Acceleration associated with the Earth’s spin

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Homework Help Overview

The discussion revolves around calculating the acceleration associated with the Earth's rotation at the equator. The original poster attempts to address the problem by considering the forces acting on the Earth and the implications of angular acceleration.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the distinction between angular acceleration and the acceleration experienced by a point on the Earth's surface due to its rotation. There are discussions about the correct formula to use and the direction of the acceleration.

Discussion Status

Some participants have offered guidance on the correct interpretation of the problem, suggesting that the acceleration should be calculated based on the Earth's angular speed and the radius at the equator. There is an acknowledgment of the direction of the acceleration as radially inward, although some initial confusion is noted.

Contextual Notes

Participants reflect on their understanding of circular motion and the forces involved, indicating a need to clarify concepts related to rotational dynamics. There is a recognition of the difference between the acceleration due to gravity and the acceleration due to the Earth's spin.

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Homework Statement



Calculate the acceleration associated with
the Earth’s rotation about its axis (assume an equatorial point).

Homework Equations



About center of mass motion
Γ=Iα

The Attempt at a Solution


Since the external forces acting on the Earth are gravitational forces and hence there is no torque acting on the earth.
Hence the acceleration associated with
the Earth’s rotation about its axis (assume an equatorial point) is zero.
 
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You've found the angular acceleration, but I believe the question is asking for the acceleration of a point of the Earth's surface on the equator due to Earth's spin. In other words, if you were standing at the equator, what would the component of your acceleration associated with the Earth's rotation be?
 
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o.k. I got it.
Thank you.
 
Then, the acceleration would be Rω2 towards the center where ω is the angular speed of the Earth rotation and R is the distance between the center of the Earth and its equator,wouldn't it?
 
That looks about right. And what direction is the acceleration in?
 
The acceleration is towards the center of the earth, radially inward.
 
Is it? Remember we're talking about the acceleration associated with the Earth's spin, not its gravity.
 
Let's model the Earth as a spinning ball for this problem.
I am sitting on the equator.
Now from an inertial frame,I will be in a uniform circular motion with angular speed ω and radius R.
according to Newton's 2nd Law of motion,
F = ma = 2 R(-## \hat r ##)
So ,the direction is radially inward.
 
Pushoam said:
So ,the direction is radially inward.
I apologize, I was mistaken. Of course the direction is radially inward. Otherwise the point wouldn't be kept in circular motion. It's been awhile since I took my last physics class. :rolleyes:
 
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