# Homework Help: Find the centripetal acceleration of the moon

1. Jun 7, 2014

### BrainMan

1. The problem statement, all variables and given/known data
The moon circles the earth with a period of 27.3 days at a distance of about 250000 mi. Find the centripetal acceleration of the moon.

2. Relevant equations
ac = v2/r

3. The attempt at a solution
I first found the velocity by converting 2 pi radians per 27.3 days to radians per second.
2 pi / 27.3/ 24/ 60/60 = 2.66 x 10-6 radians per second.
Then I converted miles to meters to find the radius.
250000 x 1609.34 / 2 pi = 631986340.1
Then I plugged these numbers into the above equation to find the acceleration and got 1.12 x 10-20 rad/s. The correct answer is 2.85 x 10-3 rad/s

Last edited: Jun 7, 2014
2. Jun 7, 2014

### dauto

Seems like you're confusing the angular velocity with the velocity. Also 250000miles is the radius already. No need to divide by 2 pi. Finally, you made some other mistake. I can't tell what it is since you didn't post your calculation. Don't just describe your calculation. Post it.

3. Jun 7, 2014

### BrainMan

Sorry (2.66 x 10-6)2/631986340.1 = 1.12 x 10-20

4. Jun 7, 2014

### AlephZero

In your formula ac = v2/r, v is the velocity in meters/second, not the angular velocity in radians/second.

There is a different formula for the acceleration that uses angular velocity and radius, if you want to do it that way.

5. Jun 7, 2014

### BrainMan

OK I see. Is the 250000 mi the radius or the circumference?

6. Jun 7, 2014

### dauto

That's the distance between the moon and the earth. Draw a picture of the orbit, and remember that the Earth barely moves at all.

7. Jun 7, 2014

If it is 250000 mi above the Earth, it should not be the radius. Thou should also include the Radius of the Earth. Am I wrong?

8. Jun 7, 2014

### BrainMan

I understand that. How do I find the velocity in m/s?

9. Jun 7, 2014

### Nathanael

Find the circumference of the orbit (in meters) and divide it by however many seconds are in 27.3 days

10. Jun 7, 2014

### BrainMan

OK I got it right! Thanks!

11. Jun 7, 2014

### dauto

That's negligible specially considering that the moon's orbit really isn't circular. We're going for a ball park calculation here.