# Is conservation of angular momentum responsible for rotating a rigid body when it slows down an internal wheel?

Suppose that there is a rigid body, such as a satellite, which contains inside it a wheel that is spinning at a constant rate. This means that the satellite has a certain, constant, angular momentum vector $$\vec L$$. Now suppose that the internal wheel is slowed down by means of some brakes. My understanding is that no net torque acts on the system in this process (by principle of equal and opposite reaction from Newton's 3rd law). Therefore, $$\vec L$$ is constant, and the satellite must compensate the slowing down of its internal wheel by itself (the satellite "outer structure") gaining rotation speed. Therefore, slowing down an internal spinning wheel will rotate the spacecraft due to conservation of angular momentum (see the diagram below). Is my thinking here correct?

• The satellite does not have angular momentum, the wheel has. – John Alexiou Jul 10 at 6:59
• – PM 2Ring Jul 10 at 7:17
• Don't brakes work by applying Torque in the opposite direction? Please correct me if wrong. – Vamsi Krishna Jul 10 at 10:18

If initially the wheel has angular momentum $$\vec{L}$$ and the satellite $$0$$, and brakes are applied between them, then some of that angular momentum is going to be transferred to the satellite.
$$\Delta \text{(angular momentum)} = \text{(torque)} \cdot \Delta \text{(time)}$$