Answer :
Final answer:
To convert the given rotation rate in revolutions per minute to angular speed in degrees per second, we can use the formula Angular Speed (in degrees/second) = Angular Speed (in radians/second) × 180/π. By substituting the given values, the angular speed is approximately 2995.48 degrees/second.
Explanation:
To calculate the angular speed in degrees per second, we need to convert the given rotation rate in revolutions per minute to radians per second. Since 1 revolution is equal to 2π radians, the angular speed in radians per second is calculated as follows:
Angular Speed (in radians/second) = Rotations per minute × 2π / 60
Substituting the given rotation rate of 500 revolutions per minute into the formula:
Angular Speed = 500 × 2π / 60
Simplifying the expression:
Angular Speed ≈ 52.36 radians/second
Next, to convert radians to degrees, we know that 1 radian is equal to 180/π degrees. So, we can calculate the angular speed in degrees per second by multiplying the angular speed in radians per second by 180/π:
Angular Speed (in degrees/second) = Angular Speed (in radians/second) × 180/π
Substituting the value of the angular speed in radians/second, we get:
Angular Speed = 52.36 × 180/π
Angular Speed ≈ 2995.48 degrees/second
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