Answer
The angular momentum of the beetle-disk system remains the same.
The magnitude of the beetle's angular momentum and angular velocity both decrease.
The magnitude of the disk's angular momentum and the magnitude of the disk's angular velocity both increase.
Work Step by Step
Since there is no external torque on the system, the angular momentum of the beetle-disk system remains the same.
We can write a general expression for the angular momentum:
$L = I~\omega$
Since the beetle walks opposite the direction of rotation, the magnitude of the beetle's angular velocity $\omega$ will decrease, which in turn decreases the magnitude of the beetle's angular momentum.
The magnitude of the beetle's angular momentum and angular velocity both decrease.
Therefore, the magnitude of the disk's angular momentum must increase, which means that the magnitude of the disk's angular velocity must also increase.