how can we say that torque is equal to power / angular velocity though we know that torque is equl to I x (change of angular velocity over time ). and how can we relate torque to (angular velocity) , as we know that a rotating gear at constant angular velocity has no torque on it or bettter saying the sum of all torques on it are equal to zero, so how can we say that torque is equal to the power of the rotating gear over the constant angular velocity ???? arent we contradicting ourselfs ?? how can a torque exist on a constant angular velocity rotating gear ???? I am confused ??
If you push with a force F a block on a table with friction such that the block moves at constant speed v, then the power you produce is Fv. So the conundrum here would be F=ma, but the block is not accelerating? The reason is that we have forgotten to take into account that there is friction. In the presence of friction, if you don't push, the block doesn't even move.
so u're saying that the torque calculated on the rotating disk is due the force that initialy rotated the disk ?? which means initially accelerated the disk before it reached its equilibriumed state (acceleration = 0) ? right ???
No, in the example P=Fv, I am giving the constant force (equal and opposite to the friction) you need to apply to keep the block moving at a constant speed.
Why do you think these ideas are mutually exclusive? Try writing them in equation form and see if they make more sense. One thing that may be confusing you - typically that first relationship is written the other way around: power equals torque times angular velocity. Saying that all torques sum to zero is different from saying that the torque at constant velocity is zero. It is not [necessarily] true to say a rotating object at constant speed has no torque on it: there may an input and an output torque that are equal. Power and energy work the same way.