Concept explainers
A uniform rod of mass m and length 5a is bent into the shape shown and is suspended from a wire attached at point B. Knowing that the rod is hit at point A in the negative y direction and denoting the corresponding impulse by
The velocity of the mass centre
Answer to Problem 18.150RP
The velocity of the mass centre
Explanation of Solution
Given information:
The mass of the rod is
The below figure represent the schematic diagram of the rod section.
Figure-(1)
Write the expression of length of the section OA.
Here, the total length of the rod is
Write the expression of length of the section AB.
Write the expression of length of the section BC.
Write the expression of length of the section CD.
Write the expression of length of the section DE.
Write the expression of mass of the section OA.
Here, the total mass of the rod is
Write the expression of mass of the section AB.
Write the expression of mass of the section BC.
Write the expression of mass of the section CD.
Write the expression of mass of the section DE.
Write the expression of moment of inertia of section OA in
Write the expression of moment of inertia of section OA in
Write the expression of moment of inertia of section OA in
Write the expression of moment of inertia of section OA in
Write the expression of moment of inertia of section AB in
Write the expression of moment of inertia of section AB in
Write the expression of moment of inertia of section AB in
Write the expression of moment of inertia of section AB in
Write the expression of moment of inertia of section BC in
Write the expression of moment of inertia of section BC in
Write the expression of moment of inertia of section BC in
Write the expression of moment of inertia of section BC in
Write the expression of moment of inertia of section CD in
Write the expression of moment of inertia of section CD in
Write the expression of moment of inertia of section CD in
Write the expression of moment of inertia of section CD in
Write the expression of moment of inertia of section DE in
Write the expression of moment of inertia of section DE in
Write the expression of moment of inertia of section DE in
Write the expression of moment of inertia of section DE in
Write the expression of total moment of inertia in
Write the expression of total moment of inertia in
Write the expression of total moment of inertia in
Write the expression of total moment of inertia in
Write the expression of total moment of inertia in
Write the expression of total moment of inertia in
Write the expression of angular momentum about
Write the expression of angular momentum about
Write the expression of angular momentum about
Write the expression of velocity of mass centre
Here, the force is
Calculation:
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Conclusion:
The velocity of the mass centre
(b)
The angular velocity of the rod.
Answer to Problem 18.150RP
The angular velocity of the rod is
Explanation of Solution
Given information:
Write the expression of angular momentum in
Write the expression of angular velocity of the rod.
Here, the angular velocity in
Calculation:
Substitute
Substitute
Substitute
Substitute
Solve Equation (XXXIII), (XXXIX) and (XXXX).
Substitute
Conclusion:
The angular velocity of the rod is
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Chapter 18 Solutions
Vector Mechanics For Engineers
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