques, and apply the principle of moments to rotational equilibrium problems
- Define and calculate density, and solve for pressure in static fluid systems

## Unit at a Glance

We build this unit incrementally: starting with the basics of identifying individual forces, moving on to translational and rotational equilibrium, then ending with core properties of fluids. Each sub-topic builds on the previous to give you a complete toolkit for solving static mechanics problems.

Mastery of these concepts is required for almost all higher-level mechanics topics, including circular motion, gravitation, and fluid dynamics that you will cover later in the syllabus.

This unit is split into 5 connected sub-topics:
- [Common force types](https://www.owlsprep.com/study/cie-9702-u4-common-force-types/) — Learn to identify, define and draw free-body diagrams for all common force types encountered in mechanics.
- [Force equilibrium](https://www.owlsprep.com/study/cie-9702-u4-force-equilibrium/) — Understand and apply the conditions for translational equilibrium of rigid bodies in 1 and 2 dimensions.
- [Moment and torque](https://www.owlsprep.com/study/cie-9702-u4-moment-and-torque/) — Calculate moments of forces and use the principle of moments to solve rotational equilibrium problems.
- [Density](https://www.owlsprep.com/study/cie-9702-u4-density/) — Define density and use its relationship to mass and volume to solve basic and composite object problems.
- [Fluid pressure](https://www.owlsprep.com/study/cie-9702-u4-fluid-pressure/) — Derive and use the hydrostatic pressure equation for static fluids, and relate pressure to applied force.

## Common pitfalls

- **Wrong:** Forgetting that weight acts at the center of mass when calculating moments
  - Why it fails: This leads to incorrect moment arm values and wrong solutions for equilibrium problems
  - Correct: Always mark the weight force at the center of mass of an object unless explicitly stated otherwise
- **Wrong:** Confusing gauge pressure and absolute pressure in hydrostatic problems
  - Why it fails: Many exam questions expect absolute pressure (including atmospheric pressure) unless stated otherwise
  - Correct: Always read the question carefully to confirm which type of pressure you are required to calculate

## Cheatsheet

| Concept | Key Formula/Relationship |
| --- | --- |
| Pressure from force | $P = \frac{F}{A}$ |
| Density | $\rho = \frac{m}{V}$ |
| Moment of force | $M = F \times d_\perp$ |
| Translational equilibrium | Net force = $0$ in all directions |
| Principle of moments | Sum of clockwise moments = Sum of anticlockwise moments |
| Hydrostatic pressure | $P = P_0 + \rho g h$ |

## What's next

Begin your study of this unit with the first sub-topic on common force types, where you will learn to correctly identify and represent forces in free-body diagrams, the starting point for all mechanics problems. Once you complete all sub-topics in this unit, you can move on to the next unit covering work, energy and power.

- [Common force types](https://www.owlsprep.com/study/cie-9702-u4-common-force-types/)
- [Work, Energy and Power Unit Overview](https://www.owlsprep.com/study/cie-9702-u5-overview/)
- [Force equilibrium](https://www.owlsprep.com/study/cie-9702-u4-force-equilibrium/)

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