Centripetal Acceleration of Earth

Click For Summary

Homework Help Overview

The discussion revolves around calculating the centripetal acceleration of an object at Earth's equator due to the planet's rotation. Participants are tasked with determining both the magnitude of this acceleration and the period of rotation required for a specific centripetal acceleration value.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss how to find the radius and velocity of Earth, with some suggesting looking up values in textbooks. There are questions about the calculations performed using the centripetal acceleration formula and the implications of using escape velocity instead of rotational speed.

Discussion Status

Some participants have provided information on the radius and velocity of Earth, while others are questioning the calculations and assumptions made regarding these values. There is an ongoing exploration of the correct approach to solving the problem, with no clear consensus reached yet.

Contextual Notes

Participants note that the velocity figure referenced may be the escape velocity, which is not applicable to the problem at hand. There is also mention of the need to calculate speed based on the period of rotation, which is assumed to be one day.

shell4987
Messages
43
Reaction score
0

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.
 
Physics news on Phys.org
shell4987 said:
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.
 
shell4987 said:

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!
 
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.
 
shell4987 said:
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!
 
Doc Al said:
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!
 
shell4987 said:
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!)
 
shell4987 said:
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.
 

Similar threads

Is My Calculation of Centripetal Acceleration and Tangential Velocity Correct?
  • · Replies 12 ·
Replies
12
Views
2K
Finding proper value for centripetal acceleration in a plane rising up
  • · Replies 16 ·
Replies
16
Views
1K
Gravitation sum related to Centripetal Acceleration
  • · Replies 5 ·
Replies
5
Views
3K
Find g, measured to be 9.78 at the equator, when Earth is still
  • · Replies 17 ·
Replies
17
Views
2K
Calculating Centripetal Acceleration at Earth's Equator
  • · Replies 1 ·
Replies
1
Views
2K
How fast should the Earth spin for centripital accel. to equal gravity?
  • · Replies 8 ·
Replies
8
Views
3K
Derivation of an expression for centripetal acceleration
  • · Replies 3 ·
Replies
3
Views
2K
What actually is the centripetal acceleration formula?
  • · Replies 28 ·
Replies
28
Views
3K
Relation between the velocity vector and the acceleration vector of an object
  • · Replies 1 ·
Replies
1
Views
930
Centripetal Acceleration of Satellite
  • · Replies 7 ·
Replies
7
Views
3K