Author Topic: Episode #604  (Read 1574 times)

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Offline werecow

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Re: Episode #604
« Reply #15 on: February 08, 2017, 12:10:14 PM »
Did anyone else feel that the listener's question was only partially answered? They asked:

Quote
It seems to me if a person was traveling roughly 1000 miles an hour in a circle the cintrifical force would be enormous and without that force it seems a person would be crushed at the poles.



Looking at the diagram above, I think the answer to that (if I understand physics well enough) is that the curvature of the circle that you're traveling on is so gentle that the path of inertia is almost (but not quite) parallel to that curvature (relative to the velocity at which you're traveling). So that means that there is actually relatively little change in direction, and thus little acceleration, and by extension (since Foutward = -m*ainward), the component of the (virtual) force that is outward perpendicular to the surface of the earth is relatively small.

Or, if you like, your angular velocity is relatively small even though your velocity along the circular path of the earth's equator is pretty substantial. So, I'd guess that on a smaller planet with the same rotational speed of 1000mph measured "across the ground" (but therefore a much larger angular velocity and a much greater change in direction per unit time), you'd feel a much greater centrifugal force.

Would appreciate feedback from physicists.

Offline fuzzyMarmot

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Re: Episode #604
« Reply #16 on: February 08, 2017, 07:55:07 PM »
I think you are right on the money, werecow.

If the position of a person is r(t) (a vector in 3-space), and w is the angular velocity (a vector with magnitude equal to the angular speed and direction along the rotational axis), then the "centrifugal force" is m wx(wxr), where "x" is the cross product and m is the person's mass. This is the amount of force that gravity is "reduced by". Note that it depends on angular speed, not linear speed (i.e., "across the ground" speed).

The listener's question about the magnitude of the centrifugal force indicates that they are thinking of linear speed, not angular speed. Your explanation would have helped them a lot!

Offline Sawyer

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Re: Episode #604
« Reply #17 on: February 08, 2017, 08:15:42 PM »
To put some numbers on it:

a = (v)*(v) / r

a = (2 pi r / t)^2 / r                      t= 1 day

a = (4 pi^2) *r / (t^2)

a ~ 0.034 m/s^2

Compared this to the acceleration of gravity, which is ~9.81m/s^2.   

Offline werecow

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Re: Episode #604
« Reply #18 on: February 08, 2017, 08:42:35 PM »
Thanks for the feedback. Glad I didn't embarrass myself too much. }|:o)

Offline stands2reason

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Re: Episode #604
« Reply #19 on: February 24, 2017, 06:05:49 PM »

 

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