Isaac Newton once posed a fascinating puzzle related to the Earth’s rotation, which offers a counter-intuitive answer about where an object would land if dropped from a high tower. This question, shared in a letter to Robert Hooke in 1679, challenges our initial assumptions about motion and rotation.
The Puzzle Revisited
When letting an object fall from a tall structure while considering the Earth’s rotation, where does it land?
- Slightly to the west
- Slightly to the east
- Directly at the bottom
The solution is that the object lands slightly to the east.
Understanding the Dynamics
The Earth rotates from west to east. Initially, one might assume the object would land slightly to the west because of the Earth’s eastward spin during the fall. However, this ignores the fact that the object, like the tower, is already moving with the Earth’s rotation. It may seem logical next to expect it to fall directly beneath the tower, but that is also incorrect.
The answer lies in the conservation of angular momentum, a principle determining the properties of rotating bodies. As the object falls, it behaves like a spinning ice-skater who spins more quickly by pulling in their arms. Although the object’s mass doesn’t change position the same way, its angular velocity does increase as it drops closer to Earth’s rotational axis.
This increase in angular velocity means the object spins slightly faster than the Earth’s surface as it descends, resulting in a landing site slightly eastward from the point directly below the drop. For instance, if we consider an object released from the Eiffel tower on the equator, the displacement to the east would be approximately 11 centimetres.
The Science Behind the Spin
The phenomenon can be explained by keeping angular momentum constant. The mathematical relationship wr2 describes this, where w stands for angular velocity, and r represents the distance to the axis of rotation. As r reduces during the fall, angular velocity w must rise, leading the fallen object to exceed the rotational speed of the Earth’s surface slightly.
The details of this classic puzzle and its mechanics are further elaborated in David Acheson’s book, Wonders in Motion, The Story of Dynamics, which delves into the history and underlying science.
Reporting based on coverage first published by theguardian.com.