Final answer:
The magnitude of the angular acceleration of the pulley can be calculated using the equation τ = Iα, where τ is the torque applied to the pulley, I is the moment of inertia of the pulley, and α is the angular acceleration. In this case, the steady downward force applied to the wire is equivalent to the torque applied to the pulley. Therefore, using the given values, we can calculate the magnitude of the angular acceleration as 0.5 rad/s².
Step-by-step explanation:
The magnitude of the angular acceleration of the pulley can be calculated using the equation:
τ = Iα
Where τ is the torque applied to the pulley, I is the moment of inertia of the pulley, and α is the angular acceleration.
In this case, the steady downward force applied to the wire is equivalent to the torque applied to the pulley.
Therefore, we can use the equation:
τ = F × r
Where F is the force and r is the radius of the pulley. Plugging in the values, we get:
τ = 15 N × 0.2 m = 3 N·m
Now, we can rearrange the first equation to solve for α:
α = τ / I
Plugging in the values, we get:
α = 3 N·m / 6 kg·m² = 0.5 rad/s²
Therefore, the magnitude of the angular acceleration of the pulley is 0.5 rad/s².