Final answer:
The average angular acceleration of the Rolls-Royce Trent 1000 fan during the specified time interval is approximately 628.32 rad/s². This calculation is derived from the change in angular velocity, which is 700 pm, over 7 seconds. The conversion to rad/s² involves multiplying by 2π, resulting in the final answer.
Step-by-step explanation:
To find the average angular acceleration, we first need to calculate the change in angular velocity. From the given information, the fan goes from 1500 pm to 2200 pm in 7 seconds. The change in angular velocity (δω) can be found by subtracting the final angular velocity (2200 pm) from the initial angular velocity (1500 pm): δω = 2200 pm - 1500 pm = 700 pm. To find the average angular acceleration (α), we can use the formula: α = δω / δt. Where δω is the change in angular velocity and δt is the change in time. Plugging in the values, we get α = (700 pm) / (7s) = 100 pm/s. Since we need to express the answer in rad/s², we need to convert the units. One rotation (rev) is equivalent to 2π radians. Therefore, we can convert pm/s to rad/s by multiplying by 2π: α = (100 pm/s) * (2π rad/rev) = 200π rad/s² ≈ 628.32 rad/s².