Mechanical Calculations - MA, VR and Gear RPM
Mechanisms multiply force, speed or movement - and the maths says by how much. Learn to calculate mechanical advantage, velocity ratio and the output speed of a gear train, and remember these are ratios with no units.
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The maths of mechanisms ⚙️
A mechanism takes an input force or motion and changes it - making a force bigger, or a speed faster, or turning one movement into another. The **calculations** tell you by exactly how much. This module covers the three you need: **mechanical advantage (MA)**, **velocity ratio (VR)** and the **output speed of a gear train**. A warning up front: all three are **ratios**, so they have **no units**.
The words you need 📐
Four terms run through the calculations.
Match each quantity to its formula 🔗
- Mechanical advantage
- Velocity ratio
- Gear ratio
- Efficiency
- Load divided by effort
- Distance moved by effort divided by distance moved by load
- Driven gear teeth divided by driver gear teeth
- Mechanical advantage divided by velocity ratio, times 100
What is mechanical advantage? 🏋️
Mechanical advantage (MA) is calculated as which of these?
- The load divided by the effort
- The effort divided by the load
- The load added to the effort
- The load multiplied by the effort
The MA formula 🧮
For any lever or mechanism: **MA = load / effort** If MA is **greater than 1**, the mechanism magnifies your effort - a small effort moves a large load. Because it divides one force by another, MA is a **ratio with no units**. A longer effort arm gives a bigger MA.
Find the mechanical advantage 🔢
An interactive activity.
Force ratio vs movement ratio ⚖️
MA and VR look similar but measure different things - one is about force, the other about distance.
Find the velocity ratio 📏
An interactive activity.
Small drives large 🔃
A small driver gear turns a larger driven gear. Compared with the driver, how does the driven gear turn?
- More slowly, with greater turning force
- More quickly, with greater turning force
- At exactly the same speed and force
- It does not turn at all
Which have no units? ✅
Select the TWO quantities that are ratios and so have NO units.
- Mechanical advantage
- Velocity ratio
- Effort
- Load
Work out a gear speed 🪜
An interactive activity.
Find the driven gear speed 🔧
An interactive activity.
Choose the mechanism 🎬
An interactive activity.
The grade-9 habit 🌟
Learn the three formulas cold: **MA = load / effort**, **VR = effort distance / load distance**, and **driven rpm = driver teeth x driver rpm / driven teeth**. Then the mark-saver: MA, VR and gear ratio are all **ratios**, so they have **no units** - never write newtons after an MA. And read gears the right way round: a **large driven gear turns slower with more force**, a **small one turns faster**.