Acc. due to earth's rotation - Thought Experiment

  1. Hi All,

    I have always been haunted by this basic question and will be grateful to anyone who can shed light on this!

    Please consider this experiment - A cube is kept on a plane horizontal surface on the equator (where the earth's rotational speed is the maximum). If the friction between the cube and the surface is zero, will the cube move on the surface in direction opposite to the earth's rotation? Or rather, will the cube stay stationary and the plane move along with the earth since there is no friction to drag the cube forward with it?

    I have never understood why we do not feel the earth rotate, since it's an angular motion despite constant speed, so everything on earth is constantly accelerating. Is it because the acceleration is too small?

    Thanks!
    Manish
     
  2. jcsd
  3. Drakkith

    Staff: Mentor

    We don't feel the Earth rotate for a few reason:

    1. The rotation of the Earth is too slow for its size to be noticeable unless you perform specific experiments to look for it.

    2. We are already moving (rotating) with the Earth's surface, so unless there is so force to stop us, we will continue to move with the Earth's rotation even in the absence of friction. In your example the cube is initially in motion, so when it is placed on a friction-less surface it stays in motion and doesn't slide anywhere. Both the plane and the cube remain stationary with respect to the Earth's surface.
     
  4. Thanks very much Drakkith. That clears it up for me.
     
  5. Nathanael

    Nathanael 1,132
    Homework Helper

    Hello and welcome,

    Haunted in the enjoyable way, I hope!

    My first thoughts (after reading the rest) were that it doesn't matter if it is at the equator or not, since that should only affect the magnitude of the effect (if the effect is there).

    Force of friction is not necessary to move in rotation with the Earth. The cube would "want" to move in a straight line tangent to the rotation of Earth. A frictional force would only affect that "straight-line" or "tangent" motion of the cube (it would slow it down that way).

    What keeps you moving in rotation with the Earth is that it is pulling you "downwards" (which just means "towards the center of rotation").

    Someone should correct me if I'm wrong on this part;
    I think, if we were somehow to feel the Earth's rotation, it would be felt upwards. The way I understand it, the reason we don't feel it, is that it's along the same axis as gravity, so the only effect it causes is that the "feeling of gravity" is weakened a bit. (And the ground pushes up on you a little less hard.)

    From a loose perspective, you could say "the feeling of rotational motion is overcome by the feeling of gravity"
     
  6. Nathanael

    Nathanael 1,132
    Homework Helper

    It doesn't take a force to stop us from moving with the Earth's rotation, it takes a force to keep us doing it (gravity).
     
  7. Drakkith

    Staff: Mentor

    My apologies, I wasn't clear. Gravity accelerates us towards the surface of the Earth, but it does not keep us moving tangentially to the rotation. That is the result of our current motion.
     
  8. Matterwave

    Matterwave 3,816
    Science Advisor
    Gold Member

    This is only true at the equator. Anywhere else, the centrifugal force is off-axis (unless you're at the poles, where the centrifugal force is 0), it points perpendicularly directly away from the axis of rotation and therefore not directly away from the center of the Earth.

    A plumb line not located at the equator would not point directly towards the center of the Earth, but slightly away from it due to this effect.
     
  9. The cube has inertia. If there are no forces acting on it then it will keep doing whatever it was doing.

    Objects appear to weigh less at the equator than at the poles. I recommend you work out how much less to prove to yourself how significant it is or isn't.
     
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