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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?

enter image description here

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  • $\begingroup$ The satellite does not have angular momentum, the wheel has. $\endgroup$ – John Alexiou Jul 10 at 6:59
  • $\begingroup$ Related: en.wikipedia.org/wiki/Reaction_wheel $\endgroup$ – PM 2Ring Jul 10 at 7:17
  • $\begingroup$ Don't brakes work by applying Torque in the opposite direction? Please correct me if wrong. $\endgroup$ – Vamsi Krishna Jul 10 at 10:18
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Since the satellite and the wheel are connected by an axle, they can exchange equal and opposite quantities of angular momentum, such as the total momentum is conserved,

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.

The basic law here for each body is

$$ \Delta \text{(angular momentum)} = \text{(torque)} \cdot \Delta \text{(time)} $$

and since the brake torque is applied in equal and opposite quantities on the two bodies over the same amount of time, the change in momentum on one body is transferred to the other body in the opposite sense.

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