Concept explainers
Calculate the angular velocity of frame and moment of inertia of pulley and frame about rod CD.Coller A and B slide on frame collars are attached by a cord to slide over a frame.
Answer to Problem 17.89P
Angular velocity of the frame is
Explanation of Solution
Given information:
Mass of coller A =
Mass of coller B =
The velocity of coller A at position
Concept used:
Conservation of angular momentum.
Conservation of energy.
calculation:
component of velocity for coller A,
For position 1,
From equation (1),
Potential energy,
Kinetic energy,
Angular momentum,
For position 2,
Potential energy,
Kinetic energy,
Angular momentum,
By conservation of angular momentum,
By conservation of energy,
Further solving we get
Considering only the positive value.
Hence,
Moment of inertia of pulley and frame is 0.0507 kg.m2
To find the angular velocity of the frame, we have
Conclusion:
By applying conservation of angular momentum and conservation of energy for initial and find the position of coller relative to the frame we get,
Angular velocity of the frame is
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Chapter 17 Solutions
Vector Mechanics For Engineers
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