Centrifugal Force due to Rotation of the Earth
Even though Earth is treated as an inertial frame, it is actually not so. Earth spins about its own axis with an angular velocity ω. Any object on the surface of Earth (rotational frame) experiences a centrifugal force. The centrifugal force appears to act exactly in opposite direction from the axis of rotation. It is shown in the Figure 3.48.
The centrifugal force on a man standing on the surface of the Earth is Fc = mω2r
where r is perpendicular distance of the man from the axis of rotation. By using right angle triangle as shown in the Figure 3.48, the distance r = R cos θ
Here R = radius of the Earth
and θ = latitude of the Earth where the man is standing.
Calculate the centrifugal force experienced by a man of 60 kg standing at Chennai? (Given: Latitude of Chennai is 13°
The centrifugal force is given by Fc = mω2 R cosθ
The angular velocity (ω) of Earth = 2π/T.
where T is time period of the Earth (24 hours)
The radius of the Earth R = 6400 Km = 6400 × 103 m
Latitude of Chennai =13°
A 60 kg man experiences centrifugal force of approximately 2 Newton. But due to Earth’s gravity a man of 60 kg experiences a force =mg = 60 × 9.8 = 588N. This force is very much larger than the centrifugal force.