Specifying angular displacement completely To completely specify an angular displacement as a vector quantity for a rigid body, one must fix which of the following?
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ADirection of the axis of rotation
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BMagnitude of the angular displacement
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CSense of angular displacement (clockwise or anticlockwise along the axis)
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DAll of these
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EOnly the magnitude is sufficient in all cases
Answer
Correct Answer: All of these
Explanation
Introduction / Context:Angular displacement in rigid-body kinematics is often represented as a vector (axis–angle). To avoid ambiguity, both direction and sense relative to the axis, as well as the magnitude, must be defined.
Given Data / Assumptions:
- Small or finite rotations of a rigid body about a fixed axis.
- Right-hand rule convention for vector direction is used.
Concept / Approach:An axis–angle description includes: (1) direction of the rotation axis (unit vector), (2) magnitude of rotation (angle), and (3) sense of rotation along that axis (right-hand rule specifying positive direction). Without any of these, the specification is incomplete or ambiguous.
Step-by-Step Solution:
Choose a reference coordinate system.State the axis direction (e.g., +z).State the angle (e.g., 30 degrees or π/6 radians).State the sense (e.g., counterclockwise viewed along +z, per right-hand rule).Verification / Alternative check:In 3D, finite rotations are non-commutative; thus specifying only an angle is insufficient. Axis specification is essential.
Why Other Options Are Wrong:
- Any single attribute alone (only magnitude, only direction, or only sense) does not capture the full rotational description.
Common Pitfalls:Ignoring the sense of rotation or failing to use a clear convention (right-hand rule) when communicating rotations.
Final Answer:All of these