How to calculate the speed at which the cutter edge is turning

It is important to understand that the rotational speed of a spinning object, a drill bit, a skill saw blade, a router bit, stays the same when the tool is on. It spins at a certain number of rotations or revolutions per minute. But the outside edge of the cutting piece, the blade or the bit goes faster as the size of that piece increases.  That is important considering how different woods react to temperature.

The formula for calculating the speed of the outside edge is: 

 Cutter RMP X cutter diameter X pi (3.14) = cutter distance per minute 

Notice that your answer will be in "inches per minute". You can divide that number by 60 to get inches per second.

Notice that D (diameter) X pi  or  2R (radiuses) X pi is what we use to calculate circumference (outside edge) of circles.

Exercise: Outside edge speed exercise complete the chart 

Belts and Gears

Remember the rotational direction of a belt setup remains the same. When gears are meshed the driven gear rotates in the opposite direction. 

The ratios formula remains the same when you are counting the teeth of the two gears. 

If gear A is rotating at 850 RPM, what is rotational speed (RMP) of the gear B?   

How Fast Tools are Turning

Revolutions Per Minute-RPM (How quickly something turns)

Most electric motors have a fixed rotational speed. They are either on or off. Unlike a car, you don’t usually have an accelerator lever to vary the speed of the motor. For the best cutting performance of different materials, cabinetmakers sometimes need to change the rotational speed of the cutter. To do that the machine may allow for a change in gearing.

Gear Ratios:

The formula for calculating the change in rotational speed (RPM) is:

RPM of the motor X diameter of the motor pulley (drive gear) =  RPM of the cutter
                                  diameter of the driven pulley (driven gear)

Notice that if the two diameters are the same, the RPM does not change. The gear ratio is 1:1 (any number divided by the same number is one)

Exercise 1: Motor RPM Exercise Complete the table

Study Guides from Vancouver Island University Carpentry Program

This is a resource I found from Vancouver Island University for their Carpentry program.

As a preparation to the math requirements for their program they have put together some study guides for the procedural math materials...How to Guides.

They may be useful to some students at RTC. There is no applied mathematics in these resources--no real-life woodworking examples.

Trades Math Study Guides
SG 1 Decimal Review
SG 2 Adding and Subtracting Fractions
SG 3 Converting Fractions to Decimals and Vice versa
SG 4 Units of Measurement 
SG 5 Calculating Area, Perimeter and Volume 
SG 6 Exponents and Square Roots
SG 7 Percentages
SG 8 Using Imperial and Metric Rulers
SG 9 Using Pythagoras
SG 12 Ratio and Proportion