# a turbine has a mass of 1200kg and a radius of 0.8m. Calculate the braking torque required to slow it down from 50 rev per second to rest in 1 minute

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### 1 Answer

You need to remember that torque, angular acceleration and moment of inertia are related by `tau = alpha*I` .

You should notice that the initial angular velocity is `omega_1 ` = 50 rev/s and the final angular velocity is `omega_2` = 0 (rest).

You need to convert 50 rev/s in rad/s such that:

`omega_1 = 50*2pi = 314 rad/s`

You need to calculate the angular acceleration such that:

`alpha = (omega_2 - omega_1)/t = (0-314)/60`

Notice that the time is expressed in seconds and the given period of slowing down is of 1 minute = 60 seconds.

`alpha = -5.23`

Considering the shape of turbine as the shape of a solid wheel yields:

`I = MR^2/2 = 1200*0.8^2/2 = 600*0.8*0.8 = 384 Kgm^2`

Hence, `tau` = -5.23*384 = -2008.32Nm

**Hence, evaluating the braking torque needed for slowing down the turbine from 50 rev/s to rest yields `tau` = -2008.32Nm.**