Question Video: Calculating the Angular Momentum of a Solid Metal Sphere Physics • 9th Grade

A solid metal sphere is rotating with an angular speed of 12.6 rad/s. It has a moment of inertia of 0.0200 kg⋅m². What is the angular momentum of the sphere?

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Video Transcript

A solid metal sphere is rotating with an angular speed of 12.6 radians per second. It has a moment of inertia of 0.0200 kilograms meters squared. What is the angular momentum of the sphere?

Let’s say that this here is our sphere, and in our problem statement, we’re told that it’s rotating with a certain angular speed. Now, we don’t know where the axis of rotation of the sphere is. It could be, for example, through a point on the sphere or that axis could be somewhere outside the sphere. But wherever it is, we know the sphere’s angular speed as it moves about that axis. We’ll refer to that speed as 𝜔. And we’re also told about the sphere that it has a given moment of inertia. This quantity, which we’ll represent using the letter capital 𝐼, is a rotational analog to mass. In other words, what mass is to linear motion, how it affects that motion through inertia, the moment of inertia 𝐼 is to rotational or angular motion.

We could say that the larger an object’s moment of inertia is, the harder it is to begin rotating or turning that object. Knowing moment of inertia and angular speed for the sphere, we want to calculate its angular momentum. And that is equal to the product of moment of inertia and angular speed. We could think of angular momentum as the product of the degree of difficulty in getting some object to rotate by the actual speed with which it is rotating. And this gives us how much momentum the object has in an angular direction. So when we substitute in the given values for 𝐼 and 𝜔, to three significant figures, we find a result of 0.252 kilograms meters squared per second. Note that we’d leave out of our final answer the units of radians because these are dimensionless. And so the angular momentum of our solid metal sphere is 0.252 kilograms meter squared per second.

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