# Question Video: Calculating the Angular Momentum of Earth Physics • 9th Grade

Earth has a moment of inertia about its axis of rotation of 9.69 × 10³⁷ kg⋅m² and an angular speed of 7.29 × 10⁻⁵ rad/s. What is the angular momentum of Earth due to its rotation?

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### Video Transcript

Earth has a moment of inertia about its axis of rotation of 9.69 times 10 to the 37th kilograms meters squared and an angular speed of 7.29 times 10 to the negative fifth radians per second. What is the angular momentum of Earth due to its rotation?

Let’s say that this is the Earth and the axis that it rotates about. And we’re told that as it does this, it has a particular value for its moment of inertia, we’ll call that 𝐼, and that this rotation happens at a given angular speed, we’ll call it 𝜔. Given this information, we want to solve for the angular momentum of Earth due to its rotation, we can call this capital 𝐿. We can recall that, in general, the angular momentum of an object is equal to its moment of inertia multiplied by the speed with which it rotates. So 𝐿 is equal to 𝐼 times 𝜔. And if we substitute in the given values for these terms and then calculate 𝐿, to three significant figures, we find it’s 7.06 times 10 to the 33rd kilograms meter squared per second.

Note that, in this result, we don’t have the units of radians. That’s because radians are a dimensionless quantity. When we report our final answer then, we say that Earth has an angular momentum of 7.06 times 10 to the 33rd kilograms meter squared per second.