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I have the following question based on a paragraph from my Physics textbook (I am translating, so the result might not be the most elegant):

It states that due to the centripetal force resulting from Planet Earth's movement, the Normal force becomes slanted away from a purely vertical line towards the centre of Planet Earth. This way the resultant force between gravity and the normal force gives us the centripetal force. It adds that this way Earth's rotation not only reduces weight and falling acceleration but also diverts them away from the vertical direction.

I am confused: First of all, on the previous page it stated that N = GmM/R^2-ma, with ma referring to the centripetal force. From this equation I had understood that the Normal Force is simply less around the equator, which was confirmed by several online sources who compare it to the reduced Normal Force in an elevator on its way down. So why would it become slanted?

Beyond that, I am lost as to the diversion of the direction of free fall…

Can somebody clear things up?

Qmechanic
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2 Answers2

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There are three real forces acting on the object: gravitation force towards the center of earth, normal force and friction. Normal force, as implied by its name, is normal to the surface. Assuming spherical earth, the normal direction is away from center of earth. Friction is perpendicular to the normal.

If earth and object were standing still, the gravitation and normal forces would equal each other. But the object is moving in a circle. So the vector sum of all three forces towards the center of circle should be equal the mass x radial acceleration. At the orthogonal direction, the body is not accelerating, so components of forces along that axis are summed to zero. These equations allow you to calculate the normal force and friction. The vector sum of normal force and friction is the "slanted normal".

The term mass x radial acceleration is coined centripetal force.

The above description is from an inertial frame.

In a non inertial frame, centripetal force is not there because it did not exist to begin with. The three true forces, gravitation, normal and friction do appear. Centrifugal force is added to "explain the physics" in the accelerating frame.

npojo
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Image of obbject on Earth's surface

When you're not on the equator, you're travelling in a circle whose centre is not the centre of the earth. As you would know, gravity always acts towards the centre and centripetal force (which isn't actually a force but an effect) acts towards the centre of the latitudinal circle you're on(the green circle). So the contact force needs to balance out these two forces. If the contact force was acting only along the line joining centre to your location(along $r$), you would have a component of the centripetal force acting perpendicular to $r$ which won't be balanced out. So, the contact force has to be slanted and won't be along $r$ . A similar logic goes for free fall

Skawang
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