Concept explainers
Find the speed of the rod relative to the tube when
Answer to Problem 17.88P
The speed of the rod relative to the tube when
Explanation of Solution
Given information:
The mass
The mass
The angular velocity
Calculation:
Consider l is the length of the rod and the tube and O is the point of intersection of the tube and axle.
Write the equation of the centroidal mass moment of inertia
Write the equation of the centroidal mass moment of inertia
Write the equation of the tangential equation of the tube using kinematics.
Substitute
Write the equation of the tangential equation of the rod using kinematics.
Substitute
Find the equation of angular momentum about point O.
Substitute
Find the equation of kinetic energy.
Substitute
Substitute Equation (1) in Equation (2),
All the motion in the system is horizontal. Therefore, the potential energy is zero.
Consider the initial position.
At the initial position, the initial angular velocity of the system is 5 rad/s and the radial velocity is zero.
Find the angular momentum at the initial position using equation (1).
Substitute 0 for x.
Substitute 6 kg for
Find the kinetic energy at initial position using equation (3).
Substitute
Consider the final position.
Find the angular momentum at the final position using equation (1).
Substitute 0.4 m for x.
Substitute 6 kg for
Find the kinetic energy at final position using equation (3).
Substitute
Consider the conservation of angular momentum.
Substitute
Find the speed of the rod relative to the tube when
Consider the conservation of energy.
Substitute
Substitute
Thus, the speed of the rod relative to the tube when
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Chapter 17 Solutions
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