Calculating torque for a designed flywheel ?

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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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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 acceleration . 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..