Calculating torque for a designed flywheel ?

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To calculate the torque applied by a flywheel on a connected shaft, the formula involves angular acceleration and moment of inertia, not angular velocity. The torque generated by the flywheel is limited and depends on its design and connection to the shaft. Understanding the relationship between torque, power, and angular acceleration is crucial for accurate calculations. However, determining the angular acceleration of the shaft without experimental testing poses a challenge. The discussion emphasizes the need for practical testing to obtain precise values.
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How to calculate how much torque a given flywheel with a given moment of inertia I and angular velocity w will apply on a shaft (with given dimensions) its connected to ?
 
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The torque is just angular acceleration times moment of inertia. It is not a function of angular velocity.
 
But that is why the question arises. Its is not like the flywheel can generate whatever torque I need it to . If i connect a rotating flywheel to a shaft with a gearing and wheel at the end I need to know how much torque does it apply so as to then know what is the power and angular accleration . Its not the otherway around . Even if torque is a function of alpha(angular acceleration) I can't find out the alpha of shaft connected without testing can I ? Thats is why I want to know whether there was any way to know without experimenting .

Thanks..
 

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