Find the angular velocity in radians per second for a wheel turning at the rate of 450 revolutions per minute. (Answer will be in terms of pi)
2π rad per revolution , 60 sec per min
v = (450 / 60) * 2π
To find the angular velocity in radians per second, we need to convert the given rate from revolutions per minute to radians per second.
1 revolution is equal to 2π radians (since the circumference of a circle is 2π times the radius).
First, let's convert 450 revolutions per minute to revolutions per second:
Revolutions per second = 450 revolutions per minute / 60 seconds per minute
Revolutions per second = 7.5 revolutions per second
Next, we can convert revolutions per second to radians per second using the conversion factor:
Radians per second = (Revolutions per second) * (2π radians / 1 revolution)
Radians per second = 7.5 revolutions per second * 2π radians per revolution
Radians per second = 15π radians per second
Therefore, the angular velocity in radians per second for a wheel turning at the rate of 450 revolutions per minute is 15π radians per second.