At ground level g is 9.8m/s^2. Suppose the earth started to increase its angular velocity. How long would a day be when people on the equator were just 'thrown off'? Why is the expression 'thrown off' a bad one?

Hello there.

At ground level g is 9.8m/s^2. Suppose the earth started to increase its angular velocity. How long would a day be when people on the equator were just 'thrown off'? Why is the expression 'thrown off' a bad one?

People would not be thrown off.

Let s = rate of rotation

Let r = radius of earth = 6,400km

Then solving (s^2) r = g will give the desired rate, from which length of day is inferred.

People would not be thrown off. They would simply move eastward in a straight line while the curved surface of earth fell away from beneath them.