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.