Why do all objects fall at the same rate in a vacuum?

All objects fall at the same rate in a vacuum due to the uniform acceleration caused by gravity.

In more detail, this phenomenon is a fundamental principle of physics, as stated by Galileo Galilei and later confirmed by Albert Einstein in his theory of general relativity. When in a vacuum, where there is no air resistance or friction to slow things down, all objects, regardless of their mass, will fall at the same rate. This rate is known as the acceleration due to gravity, which on Earth is approximately 9.81 m/s².

The reason behind this is that gravity acts uniformly on all objects. In a vacuum, the only force acting on a falling object is gravity. This force is proportional to the mass of the object, as stated by Newton's second law of motion (Force = mass x acceleration). Therefore, an object with twice the mass of another will experience twice the gravitational force. However, because the object also has twice the mass, it requires twice the force to achieve the same acceleration. As a result, the two cancel each other out, and all objects fall at the same rate, regardless of their mass.

Understanding Newton's first law, often referred to as the law of inertia, further solidifies why objects in a vacuum are not slowed by air resistance or other forces, leading to a consistent falling speed. Moreover, Newton's third law of motion explains the interaction between two objects, such as a falling object and the Earth, highlighting the mutual forces that do not affect the uniform fall rate in a vacuum.

This principle can be difficult to observe in everyday life because we are not usually in a vacuum. Air resistance can significantly affect the rate at which objects fall, making lighter or less aerodynamic objects fall slower than heavier or more aerodynamic ones. However, in a vacuum, where there is no air to provide resistance, this principle becomes clear.

IB Physics Tutor Summary: In a vacuum, all objects fall at the same speed because gravity pulls on them equally, without air resistance to slow any down. This happens due to gravity's uniform force and is explained by physics laws from Galileo and Einstein. Simply, in a vacuum, an object's mass doesn't change how fast it falls, showing gravity's equal effect on everything.