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In mechanics and mathematical modelling, various idealised objects are used to simplify real-world scenarios. These terms describe the objects and their properties, allowing complex systems to be analysed more easily.

A **particle** is an object with mass but no size or shape. This assumption simplifies problems by neglecting rotational effects and treating all forces as acting on a single point.

- No dimensions — considered a point mass.
- Forces such as friction and air resistance are often ignored.

A **rod** is an object with length but no thickness, and it is usually assumed to be rigid.

- One-dimensional — has length but no width or depth.
- Cannot bend or stretch (assumed to be perfectly rigid).
- Examples include beams, poles, or thin bars.

A **lamina** is a two-dimensional flat object with mass but negligible thickness.

- Has area but no thickness.
- Mass is distributed evenly across its surface.
- Examples include thin sheets or plates.

A **uniform body** has mass distributed evenly throughout its volume or area.

- Mass is assumed to be consistent in all parts.
- The centre of mass is at the geometric centre of the object.

A **non-uniform body** has mass that is not distributed evenly, meaning certain parts are heavier or lighter.

- The centre of mass is not necessarily at the geometric centre.
- Mass distribution can vary across the object.

A **light object** is an object with negligible mass compared to other elements of the system, allowing it to be ignored in calculations involving forces.

- Mass is considered negligible (approximated as zero).
- Often used for strings, pulleys, or wires in problems.

An **inextensible string** is a string that does not stretch under tension.

- Constant length, regardless of forces applied.
- Used in problems involving tension, such as pulley systems.

A **smooth surface** assumes no friction between the object and the surface.

- Negligible resistance to motion across the surface.
- Friction is ignored in calculations.

A **rough surface** includes friction between the object and the surface.

- Opposes motion and slows down moving objects.
- Frictional forces must be considered in calculations.

A **wire** is a thin, rigid length of material that can be modelled like a rod or a string, depending on the context.

- Thin, one-dimensional object.
- Can be smooth or rough depending on the problem.

A **bead** is a particle that can move freely along a wire or string without friction.

- Moves along a wire or string.
- Often assumed to have negligible friction with the wire.

A **peg** is a fixed point used in problems where an object, like a string or rod, is hung or pivoted.

- Can be smooth (no friction) or rough (with friction).
- Used to analyse rotational motion or tension in strings.

In most models, **gravity** is treated as a constant force acting vertically downward with an acceleration of:

\[g \approx 9.8 \, \text{ms}^{-2}\]

- Force due to gravity acts on the mass of an object.
- In many problems, air resistance is neglected, simplifying the motion under gravity.

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