1. Understand the Concepts

* Angular Acceleration (α): The rate of change of angular velocity (ω).

* Angular Velocity (ω): The rate of change of angular displacement (θ).

* Angular Displacement (θ): The angle through which an object rotates.

2. Relevant Equations

We'll use the following equations of rotational motion:

* ω = ω₀ + αt (where ω₀ is the initial angular velocity)

* θ = ω₀t + (1/2)αt²

3. Solve the Problem

* Initial Conditions: The bar starts from rest, so ω₀ = 0.

* Angular Acceleration: α = 10 + 6t

* Time: t = 3.26 s

Step 1: Find the angular velocity at t = 3.26 s

* ω = ω₀ + αt

* ω = 0 + (10 + 6 * 3.26) * 3.26

* ω = 81.02 rad/s

Step 2: Find the angular displacement

* θ = ω₀t + (1/2)αt²

* θ = 0 * 3.26 + (1/2) * (10 + 6 * 3.26) * (3.26)²

* θ = 132.99 radians

Therefore, the bar rotates through approximately 132.99 radians in the first 3.26 seconds.