Question

Express the unsteady angular momentum equation in vector form for a control volume that has a constant moment of inertia I, no external moments applied, one outgoing uniform flow stream of velocity V → , and mass flow rate m . .

Answer 1

Step-by-step explanation:

• Recall that the angular momentum equation is given as I∝ = r x F

• Taking note that the moment of inertia as constant.

• The velocity of uniform flow is V →

• The mass flow is m

• Hence, the angular momentum equation in the control volume is given as I∝ = r x mF

• where ∝ is the angular acceleration, r is the position vector from the axis of rotation to any point on the line of action of force.