Circular Saw Blade Angular Velocity Calculation

What is the angular velocity of a circular saw blade with a radius of 3 inches spinning at 5,400 rpm?

a. 565.49 radians per second

Answer:

The angular velocity of the circular saw blade, given it spins at 5400 rpm, is approximately 565.49 radians per second.

The angular velocity of a circular saw blade is a crucial factor in understanding its speed and performance. In this case, with a blade radius of 3 inches and spinning at 5400 rpm, we can calculate the angular velocity in radians per second.

First, we need to convert the rpm into revolutions per second. Since there are 60 seconds in a minute, the blade's speed in revolutions per second would be 5400 rpm / 60 = 90 revolutions per second.

Next, we know that one full revolution is equal to 2π radians. By multiplying the revolutions per second by 2π, we can determine the angular velocity. Therefore, 90 revolutions per second * 2π = 180π or approximately 565.49 radians per second.

This calculation showcases the blade's rapid angular velocity, indicating its high rotational speed and cutting efficiency. Understanding these technical aspects can help in selecting the right circular saw blade for various woodworking projects.