# Estimating the Diameter and Linear Speed of a Circular Saw Blade

## What is the angular velocity of the blade of an electric saw that rotates at 2600 rev/min?

Assuming the typical saw used to saw boards in home construction and renovation is a circular saw, what is the diameter of the blade? What is the linear speed in m/s of a point on the rim of the circular saw blade?

## Answer:

The angular velocity of the blade of an electric saw rotating at 2600 rev/min is approximately 271.83 rad/s. To estimate the diameter of the blade used for sawing boards in home construction and renovation, we can consider a typical range of 7-10 inches (17.8-25.4 cm) for the diameter. The linear speed in m/s of a point on the rim of the circular saw blade is estimated to be around 28.0 m/s.

## Final Answer:

To estimate the diameter of a typical saw used for home construction and renovation, we need to calculate the linear speed of a point on the rim of the circular saw blade. The linear speed can be determined using the formula v = rω, where v is the linear speed, r is the radius, and ω is the angular velocity.

Considering a blade diameter of 7.25 inches, the linear speed of a point on the rim of the circular saw blade is estimated to be approximately 25.03 m/s.

**Explanation:**

To estimate the diameter of the saw, we need to calculate the linear speed of a point on the rim of the circular saw blade. The formula for linear speed is given by v = rω, where v is the linear speed, r is the radius, and ω is the angular velocity.

First, we need to convert the angular velocity from rev/min to rad/s. There are 2π radians in one revolution, so the angular velocity is 2600 rev/min * 2π rad/rev * 1 min/60s = 271.83 rad/s.

To find the linear speed, we need to know the radius of the circular saw blade. Assuming a blade diameter of 7.25 inches, the radius would be half of the diameter, which is 7.25 inches / 2 = 3.625 inches. Converting this to meters, we get 3.625 inches * 0.0254 m/inch = 0.092075 meters.

Using the formula v = rω, we can now calculate the linear speed. v = 0.092075 meters * 271.83 rad/s = 25.03 m/s. Therefore, the linear speed of a point on the rim of the circular saw blade is approximately 25.03 m/s.