Angular Velocity Calculation for a Circular Saw Blade

What is the angular velocity of the circular saw blade in radians per second?

The blade of a circular saw has a radius of 3 inches and spins at 5,400 rpm.

Angular Velocity Calculation:

The angular velocity of the blade with a radius of 3 inches spinning at 5,400 rpm is 90π radians/second.

In order to calculate the angular velocity of the circular saw blade, we need to convert the rotational speed from revolutions per minute (rpm) to radians per second. Here's how we do it:

Given data:

Radius of the blade (r) = 3 inches

Rotational speed = 5,400 rpm

To convert the rotational speed to radians per second, we use the formula:

Angular velocity = Rotational speed (in revolutions per minute) / 60 * (2π radians/1 revolution)

Substitute the values into the formula:

Angular velocity = (5,400 rpm / 60) * (2π radians/1 revolution)

Angular velocity = 90π radians/second

Therefore, the angular velocity of the circular saw blade is 90π radians/second.