Centripetal Acceleration of Earth

[shell4987]

Homework Statement

(a) What is the magnitude of the centripetal acceleration of an object on Earth's equator owing to the rotation of Earth? (b) What would the period of rotation of Earth (in minutes) have to be for objects on the equator to have a centripetal acceleration with a magnitude of 9.80 m/s2?

Homework Equations

a=v squared/r and T=(2(pi)(r))/v

The Attempt at a Solution

How do I find out the radius of the Earth? Let alone the velocity of the Earth? I think if I knew those two that maybe I could solve this problem.

 

[Doc Al]

How do I find out the radius of the Earth?

Look it up!

Let alone the velocity of the Earth?

Once you have the radius, you should be able to figure out the speed of a point on the equator.

 

[nrqed]

Homework Statement

(a) What is the magnitude of the centripetal acceleration of an object on Earth's equator owing to the rotation of Earth? (b) What would the period of rotation of Earth (in minutes) have to be for objects on the equator to have a centripetal acceleration with a magnitude of 9.80 m/s2?

Homework Equations

a=v squared/r and T=(2(pi)(r))/v

The Attempt at a Solution

How do I find out the radius of the Earth? Let alone the velocity of the Earth? I think if I knew those two that maybe I could solve this problem.

They assume that you will look up the radius of the Earth in your book. You have to calculate the speed using the fact that you know the period of rotation!

 

[shell4987]

Okay, I looked up all of my information in the book and got the radius to be 6.37e6 and the velocity to be 11.2km/s, I attempted part (a) and got the answer to be 2.0e13m/s squared and that came out to be wrong, what did i do wrong for that, i used the a=v squared/r formula with 11200 m/s as velocity and 6.37e6m as the radius? Am I doing something wrong here?

And for part (b) I solved it and got it correct. Thank you.

 

[Doc Al]

Okay, I looked up all of my information in the book and got the radius to be 6.37e6 and the velocity to be 11.2km/s,

Show how you calculated the velocity. Even if you assume that speed, how did you calculate an acceleration of 2.0e13!

 

[shell4987]

Show how you calculated the velocity. Even if you assume that speed, how did you calculate an acceleration of 2.0e13!

I converted 11.2km/s (the velocity of the Earth) into meters by multiplying it by 1000, therefore getting 11200 m/s, then i put that into the a= v squared/r formula and used r as 6.37e6m... ahh i don't know what I'm doing wrong!

 

[Doc Al]

I converted 11.2km/s (the velocity of the Earth)

You want the rotational speed of the Earth's surface. Figure it out using period (one day) and the Earth's radius.

therefore getting 11200 m/s, then i put that into the a= v squared/r formula and used r as 6.37e6m

Even using your numbers you won't get anywhere near the answer you got. (Check your arithmetic!)

 

[dynamicsolo]

Okay, I looked up all of my information in the book and got the radius to be 6.37e6 and the velocity to be 11.2km/s,

Just for your future reference, take a look at the source (a table in your text?) where you found this velocity figure. This is the *escape* velocity of the Earth, which won't be of help to you in the problem.