A turbine is spinning at 3600 rpm. Friction in the bearings is so low that it takes 15 min to coast to a stop. How many revolutions does the turbine make while stopping?
To determine the number of revolutions the turbine makes while stopping, we need to convert the time it takes to stop from minutes to seconds, and then calculate the number of revolutions based on the given information.
Given:
- Initial speed of the turbine: 3600 rpm
- Time to coast to a stop: 15 min
First, let's convert the time to seconds:
1 minute = 60 seconds
15 minutes = 15 * 60 = 900 seconds
Next, we can calculate the number of revolutions the turbine makes while stopping. Since we know the initial speed of the turbine and the time it takes to stop, we can determine the angular displacement.
Angular displacement (θ) can be calculated using the formula:
θ = ω * t
where:
θ = angular displacement
ω = angular velocity (in radians per second)
t = time (in seconds)
To calculate the angular velocity, we need to convert the initial speed from rpm to radians per second:
1 revolution = 2π radians
1 minute = 60 seconds
Angular velocity (ω) = (3600 rpm) * (2π radians/1 revolution) * (1 minute/60 seconds)
= (3600 * 2π) / (60)
= 120π radians/second
Now, we can calculate the angular displacement:
θ = (120π radians/second) * (900 seconds)
= 108,000π radians
Since 1 revolution is equivalent to 2π radians, we can convert the angular displacement to revolutions:
Number of revolutions = (108,000π radians) / (2π radians/revolution)
= 54,000 revolutions
Therefore, the turbine makes approximately 54,000 revolutions while coasting to a stop.