In a rigid rotating link OA, how is the velocity of point A expressed relative to O___________________?
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Answer: B. perpendicular to OA
Explanation
Rigid body kinematics dictates that the linear velocity vector of any point on a rotating arm is tangent to its path. Since the path of point A is a circle centered at O, the tangent line is always perpendicular to the radius vector OA. This directional requirement stems from the cross product of angular velocity and the position vector of the point. Linear velocity equals the product of angular velocity and the radial distance from the center of rotation. Vector analysis confirms that rotational velocity vectors act orthogonally to position vectors in planar motion. Understanding this geometric relationship is essential for constructing accurate velocity polygons for complex machinery.
A velocity vector parallel to the link would imply radial motion rather than circular rotation around the center. An angle of forty-five degrees represents an arbitrary vector direction that contradicts rigid body rotational mechanics. Directing the velocity along the line AO points toward the center, which violates the tangential nature of rotation.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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