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Imagine you have a spinning mass (holded by a massless string say). And you increase the radius of the string with a constant rate, at the same time than exerting a perpendicular force on the mass so as to keep the angular velocity constant. Then tangential acceleration (tangential velocity is w*r) of the mass should be w*r' (as w is constant), where w is angular velocity and r' is the time derivative of the radius.

However, when I saw the same situation in Feynman's physics lectures book, I was dazzled. He, instead, considers the change in angular momentum, which is 2*m*r*r'*w, and that is equal to the torque, which is F*r. So te force exerted is 2*m*r'*w, and the acceleration, 2*r'*w.

So..how come this is double the previous result?? Where have I flawed my reasoning?

Thank you in advance