Question

A turbine is spinning at 3400 rpm. Friction in the bearings is so low that it takes 16 min to coast to a stop. How many revolutions does the turbine make while stopping?

Answer 1

To find the number of revolutions the turbine makes while stopping, multiply the angular velocity by the time taken to stop.

Step-by-step explanation:

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. Since there are 60 seconds in a minute, we can multiply 16 minutes by 60 to get 960 seconds. Next, we can calculate the angular velocity of the turbine in radians per second by taking the given rotation rate of 3400 rpm (revolutions per minute) and multiplying it by 2π to convert to radians. So, the angular velocity is (3400 rpm) * (2π radians/minute) = (3400 * 2π) radians/minute. To find the number of revolutions, we multiply the angular velocity by the time taken to stop. Therefore, the number of revolutions the turbine makes while stopping is (3400 * 2π) * 960 seconds.

Answer 2

N = 27,887 revolution

Step-by-step explanation:

given,

turbine is spinning = 3400 rpm

time = 16 min = 16 × 60 = 960 s

`\omega_i = (2\pi\ N)/(60)`

`\omega_i = (2\pi\ 3400)/(60)`

`\omega_i = 356.05\ rad/s`

`\omega_f = 0`

`\theta = ((\omega_i+\omega_f)/(2))t`

`\theta = 2 \pi N`

`2 \pi N = ((356.05+0)/(2))* 960`

`N = (((356.05+0)/(2))* 960)/(2 \pi)`

N = 27,887 revolution