Again, we will need to describe this with an mathematical function if the height is not constant. From the definition of the moment of intertia, it seems that we need to use discs and a double integral here, which is weird because the lecturer insists we don't need to know any multivariable calculus in order to solve this question. Also, if the rope rolls without slipping about a frictionless pully, a/R where a is the acceleration of. Moments of Inertia with Double Integrals - Vector Calculus Application Mu Prime Math 29.2K subscribers Subscribe 12K views 2 years ago Explanation of how to use multivariable calculus (multiple. Moving from left to right, the rate of change of the area will be the height of the shape at any given \(x\)-value times the rate at which we are moving left to right. So you will have ( T 2 T 1) R I pulley where T 1 and T 2 are the tensions on either side of the pulley, R is the radius of the pulley, I pulley the moment of inertia of the pulley and the angular acceleration of the pulley. ![]() \)) we will move left to right, using the distances from the \(y\)-axis in our moment integral (in this case the \(x\) coordinates of each point).
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