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ckynard · Nov 25, 2007, 09:19 PM

Hi. I have a couple of physics questions and I don't know where to begin:

1. Earth's radius is 6.38 times 10 to the 6th power m and it completes one revolution every day. What is the tangential speed of a person standing on the equator?

2. Earth circles the sun at a distance of 1.50 times 10 to the 11 power m. What is the magnitude of the centripetal acceleration of Earth in its orbit?

I feel like there is a constant that I don't have to solve the equation. Any help is greatly appreciated. Thanks!!

ebaines · Nov 26, 2007, 10:20 AM

To calculate the tangential velocity of things that go in circles (like the person standing on the equator in problem 1), use: $v = \omega \cdot R$ , where $\omega$ is the rotational velocity in radians/sec and $R$ is the radius of the earth. So for the first problem you need to determine the rotational speed of the earth in radians/sec. You know it's 1 revolution per day, or 2 $\pi$ radians/day, so convert that to radians/sec and multiply by the radius of the earth in meters to get the tangential velocity in meters/sec.

For the second problem, you should know that the centripetal acceleration is calculated from $a=R \cdot \omega ^2$ . So here you need to determine $\omega$ for the earth in its orbit in radians/sec, square that, and multiply by the radius of the orbit to get acceleration in meters per second squared.