Mechanical Advantage refers to the ratio between effort and load of a system/machine. Velocity Ratio refers to the ratio of speeds of the load and effort. Both these concepts are proportional to each other i.e. increases MA increases VR, and vice versa.
Mechnical \ Advantage \propto Velocity \ Ratio$$
### Definition
##### MA (Mechanical Advantage)
Mechanical Advantage conceptually refers to the ***force amplification*** of a machine. Machines with high MA (i.e. > 1) amplify the force of the effort by a huge factor. Similarly, machines with lower MA (i.e. < 1) means more effort force is required to produce a load force. It is a scalar quantity, and being a ratio, is **unitless**.
##### VR (Velocity Ratio)
Velocity Ratio conceptually refers to the ***speed reduction*** (well, technically velocity) of a machine. Higher VR (i.e. >1) results in the load component moving much *slower* than the effort component. Lower VR (i.e. < 1) results in a faster moving load component, compared to the effort component.
**It is *very* useful to note that $velocity \ = \ \frac{displacement}{time}$ , and as such, since the machine operates in the *same* timeframe (i.e. velocity = displacement) , a lower VR also means the load components moves further than the effort component.**
##### Connection
As mentioned previously, MA and VR are directly linked to another. In an *ideal machine*, with 100% efficiency, MA = VR. Usually, due to friction and whatnot, that is not the case. But VCAA uses ideal machines, so assume MA = VR.
### Calculating MA and VR
##### Mechanical Advantage
At it's very essence, mechanical advantage is simply the load force divided by the effort force. As such, the VCAA formula is:
MA = \frac{F_{Load}}{F_{Effort}}
However, this formula can be translated into many other formulas relating to simple machines:
* **Levers**:
* 
* [](Gear.md#MA)
##### Velocity Ratio
Velocity Ratio, as the name suggests, is the ratio of the velocities of the effort and the load. The formula is:
VR = \frac{v_{effort}}{v_{load}} = \frac{dist_{effort}}{dist_{load}}
### Applications
##### High MA
A good, simple example of a machine with high mechanical advantage is a bicycle with on a low gear, such as gear 1. Usually used when moving uphill, and a lot of force is required to overcome gravity, gear 1 amplifies the force. However, the drawback is the high velocity ratio, which means we need to either pedal faster, or do more pedals to move the same distance.
##### Low MA
So why bother with having a lower mechanical advantage? If a machine's mechanical advantage is < 1, then it's VR is also < 1. This means the machine acts as a **velocity amplifier**, but a **force reducer**. Again, with a gear-system bicycle, think of the higher gears. Gear 8 require a lot of effort to push, but results in the bike moving much faster.