Math Problem Statement

A 8-inch diameter circular saw blade spins at 3,200 revolutions per minute. Find the angular speed of the blade in degrees per minute. Round your answer to the nearest tenth. You do not have to include units.

Solution

To find the angular speed of the saw blade in degrees per minute, we follow these steps:

Step 1: Convert revolutions per minute to degrees per minute

Since 1 revolution equals 360 degrees, we multiply the number of revolutions per minute (3,200) by 360 to get the angular speed in degrees per minute.

Angular speed=3,200revolutions per minute×360degrees per revolution\text{Angular speed} = 3,200 \, \text{revolutions per minute} \times 360 \, \text{degrees per revolution}

Angular speed=1,152,000degrees per minute\text{Angular speed} = 1,152,000 \, \text{degrees per minute}

So, the angular speed of the blade is 1,152,000 degrees per minute.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

  1. What is the angular speed in radians per minute?
  2. How do you convert between angular speed in degrees and radians?
  3. What is the relationship between angular speed and linear speed at the blade's edge?
  4. If the blade spins faster, say 4,000 revolutions per minute, what is the new angular speed?
  5. How would the blade's angular speed change if the diameter doubled?

Tip: Angular speed is often easier to calculate in radians, as 1 revolution is 2π2\pi radians.

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Math Problem Analysis

Mathematical Concepts

Angular speed
Unit conversion
Revolutions per minute (RPM)

Formulas

Angular speed (degrees/min) = revolutions per minute × 360

Theorems

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Suitable Grade Level

Grades 9-11