# When you stand on the observation deck of the Empire State Building in New York, is your linear speed due to the Earth's rotation greater than, less than, or the same as when you were on the ground floor?

##### 1 Answer

Linear speed due to the Earth's rotation is greater than observer's linear speed when he is at the ground floor.

#### Explanation:

Look at the following picture showing rotation of earth and speed at various latitudes.

All point on the earth rotate in front of the sun over a period of 24 hours. The points on the equator have the highest rotational speed and the ones at poles have the lowest, zero speed.

If

We know that the Empire State Building is situated at

The linear speed of observer when located at ground floor level is

Let

The linear velocity of observer due to rotation of earth now is

Comparing equations (2) and (3) we know that linear speed due to the Earth's rotation is greater than observer's linear speed when he is at the ground floor.