Find the centripetal acceleration of the moon

[BrainMan]

Homework Statement

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.

Homework Equations

a_c = v²/r

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

 

[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.

 

[BrainMan]

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.

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

 

[AlephZero]

In your formula a_c = 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.

 

[BrainMan]

In your formula a_c = 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.

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

 

[dauto]

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

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.

 

[adjacent]

at a distance of about 250000 mi.

250000miles is the radius already.

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?

 

[BrainMan]

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.

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

 

[Nathanael]

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

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

 

[BrainMan]

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

OK I got it right! Thanks!

 

[dauto]

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?

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