A body is whirled in a horizontal circle at the rate of 800 revolutions per minute. Determine the angular velocity
Answer Details
To determine the angular velocity of a body whirled in a horizontal circle at a rate of 800 revolutions per minute (rpm), we need to convert this to the standard unit of angular velocity, which is radians per second (rad/s).
Here’s how you can calculate it:
First, understand that one complete revolution is equal to 2π radians.
The body completes 800 revolutions in one minute.
Now let's perform the conversion:
Convert the revolutions per minute to revolutions per second:
\( \frac{800 \text{ revolutions}}{1 \text{ minute}} \times \frac{1 \text{ minute}}{60 \text{ seconds}} = \frac{800}{60} \text{ revolutions per second} \), which simplifies to approximately \( 13.33 \text{ revolutions per second} \).
Convert revolutions to radians by multiplying by \(2π\) radians per revolution:
\( 13.33 \text{ revolutions per second} \times 2π \text{ radians per revolution} = 26.66π \text{ radians per second} \).
Rounding up the decimal to a consistent significant figure, the angular velocity is approximately 26.7π radians per second.