Question

The world's tallest building is the Taipei 101 Tower in Taiwan, which rises to a height of 508 m (1667 ft). (a) When standing on the top floor of the building, is your angular speed due to the Earth's rotation greater than, less than, or equal to your angular speed when you stand on the ground floor?

Answer 1

The angular speed of a person at the top floor of a tall building like Taipei 101 or Burj Khalifa, due to Earth's rotation, is essentially the same as it is on the ground floor, as Earth rotates as a solid body.

Step-by-step explanation:

Angular Speed on Top vs. Ground Floor

The question pertains to the difference in angular speed experienced when standing on the top floor of a tall building compared to the ground floor. Because angular speed (ω) for a spinning object (in this case, the Earth) is given by ω = v/r, where 'v' is the linear speed and 'r' is the radius, standing on the top floor of a tall building would increase your distance (radius) from the Earth's axis of rotation. However, as the Earth rotates as a solid body, every point on its surface has the same angular speed, regardless of its radius. So, if we ignore the insignificant increase in linear velocity due to the increased radius at the top of a tall building like Taipei 101 or the Burj Khalifa, the angular speed would essentially remain equal at both locations.