Centripetal acceleration?

Question

two people on earth. one at the equator and one at the north pole. which one has the larger centripetal acceleration? is it the one at the north pole because his period is much shorter and therefore his acceleration is greater?

Answer 1

The period is the same for both (about 24 hours). But the person at the equator travels about 24,900 miles in that time (the circumference of the earth). The person at the pole has no velocity because he traveled zero distance (a circle with a radius of zero).

Since centripetal acceleration = v^2 / r, the person with zero velocity (at the pole) has basically zero centripetal acceleration.

So, the person at the equator has the greater acceleration.

Answer 2

The person at the equator would experience the greater acceleration. Centripetal acceleration is equal to the radius times the angular velocity squared. At the north pole, the radius would be zero, that is, the person is on the axis of rotation, so the centripetal acceleration would be essentially zero.

At any other location on the planet, the angular velocity is one rotation every 24 hours, so the magnitude of the centripetal acceleration is dependent on the radius only. The person on the equator has the largest radius, the radius of the earth, so she would experience the greatest acceleration.

Answer 3

Centripetal acceleration is given by:

a_c = v²/r

The radius "r" is larger at the equator than either of the poles, therefore, based on this metric the cent accel is smaller than at the pole.

What about the velocity at these two locations....the linear velocity? Is the day longer at the pole than at the equator or the other way around?

This metric will give you the velocity. If they are different will it be enough to offset the effective difference between the radii at these two places?

Some questions you should know already.....this will help you answer your question. It won't help you much if you are handed all the answers. If this doesn't win me points.....I don't care in the least. I'm not here to win points, but to actually 'help' people. I'm hoping the information I've given you is plenty to be of help, but also shy enough that you can easily think it thru and answer it to completion.

Answer 4

The one at the equator since the acceleration is related to the distance from the axis of rotation.

a=-r*w^2

The angular speed is the same, each rotates 360 degrees in 24 hours. At the equator the r will be the radius of the Earth, while at the pole it will be 0 directly on the pole.


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