What is this formula for?/What is it called?

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The formula S*r=1/2*m*r^2*a/r represents the relationship between torque, moment of inertia, and angular acceleration. In this context, S denotes force, r signifies radius, 1/2*m*r^2 is the moment of inertia, and a/r indicates angular acceleration. The equation is confirmed to express torque as the product of moment of inertia and angular acceleration, clarifying its application in problems involving rotational dynamics and tension in coiled wires around cylinders.

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I have a formula, S*r=1/2*m*r^2*a/r

The problem is that it is unlabeled, and I am not 100% sure what this is supposed to be for. As near as I can tell, it is for something with inertia, and involving tension on a wire coiled around a cylinder. Is this correct? Does anyone know if this is simply a derived equation for a specific problem, or a general use equation? Thank you.
 
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r cancels out.
 
I know, but this is a formula that was supplied for a problem, and I am attempting to figure out what everything is. I think I have it narrowed down that S*r is supposed to be torque, and everything else on the right is supposed to represent inertia times the angular momentum, but I am not sure.
 
You are on the right track, I see it as torque = (moment of inertia) x angular acceleration.
S is force, r is radius, 1/2 m rsq is moment of inertia, and a is linear acceleration, a/r is angular acceleration.
 

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