The given figure represents a rotating system with two bodies, A and O. We need to determine the angular velocity of A with respect to O at the instant shown in the figure. To do this, we will consider the motion of both bodies and their relative angular velocities.

Motion of Body A:
- Body A is rotating about a fixed axis passing through point A, which is perpendicular to the plane of the figure.
- The direction of rotation is counterclockwise, as indicated by the arrow.
- The angular velocity of A with respect to an inertial frame is denoted as ωA.

Motion of Body O:
- Body O is stationary; hence, its angular velocity with respect to the inertial frame is zero.

Relative Angular Velocity:
- The angular velocity of A with respect to O can be determined by subtracting the angular velocity of O from the angular velocity of A.
- Mathematically, ωA/O = ωA - ωO.

Determining the Angular Velocity of A with respect to O:
- From the given figure, we can observe that point A on body A is at a certain distance from point O on body O.
- Let's denote this distance as r.
- The angular velocity of A with respect to O can be expressed as the product of the angular velocity of A with respect to the inertial frame (ωA) and the ratio of the distance from O to A (r).
- Mathematically, ωA/O = ωA * r.

Summary:
- The angular velocity of A with respect to O at the instant shown in the figure is given by the product of the angular velocity of A with respect to the inertial frame (ωA) and the distance from O to A (r).
- By considering the motion of both bodies and their relative angular velocities, we can determine the angular velocity of A with respect to O.