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

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The formula S*r=1/2*m*r^2*a/r is related to torque and rotational dynamics. It appears to express the relationship between torque, moment of inertia, and angular acceleration. S represents force, r is the radius, 1/2*m*r^2 denotes the moment of inertia, and a/r indicates angular acceleration. The discussion suggests that the formula may be derived for a specific problem involving inertia and tension in a coiled wire around a cylinder. Understanding this formula is essential for analyzing rotational motion and dynamics.
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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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