# Moments, Levers and Gears

## Moments, Levers and Gears Revision

**Moments, Levers and Gears**

Objects rotate due to the **turning effect** of the force that is acting on them. The magnitude of the** turning effect **depends on the **f****orce** and the** distance** from the pivot that this force is applied. This** turning effect** is called a **moment**.

**Moments**

Force or multiple forces acting on an object about a pivot could cause the object to rotate. The **moment **of this force is its turning effect.

The **moment **of a force is given by the following equation:

\textcolor{aa57ff}{\text{Moment} = \text{Force} \times \text{distance}}

and you may see this written as:

\textcolor{aa57ff}{M = Fd}

- \textcolor{aa57ff}{M} is the
**moment**of the force in**Newton-metres**, \left(\text{Nm}\right) - \textcolor{aa57ff}{F} is the
**force**in**Newtons**, \left(\text{N}\right) - \textcolor{aa57ff}{d} is the
**perpendicular****distance**from the pivot to the line of action of the force in**metres**, \left(\text{m}\right).

Therefore if the force or distance from the pivot is large, the **moment** (turning effect) is larger.

For the largest possible **moment**, the force must be applied at a **right angle** to the object.

If an object is **balanced** and is stationary, this means that the **total clockwise moment** about the pivot is equal to the **total anticlockwise moment**. It will not turn.

An example of a **moment** in action is when a spanner is used to turn a nut. The nut is the pivot, and the force is applied onto the handle of the spanner. A shorter spanner would mean a reduced turning effect, so it would require more force to turn.

**Levers and Gears**

**Levers**

If we want to decrease the **force** needed, then we can increase the **distance** from the pivot. Levers are used for this purpose.

By adding a long lever to a system, the **distance** from the pivot increases, and therefore less **force** is required for the **turning effect**.

An example of a lever is the long handles on a wheel barrow. These long handles increase the distance between you and the pivot (the wheel), meaning less **force** is required for the turning effect. This makes lifting the wheelbarrow a lot easier.

**Gears**

Gears are used to transmit the **rotational effect** of a force. The teeth of the gears in a gear system will interlock, meaning that one gear will cause the next to turn, but in the opposite direction.

The** moment **can be increased or decreased depending on the size of the gears. If a bigger gear transmits a force to a smaller gear, the** moment **is decreased, because in the smaller gear the **distance to the pivot** (centre of the gear) is less.

**Example: Calculating Moments**

Two masses are placed on a surface on a pivot. The surface is balanced. Calculate the distance **𝑥.**

**[3 marks]**

The question says the surface is balanced. Therefore we know that the moments should be equal:

\text{Total anticlockwise moment = Total clockwise moment}

M = Fd

F_{1} \times d_{1} = F_{2} \times d_{2}

We can **rearrange **this equation:

d_1 = \dfrac{F_{2} \times d_{2}}{F_1}

x = d_1 = \dfrac{\textcolor{00d865}{8\: \text{N}} \times \textcolor{10a6f3}{20 \: \text{m}}}{\textcolor{aa57ff}{25 \: \text{N}}}

x = \dfrac{160 \: \text{Nm}}{\textcolor{aa57ff}{25 \: \text{N}}} = 6.4 \: \text{m}

## Moments, Levers and Gears Example Questions

**Question 1**: A spanner is used to turn a nut. Calculate the moment of the system.

**[2 marks]**

\begin{aligned} M &= Fd \\ M &= 6 \: \text{N} \times 0.5 \: \text{m} \\ M &= \bold{3} \: \textbf{Nm} \end{aligned}

**Question 2**: A beam is being held up by a rope. The tension in the rope is 13 \: \text{N}. There is also a mass on the beam that weighs 45 \:\text{N}.

Calculate the moment of the system.

**[3 marks]**

The moments are not balanced because they are acting in the same direction (clockwise).

\begin {aligned} \text{Total moment} &= F_{1} \times d_{1} + F_{2} \times d_{2} \\ \text{Total moment} &= 13 \: \text{N }\times 6 \: \text{m} + 45 \: \text{N} \times 1 \: \text{m} \\ \textbf{Moment} &= \bold{123} \: \textbf{Nm} \end{aligned}

**Question 3**: Explain why it advantageous to use a gear system where a smaller gear transmits force to a larger gear.

**[2 marks]**

The larger gear has a larger radius, so the **distance to the pivot is larger**. The same force is transmitted and so the **moment increases**.