Satellites are often set spinning during launch to give them added stability. When astronauts visit these satellites years later, they find them still spinning. Why don't the satellites stop spinning?

Angular momentum is a crucial concept when analyzing rotating objects. It is the rotational counterpart to linear momentum.
Angular momentum (L) is defined as the product of an object's moment of inertia (I) and its angular velocity (ω): L = Iω.
This quantity is conserved in a system where no external torques act. This means if a spinning object isn't disturbed by outside forces, its angular momentum remains constant.
In the case of a satellite, once it's set spinning, its angular momentum precisely ensures it keeps spinning unless influenced by external factors.
This principle is fundamental in rotational dynamics and helps explain why satellites, once set in motion, continue to spin.

External torque refers to a force that causes an object to rotate. When a torque is applied, it changes the rotational motion of the object.
Mathematically, torque (τ) is described by the equation τ = r × F, where τ is the torque vector, r is the position vector, and F is the force vector.
For a satellite in space, the lack of significant external torques is essential. This is because torque can significantly influence angular momentum.
External forces such as thrusters or collisions could alter the satellite's rotation. However, in the vacuum of space, these forces are often negligible, resulting in the conservation of its initial spin.
This lack of external torque ensures that the satellite's angular momentum stays constant, maintaining its rotation.

The vacuum environment of space plays a significant role in maintaining a satellite's stability and motion. In space, there are very few particles.
This absence of particles means minimal friction or drag that could slow the satellite down.
Essentially, the vacuum environment ensures that there's no air resistance or friction to create external torques. Consequently, the satellite's rotation is not hindered or altered.
This uniquely stable environment is why objects in space follow Newton's First Law of Motion so perfectly.
Without these external forces, satellites can spin almost indefinitely once they are set in motion.

Stability in satellites is crucial for their proper function. By spinning, satellites gain angular momentum, which provides gyroscopic stability.
This stability helps keep the satellite orientation consistent, making it easier to point sensors, antennas, and other instruments accurately.
Spinning serves as a passive stabilization method meaning no additional energy is required to keep the satellite stable.
Even years after their initial spin, satellites can remain stable and continue their missions. This gyroscopic effect is the same principle that keeps a spinning top upright.
Such stability is extremely valuable in maintaining the satellite’s operational integrity and ensuring it serves its intended purpose over a long duration.