Often there are situations where rather complex shaped objects need to be spun a

Question

Often there are situations where rather complex shaped objects need to be spun about an axis of rotation. In such cases the moment of inertia is not determined by calculation, i.e. carefully summing (mi*ri2) over the complex shape. Rather the moment of inertia is determined by experimentation, using Newton’s Laws in rotational form. Describe the experimental set-up and procedure to determine the moment of inertia of an object. You can assume you have the equipment available to you this semester in laboratory. Often there are situations where rather complex shaped objects need to be spun about an axis of rotation. In such cases the moment of inertia is not determined by calculation, i.e. carefully summing (mi*ri2) over the complex shape. Rather the moment of inertia is determined by experimentation, using Newton’s Laws in rotational form. Describe the experimental set-up and procedure to determine the moment of inertia of an object. You can assume you have the equipment available to you this semester in laboratory.

Explanation / Answer

If a consider any complex shaped object and we apply any tangential force on it (at t=0) in such a way so that it will start rotating if we provide this tangential force continuously means we are providing constant torque means angular acceleration is also constant so we can measure angular velocity at any instant (t=t) starting from (t=0). So using this formula

Omega(t) = Omega(0) + alpha*t

We can calculate alpha i.e. angular acceleration.

Then using "Toque = Moment of Inertia* Angular acceleration"

We can calculate moment of inertia of any shaped body.

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