The final angular velocity
Answer to Problem 167RP
The final angular velocity is .
Explanation of Solution
Draw the free body diagram of the door as shown in Figure (1).
Write the expression to determine the moment of inertia of the gate about .
Here, mass of the rectangular plate is and length of the plate is .
Apply conservation of angular momentum using Figure (1).
Here, applied force is , moment of external forces about is , initial and final time taken are and , and initial and final angular momentum are and .
Write the expression to determine the moment about point .
Substitute for and for in Equation (I).
Substitute for in Equation (II).
Substitute 3 s for , for and for in Equation (III).
Thus, the final angular velocity is .
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Chapter 6 Solutions
Engineering Mechanics: Dynamics