Exploring Centripetal Acceleration on a Hypothetical Planet

  • #1

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.

Answers and Replies

  • #2
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.

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