So supposedly angular momentum of a system is conserved, right? Well, consider this video:

 

 

If, hypothetically, the cat jumped while the roomba was rotating, would the cat be spinning at an angular velocity equal to whatever the angular velocity of the rotating roomba was when the cat jumped?

So supposedly angular momentum of a system is conserved, right?

 

Angular momentum is conserved if there is no net torque on the system.

 

 

If, hypothetically, the cat jumped while the roomba was rotating, would the cat be spinning at an angular velocity equal to whatever the angular velocity of the rotating roomba was when the cat jumped?

 

If the motor was engaged, yes. If the roomba was simply spinning with no torque, then the angular speed would be reduced by the same proportion that the moment of inertia increased.

Unless the cat corrected his spin or added to it with muscular input as he jumped.

This is a living animal with full control of its musculiture and not some inanimate object that responds only to forces outside itself.