A flywheel initially rotates at 600 rev per minute. After 10 seconds, the angular velocity increases to 900 rev per minute at a constant rate. The torque of [tex]$350 \pi \, \text{Nm}$[/tex] is required for the flywheel to accelerate at this rate.

(i) Find the initial and final angular momentum during the 10 seconds.

The initial and final angular momentum of a flywheel can be calculated by finding the moment of inertia from the known torque and angular acceleration, and then multiplying by the initial and final angular velocities.

Explanation:

The question refers to the calculation of the initial and final angular momentum of a flywheel in a given scenario. Angular momentum is given by the product of the moment of inertia (I) and the angular velocity (ω) (L = Iω).

To calculate the initial and final angular momentum, we first convert the revolutions per minute to radians per second (ω = RPM * 2π / 60).

Hence, the initial angular velocity is ωi = 600 RPM * 2π / 60 = 62.83 rad/s and the final angular velocity is ωf = 900 RPM * 2π / 60 = 94.25 rad/s. We can use the formula for angular acceleration (α = Δω / Δt), to find the moment of inertia, since torque (τ) equals I*α. Rearranging I = τ / α gives us the moment of inertia. Finally, we calculate the initial and final angular momentum using L = I * ω.

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