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Systems of Particles and Rotational Motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsSystems of Particles and Rotational Motion3 Marks
Question
To maintain a rotor at a uniform angular speed of $200rad s^{-1}$, an engine needs to transmit a torque of 180Nm. What is the power required by the engine? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100% efficient.
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Answer

Angular speed of the rotor, $\omega=200\text{rad/s}$ Torque required, $\tau=180\text{Nm}$
The power of the rotor (P) is related to torque and angular speed by the relation,
​​​​​​​ $\text{P}=\tau\omega$
$= 180 \times 200 = 36 \times 103 = 36kW$
Hence, the power required by the engine is 36kW.

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