1. Convert Units:

* Time: 2 minutes = 120 seconds

* Revolutions to radians: 50 revolutions * 2π radians/revolution = 100π radians

2. Determine Angular Displacement:

* The wheel starts at rest and makes 50 revolutions, meaning its angular displacement (θ) is 100π radians.

3. Use the Angular Kinematic Equation:

* We'll use the equation: θ = ω₀t + (1/2)αt²

* θ = angular displacement (100π radians)

* ω₀ = initial angular velocity (0 radians/second since it starts at rest)

* t = time (120 seconds)

* α = angular acceleration (what we need to find)

4. Solve for Angular Acceleration (α):

* Substitute the known values into the equation: 100π = (0)(120) + (1/2)α(120)²

* Simplify: 100π = 7200α

* Solve for α: α = (100π) / 7200 = π/72 radians/second²

Therefore, the constant angular acceleration of the wheel is approximately π/72 radians/second².