ROTATIONAL INERTIA Lab report help – 20210702Y

This lab features a rotor attached by a string wound around its central hub (of radius “r”) to a falling mass of mass “m”.As the mass falls from a height “H”, the rotor spins.First the rotor is allowed to spin on its own, and the fall is timed (three trials, of time t1,t2, and t3).The time is averaged and used to find the final velocity (the speed of the hanging mass as it hits the ground).It can be shown through kinematics that this velocity, v, should equal “2H/t”. Next, onto the rotor is placed a disc of mass “Mdisc” and radius “Rdisc”and then, later, a hoop of mass “Mhoop” and inner radius “R1” and outer radius “R2” is placed on the rotor.Again the falling mass is timed as it is allowed to drop three times from height “H” and the average time is used to find the velocity, v, of the falling mass just as it strikes the ground.In lab, we derived a single formula that should tell us the “Rotational Inertia”, ITotal,of the rotating object in this experiment, be it the rotor on its own, the rotor attached to the disc, or the rotor attached to the hoop.Below, you will show the derivation of that formula.You should start with the basic “Conservation of Energy” formula and work through it until you get the formula for ITotal in terms of m, H, v, g, and r. Keep in mind, you are deriving ONE formula to find the ITotal of whatever is spinning.