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The centripetal force on Earth is constantly exposing Earth to the acceleration. Why can't we feel this change of direction?

Qmechanic
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yaxraz
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2 Answers2

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At the equator, when the effect is the largest, we should feel a centrifugal correction of: $$a=\Omega_\oplus^2R_\oplus\approx\left(\frac{2\pi}{86164\,\text{s}}\right)^2\cdot6378\,\text{km}=0.0339\,\frac{\text{m}}{\text{s}^2}\approx0.00346g$$ This $0.3\%$ correction to $g$ is measurable, but imperceptible.

DanDan0101
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The centripetal force acts perpendicular to the surface that's why it just changes the direction.

Now you must be talking about centrifugal force, which is responsible for the acceleration you feel while on marry go round,

The centrifugal acceleration is $$a_{cfg} = \omega^2 r$$

Now taking $r=6400000$ m $\omega= 2\pi/ T$ we get $$a_{cfg} =\left(\frac{2\pi}{60×60×24}\right)^2×6400000 = 0.0338\ m/s^2$$

While the acceleration due to gravity is $ g= 9.8\ m/s^2$ completely overshadowing this effect.

If there were no gravity you would have surely felt it, even now you feel it, but you can't distinguish it from gravity as both are fictitious force and have same acceleration for every mass,

Pradyuman
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    I'm pretty sure gravity isn't a fictitious force – DanDan0101 Apr 05 '23 at 03:26
  • Does it have all the properties of a fictitious force?? Does it vanish in the inertial frame of reference? – Pradyuman Apr 05 '23 at 03:28
  • Well, for one, it has an action-reaction pair, which fictitious forces lack – DanDan0101 Apr 05 '23 at 03:29
  • Every fictitious force is same as gravity, and you *can't* distinguish it by any experiment from a fictitious force. That's equivalence principle . – Pradyuman Apr 05 '23 at 03:32
  • That is true if we're working in GR, but I think OP is working in the Newtonian framework, where gravity is modelled by a real, rather than fictitious force – DanDan0101 Apr 05 '23 at 03:34
  • Well Newtonian mechanics can be derived from the GR in small limits, but the reality is that gravity is fictitious force, and I'll go to length quoting KK theory that even electromagnetic force can be regarded as fictitious, if one were to accept that there's a 4th dimension of space. I.e. 5 dimensional space-time – Pradyuman Apr 05 '23 at 03:39
  • The idea here to introduce gravity as fictitious force was to show that one cannot distinguish it from gravity, and you said it yourself that this would add to gravity. That's the reason we measure fictitious forces in terms of $g$ – Pradyuman Apr 05 '23 at 03:43