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?

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:

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