Mechanical Engineering Exam > Mechanical Engineering Questions > Which of the following is correct? (For A rep...
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Which of the following is correct? (For A representing the vector representation of the axis of rotation, r the radius vector and F the force vector)
- a)A.(rxF)
- b)Ax(rxF)
- c)A.(r.F)
- d)Fx(r.F)
Correct answer is option 'A'. Can you explain this answer?
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Which of the following is correct? (For A representing the vector repr...
The correct form of the equation is given by A.(rxF). Where A represents the vector representation of the axis of rotation, r the radius vector and F the force vector. This is usually done for determining the moment of the force about the axis. That is if body is being rotated by the force about an axis.
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Which of the following is correct? (For A representing the vector repr...
Understanding the Given Options
In this question, we are dealing with vector representations that relate to rotation and torque in mechanical engineering. The vectors involved are:
- A: Axis of rotation
- r: Radius vector (from the axis of rotation to the point where force is applied)
- F: Force vector
Explanation of Each Option
- Option A: A.(r x F)
- This expression calculates the dot product of the axis vector A with the torque vector (r x F). The torque generated by the force F applied at a distance r from the axis of rotation is essential for rotational motion. This expression is valid and meaningful in the context of rotational dynamics.
- Option B: A x (r x F)
- This is a cross product operation. While it can be computed, it does not have a direct physical interpretation related to the axis of rotation and torque.
- Option C: A.(r . F)
- Here, (r . F) is a scalar product. This does not represent a physical quantity related to torque or rotation, making it incorrect in this context.
- Option D: F x (r . F)
- This expression also involves a dot product, and the resultant does not provide any information regarding torque or rotational movement.
Conclusion
The correct answer is Option A: A.(r x F), as it effectively represents the relationship between the axis of rotation and the torque generated by the force applied at a distance, adhering to the principles of rotational dynamics in mechanical engineering.
In this question, we are dealing with vector representations that relate to rotation and torque in mechanical engineering. The vectors involved are:
- A: Axis of rotation
- r: Radius vector (from the axis of rotation to the point where force is applied)
- F: Force vector
Explanation of Each Option
- Option A: A.(r x F)
- This expression calculates the dot product of the axis vector A with the torque vector (r x F). The torque generated by the force F applied at a distance r from the axis of rotation is essential for rotational motion. This expression is valid and meaningful in the context of rotational dynamics.
- Option B: A x (r x F)
- This is a cross product operation. While it can be computed, it does not have a direct physical interpretation related to the axis of rotation and torque.
- Option C: A.(r . F)
- Here, (r . F) is a scalar product. This does not represent a physical quantity related to torque or rotation, making it incorrect in this context.
- Option D: F x (r . F)
- This expression also involves a dot product, and the resultant does not provide any information regarding torque or rotational movement.
Conclusion
The correct answer is Option A: A.(r x F), as it effectively represents the relationship between the axis of rotation and the torque generated by the force applied at a distance, adhering to the principles of rotational dynamics in mechanical engineering.
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