Moments & Machines

Moments & Machines 🔧

Push a door near its hinge and it barely moves; push near the handle and it swings easily. Same force, very different results — because turning depends on **where** you push. That turning effect is called a **moment**, and it is the secret behind levers, spanners and gears.

The moment of a force 🔩

The **moment** of a force is its **turning effect** about a **pivot**: **M = F d** where M is the moment in **newton-metres (Nm)**, F is the force in newtons, and d is the **perpendicular distance from the pivot** to the line of the force.

Find the moment

An interactive activity.

Levers 🔨

A **lever** uses a moment to make a job easier. Applying the same force **further from the pivot** gives a **bigger moment**. That is why a long spanner undoes a stiff bolt more easily than a short one, and why door handles are fitted far from the hinges. Levers are **force multipliers**.

The long spanner

Why is it easier to undo a tight bolt with a long spanner than with a short one?

• The greater distance from the pivot gives a bigger moment for the same force
• A long spanner automatically applies a much bigger force
• A long spanner is heavier, so it pushes harder
• The length makes no difference to the turning effect

The principle of moments ⚖️

When an object is **balanced** — not turning — the **principle of moments** applies: **total clockwise moment = total anticlockwise moment** (about the pivot). A balanced seesaw obeys this, and you can use it to find an unknown force or distance.

Solving a balance problem

An interactive activity.

Balance the seesaw

An interactive activity.

Find the distance

An interactive activity.

Gears ⚙️

**Gears** are toothed wheels that transmit the turning effect of a force from one wheel to another. A **larger gear** turns **more slowly** but with a **greater moment** (turning effect); a **smaller gear** turns faster with less. Two meshed gears always turn in **opposite directions**.

Levers and gears

Select ALL THREE statements about levers and gears that are TRUE.

• A longer lever gives a bigger moment for the same force
• A larger gear turns more slowly but with a greater turning effect
• Two meshed gears turn in opposite directions
• A shorter lever gives a bigger moment
• A larger gear turns faster than a smaller one
• Two meshed gears always turn the same way

Match each term to its meaning

Machines summary

The moment of a force is its turning effect: M = F _____, measured in newton-metres. A longer lever gives a _____ moment for the same force. When an object is balanced, the total clockwise moment equals the total _____ moment. Two meshed gears turn in _____ directions.