Centrifugal Force: Earth Rotation & Its Effects

In summary, the magnitude of the centrifugal force is not always equal to the gravitational force, and it is only true for objects in a circular orbit analyzed in a rotating frame where it is at rest. Additionally, the Earth would disintegrate if it spun fast enough for the centrifugal force to equal the gravitational force. When standing on the Earth, there is a small centrifugal force acting, but its magnitude is much smaller than that of the gravitational force. This is because the tangential velocity near the surface of the Earth is not comparable to the orbital velocity of a satellite. However, for geostationary satellites, the equality of centrifugal force and gravitational force holds since they have the
  • #1
Luca 123
21
0
We know that the Earth is rotating, and its gravitational force is the centripetal force. So if I'm standing on the Earth, I'll feel 3 forces: Gravitational force, normal force and centrifugal force. However, the magnitude of the centrifugal force is equal to the gravitational force, so wouldn't the 2 forces cancel out, leaving the normal force to be 0? Why is the normal force I feel= the magnitude of the gravitational force, when I can feel the centrifuhal force?
 
Physics news on Phys.org
  • #2
Luca 123 said:
However, the magnitude of the centrifugal force is equal to the gravitational force
That is not always true. In fact, the only time it is true is for an object in a circular orbit analyzed in the rotating frame where it is at rest.
 
  • #3
DaleSpam said:
That is not always true. In fact, the only time it is true is for an object in a circular orbit analyzed in the rotating frame where it is at rest.
So in this case, what would the centrifugal force be? I have normal force=mg=GMm/r^2, but the centrifugal force can't be zero right? So what went wrong in my calculations?
 
  • #4
DaleSpam said:
That is not always true. In fact, the only time it is true is for an object in a circular orbit analyzed in the rotating frame where it is at rest.
Also, what if we assume that the Earth is perfectly spherical, and since I'm standing still relative to the Earth, wouldn't the centrifugal force=GMm/r^2 ?
 
  • #5
Luca 123 said:
So in this case, what would the centrifugal force be? I have normal force=mg=GMm/r^2, but the centrifugal force can't be zero right? So what went wrong in my calculations?
I am not sure what case you are referring to.

If you are referring to an object in a circular orbit analyzed in the rotating frame where it is at rest then the normal force is 0. The gravitational force is mg directed inwards, and the centrifugal force is mg directed outwards.
 
  • #6
DaleSpam said:
I am not sure what case you are referring to.

If you are referring to an object in a circular orbit analyzed in the rotating frame where it is at rest then the normal force is 0. The gravitational force is mg directed inwards, and the centrifugal force is mg directed outwards.
However, in this case, wouldn't I feel weightless? Do I feel weight(i.e. normal force=/=0) because the Earth isn't perfectly spherical?
 
  • #7
Luca 123 said:
However, in this case, wouldn't I feel weightless?
Yes. You are in orbit and people in orbit feel weightless. Surely you have seen videos of astronauts in orbit.
Luca 123 said:
Do I feel weight(i.e. normal force=/=0) because the Earth isn't perfectly spherical?
No. You feel weight because you are not in orbit.
 
  • Like
Likes gracy
  • #8
DaleSpam said:
Yes. You are in orbit and people in orbit feel weightless. Surely you have seen videos of astronauts in orbit.No. You feel weight because you are not in orbit.
I'm confused. Isn't the Earth rotating on its own axis, and we are rotating along with it? Doesn't gravity act as the centripetal force? The Earth itself is a rotating frame, so the laws of ratational motion should apply(?)
 
  • #9
Luca 123 said:
I'm confused. Isn't the Earth rotating on its own axis, and we are rotating along with it? Doesn't gravity act as the centripetal force? The Earth itself is a rotating frame, so the laws of ratational motion should apply(?)
Yes, all of this is true. What is NOT typically true is that the centrifugal force equals the gravitational force. That is only true for a circular orbit.
 
  • Like
Likes gracy
  • #10
Luca 123 said:
I'm confused. Isn't the Earth rotating on its own axis, and we are rotating along with it? Doesn't gravity act as the centripetal force? The Earth itself is a rotating frame, so the laws of ratational motion should apply(?)
Gravity acts as the centripetal force PLUS the extra overhead that tries to push you into the ground. But the ground resists, pushing back on your feet with the normal force - this is the force you 'feel'. You never feel gravity directly, it's approximately uniform on the scale of a human being. Unless you're being tidally stretched by a black hole, that is.
 
  • #11
Luca 123 said:
Also, what if we assume that the Earth is perfectly spherical, and since I'm standing still relative to the Earth, wouldn't the centrifugal force=GMm/r^2 ?
No. This is is probably the source of your confusion.
The centripetal acceleration of a point on the equator is about 0.03 m/s^2. Not even close to the acceleration of gravity.
The same value will have the centrifugal acceleration, in the non-inertial frame.
The centrifugal force is just a small fraction from the weight of an object.
 
  • #12
Luca 123 said:
the magnitude of the centrifugal force is equal to the gravitational force
The Earth would disintegrate if it would spin that fast, which would solve your problems with the normal force.
 
  • #13
Luca 123 said:
Also, what if we assume that the Earth is perfectly spherical, and since I'm standing still relative to the Earth, wouldn't the centrifugal force=GMm/r^2 ?
That's the equation for gravitational force, not the equation for centrifugal/centripetal force.
 
  • #14
You are getting confused here about the concept of orbital velocity. When an object is revolving around the Earth without moving towards or away from its center then we can say that the centrifugal force is equal to the gravitational force.
But when you are standing on Earth then it is not the case, there is a centrifugal force acting on you then too but it's magnitude is very small, this magnitude is small because the tangential velocity you would have will be nowhere near the orbital velocity for a satellite near the surface of earth. Try doing the calculations for the orbital velocity near the surface of Earth and compare it to the tangential velocity of the surface of earth.

PS. you might want to study about geo stationary satellites. They remain stationary in the sky with respect to ground (the way you are stationary when you are standing still on ground). Geostationary satellites have same angular velocity as that of Earth about its axis and for it the equality of centrifugal force and gravitational force holds true.
 

What is centrifugal force?

Centrifugal force is a fictitious force that appears to act on objects that are in motion around a central point. It is the force that is experienced by objects as they move in a curved path due to the inertia of their motion.

How does Earth's rotation affect centrifugal force?

Earth's rotation causes the centrifugal force to be directed outward from the center of the Earth. This is because objects on the surface of the Earth are constantly moving in a circular path due to the rotation, and therefore experience the centrifugal force.

How does centrifugal force affect objects on the Earth?

Centrifugal force has a very small effect on objects on the Earth's surface. However, it does contribute to the slight bulging of the Earth at the equator and the flattening at the poles. It also affects the Earth's rotation and the length of a day.

What is the Coriolis effect and how is it related to centrifugal force?

The Coriolis effect is a phenomenon that causes objects in motion on the Earth's surface to appear to deviate from a straight path. This is due to the Earth's rotation and the centrifugal force acting on the objects. The Coriolis effect is responsible for the rotation of hurricanes and the direction of ocean currents.

Can we measure centrifugal force?

Yes, centrifugal force can be measured using a centrifuge or other rotating devices. However, the force is very small and difficult to measure accurately. It is also taken into account in many scientific and engineering calculations, such as designing rotating machinery or understanding the dynamics of celestial bodies.

Similar threads

Replies
22
Views
969
Replies
15
Views
2K
Replies
24
Views
3K
  • Mechanics
2
Replies
37
Views
2K
  • Mechanics
Replies
10
Views
1K
Replies
12
Views
1K
Replies
3
Views
820
Replies
2
Views
2K
Replies
2
Views
1K
Replies
12
Views
849
Back
Top