The appropriate expression for the calculation of power by relating the angular energy in a given time.
In other words the instantaneous power of an angular accelerating body is the torque times the angular velocity
[tex]P=\tau\omega[/tex]
Where
[tex]\tau =[/tex] Torque
[tex]\omega =[/tex]Angular speed
Our values are given by
[tex]\tau = 630Nm[/tex]
[tex]\omega = 3200rev/min[/tex]
The angular velocity must be transformed into radians per second then
[tex]\omega = 3200rev/min (\frac{2\pi rad}{60s})[/tex]
[tex]\omega = 335.103rad/s[/tex]
Replacing,
[tex]P=(630)(335.103)[/tex]
[tex]P = 211.11*10^3W[/tex]
[tex]P = 211.1kW[/tex]
The average power delivered by the engine at this rotation rate is 211.1kW
