Question

If you had an object of unknown moment of inertia, describe how you could determine its moment of inertia. Develop an equation that you could use to determine "I" for that object.

Answer 1

Step1:make an arrangement such that the body rotates about an axis about which the moment of inertia is to be found out . Put a marker on any point of the body so that we can calculate how fast it is rotating

Step2: wound a string around the body and connect the other end to a known mass such that the mass is hanging under its own weight (the mass should be supported by some means so that it doesn't fall down)

Step3: leave the system such that the mass falls down making the object, whose moment of inertia to be found out, rotate.

As the body falls down the object rotates and also the known mass gains velocity: the potential energy of the mass is being converted into kinetic energy of mass and object