# Experimental Procedure Part I Theoretically Determine...

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1. Lab 127: Torque and Rotational Inertia 2. Introduction Angular force is measured in a quantity torque, represented with the symbol τ. Torque is said to be applied when a force is exerted on a rigid body pivoted around an axis. Rotational motion can be described with the equation Στ = I α, where counterclockwise rotation means torque is positive and clockwise motion means torque is negative. I is rotational inertia or object resistance to rotation, and α is angular acceleration. The rotational inertia of a rigid object (a system of particles) is defined as : I = Σm i r i 2 , where m i is the mass of the ith particle and r i is the radius for the ith object from the rotation axis. Once the mass distribution around a point of rotation is known, rotational inertia can be calculated. Theoretically, the rotational inertia of a disk rotating through its center of mass is I = 1/2MR 2 and one rotating around its diameter has a rotational inertia of 1/4 MR 2 . The theoretical rotational inertia of a ring is 1/2M(R 1 + R 2 ) 2 , where M is the mass of the ring, R 1 is the inner radius of the ring and R 2 is the outer radius of the ring. To experimentally determine rotational inertia, we used the equation I total = τ/ α where torque is caused by the weight hanging from the string, wrapped around the 3 step pulley of the rotational apparatus. We also used the equation τ = rT, where r is the radius of the step pulley and T is the tension when the apparatus is rotating. In addition to both these equations, the equation a = r α was also used where a is the linear acceleration of the string. Applying Newton’s Second Law for the hanging mass, the equation for tension can also be derived as T = m(g-a). Once the linear acceleration of the hanging mass was experimentally determined, the tension (T), torque (τ = rT) and angular acceleration (α = a/r) were obtained to determine the total rotational inertia (I total = τ/ α). 3. Experimental Procedure Part I. Theoretically Determine Rotational Inertia of Disk and Ring