Swapnil Saxena
Last Activity: 12 Years ago
This fact can be can be best understood on the basis of law of conservation of angular momenta.
When we construct a tall building we tends increase the bulk or simply mass of the earth at a particular point which is otherwise distributed evenly on its surface. As such now there is a slight increase in the moment of inertia of the system and consequently angular velocity decreases. When angular velocity decreases the time needed by the earth to complete one rotation will increase. However for the increse to be observable, the height of the buliding should be very large and building should be very bulky.
It can also be explained quite mathematically.
Assume thet the initial earth is a uniform sphere(approx.) with mass M. Its moment of inertia is 2/5MR^2
Now we constructed a bulitding of mass m using construction materal which is dispersed on the earth.
Now the moment of inertia of earth is 2/5(M-m)R^2 (R will not chage significantly) . Also the moment of inertia of the building is m(R+H/2)^2. where H is the height of the buliding
So now the anglar momenta of the system is 2/5(M-m)R^2 + m(R+h/2)^2 that would definitely > 2/5MR^2 if the height is significantly large. Then Acc to the law of angular momenta :- The final angular velocity should be less than initial one. Now since the angular velocity has decreased the time should have to increase.
Simply tall builiding tend to increse the moment of inertia of the system due to which its angular velocity decreases and duration of a day increases.