Two wheels with identical moments of inertia are rotating about the same axle. The first is rotating clockwise at 2.0 rad/s, and the second is rotating counterclockwise at 6.0 rad/s. If the two wheels are brought into contact so that they rotate together, their final angular velocity will be

w = 2 rad / s  counterclockwise

Explanation:

This is an exercise in angular momentum, we define a system formed by the two wheels in such a way that the torques during contact have been internal and the angular moeoto0o is conserved

            L₀ = L_f

We assume that the counterclockwise rotations are positive, let's look for the initial moment before the collision

           L₀ = I w₁ + I w₂

where the angular velocity of the first wheel is w₁ = - 2.00 rad / s and the angular velocity of the second wheel is w₂ = 6.0 rad / s

As the wheels collide and remain in unity, the final angular momentum after the collision

            I_total = 2 I

            L_f = I_total w

we substitute

            I w₁ + I w₂ = I_total w

            w =

             w =

             w =

let's calculate

             w =

             w = 2 rad / s

the positive sign indicates that the rotation is counterclockwise