Consider an infinitesimally thin section of the cylinder of width dr at a distance r from the axis of rotation. Let the area of cross-section of the cylinder be A. Let the density of the gas within this infinitesimally thin section of the cylinder be
. The the total mass on gas contained in the infinitesimally thin section of the cylinder will be,
The centrifugal force exerted by this infinitesimally thin section of the gas on the rest of the gas (for the gas with distance greater than r from the axis) will be,
From the ideal gas law equation we know that,
There should be a factor of 1/2 in the exponent, from integrating rdr = r^2/2. This agrees with the official answer.
ReplyDeleteIsn't the centrifugal force an fictious force that WE HAVE TO APPLY on the body (radially outwards) when working in an non inertial frame (that is, this frame rotates wrt an inertial frame)?
ReplyDeleteWhat I cannot Understand is how come the thin element is applying the centrifugal force in your explanation.
right hand integration is wrong,r square bi 2
ReplyDeleteHi,
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the angular velocity is constant why does then the centrifugal force exist?
ReplyDeletei get it know. even though the speed is constant the velocity is changing(the direction is changing) so the system is accelerating so it is an non inertial reference frame so the centrifugal force affects the gas
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