at ground level g is 9.8m/s^2 suppose the earth starts to increas its angular velocity how long would a day be when people on the equator were just thrown off
w^2/Re=g
but w= 2PI*r//Period
solve for period
To calculate the effect of an increase in the Earth's angular velocity on the length of a day, we need to consider the relationship between the Earth's rotation and the gravitational force acting on objects at the equator.
At the equator, the centrifugal force due to the Earth's rotation counteracts the force of gravity. When people are "thrown off" the Earth due to an increase in angular velocity, it means that the centrifugal force becomes greater than the force of gravity, causing objects to move away from the Earth.
To determine how long a day would be in this scenario, we should focus on the concept of the Earth's moment of inertia. The moment of inertia measures an object's resistance to changes in rotation, and it depends on the distribution of mass within the object.
When people are thrown off the Earth, it would result in mass moving away from the Earth's rotation axis, thus increasing the moment of inertia. As a consequence, the Earth's rotation would slow down, leading to longer days.
However, it is important to note that the increase in angular velocity required for people to be "thrown off" the Earth is beyond what is currently physically possible. Therefore, discussing how long a day would be in this extreme scenario is purely hypothetical.
In reality, the Earth's rotation rate and the length of a day are determined by various factors, including the distribution of mass within the Earth, tidal forces from the Moon and the Sun, and other external influences. The effects of these factors are much smaller than the extreme scenario you proposed, and they lead to relatively small changes in the length of a day over time (on the order of milliseconds).