Calculate the radial acceleration (in m/s2) of an object on the ground at the earth's equator, turning with the planet. The radius of the earth is R = 6380 km.

To solve this problem we will rely on the kinematic equations of angular motion. For this case we have that the angular velocity is equivalent to the change between the proportion and the Period.

Here,

T = Time period

= Angular velocity of the object on the ground at the Earth's equator

Now the angular acceleration of the object on the ground at the Earth's equator is

Here,

= Radial acceleration of the object on the ground at the Earth's equator

R = Radius of the Earth

Replacing,

The period of the Earth is 24Hours and the radius was previously given, then

The radial acceleration of the object on the ground at the earth's equator is

it is the second option.