a body is rotating at a steady rate, does torque acts on the body?

Torque is the rotational analog of force, which, when applied to a body causes acceleration. This fact is represented by the following equation

 τ= Iα

so, torque τ always produces some angular acceleration α in a rotating body, which means an ever changing angular speed ω. 

Thus, a body cannot rotate at a steady rate when torque is acting on it.

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