What is the derivation of centripetal acceleration on a hypothetical planet?

[rrosa522]

Homework Statement

Imagine another planet with an acceleration of 10.00 m/s^2 at its equator when ignoring the rotation of the planet. The radius is 6.2 x10^6 m. An object dropped at the equator yields an acceleration of 9.70 m/s^2. Determine the length of 1 day on this planet.

Homework Equations

The Attempt at a Solution

My teacher taught me how to solve this question, but there is just one step I don't understand
10.00m/s^2 - 9.70m/s^2 = 0.3m/s^2 (centripetal acceleration)
why does subtracting these two values give us the centripetal acceleration??
On a test, if I get a similar question I know I have to subtract the two values, but I really want to learn the reason behind it.

 

[andrewkirk]

Do you know how to derive the formula for centripetal acceleration in terms of velocity, using a vector triangle showing the change in velocity over a small increment of time $\delta t$? A similar construction can be used to justify the above formula. There's a $\cos\delta\theta$ factor in there that is approximated by 1 to get the above formula.