Engineering Mechanics: Dynamics
8th Edition
ISBN: 9781118885840
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY

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Question
Chapter 6.9, Problem 167RP
To determine

## The final angular velocity

The final angular velocity is 1.811 rad/s.

### 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 O(IO).

IO=4(13ml2)        (I)

Here, mass of the rectangular plate is m and length of the plate is l.

Apply conservation of angular momentum using Figure (1).

t1t2MOdt=(HO)2(HO)1MO=Fcos15°(0.8m)        (II)

Here, applied force is F, moment of external forces about O is MO, initial and final time taken are t1 and t2, and initial and final angular momentum are (HO)2 and (HO)1.

Write the expression to determine the moment about point O.

MOt2=IOω        (III)

Conclusion:

Substitute 60kg for m and 1.2m for l in Equation (I).

IO=4(13×60kg×(1.2m)2)=4×28.8=115.2kgm2

Substitute 90N for F in Equation (II).

MO=90N×cos15°(0.8m)MO=69.55N.m

Substitute 3 s for t2, 69.55N.m for MO and 115.2kgm2 for IO in Equation (III).