The radius of the earth's very nearly circular orbit around the s...

Question

The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10^11m. Find the magnitude of the earth's (b) angular velocity

Accepted Answer

Welcome back, everybody. We are making observations about a planet that is orbiting a star. We are told that the radius of rotation is 1.43 times 10 to the third kilometers. And we are told that it has a period of 21.3 days. And we are tasked with finding what is the angular velocity of our planet. Well, we know that angular velocity is equal to tangential velocity over the radius of orbit. And we know that our tangential velocity is also equal to two pi times the radius of orbit divided by our period. So let me sub in this value into this equation right here. You will see that for our angular velocity, we then get two pi R divided by R period tee times one over R. You'll see that the radius of orbit cancels out on top and bottom just leaving us with two pi over T for our angular velocity. But before plugging in our period of this, we need to make sure that it is in, in the right units and the units that we want is seconds here and we're given days. So let's go ahead and convert here, we know in one day that there are 24 hours and we know that in one hour there are 3600 seconds, we can go ahead and cancel out these units and then we'll just be able to multiply straight across when we plug this into our formula. So let's go ahead and do that now. So we have that are angular velocity is equal to two pi divided by 21.3 times 24 times 3600. This when you plug into our calculator, we get an angular velocity of 3.4 times 10 to the negative six radiance per seconds, which corresponds to our final answer. Choice of a. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

The radius of the earth's very nearly circular orbit around the sun is 1.5 x 10^11m. Find the magnitude of the earth's (b) angular velocity

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