Type of motion: particle moving about a fixed axis\n\nThe motion of a particle moving around a fixed axis is best described as:

Introduction / Context:
Classifying motion correctly is foundational in kinematics. This item distinguishes between translatory (linear), circular, and rotary (rotational) motion with respect to a fixed axis.

Given Data / Assumptions:

• A particle traces a path about a fixed axis.
• The axis does not translate; the body's points rotate about it.

Concept / Approach:
When points of a body (or a particle constrained to a radius) move about a fixed axis, the motion is rotational (rotary). 'Circular' describes the path shape in a plane; 'rotary' emphasizes motion about an axis, which is the defining feature here.

Step-by-Step Solution:

Verification / Alternative check:
A point on a rotating wheel follows a circular path, but the system motion is rotational about the axle. The axis criterion prioritizes the term 'rotary'.

Why Other Options Are Wrong:

• Translatory: No fixed axis or angular description.
• Circular: Describes the trajectory shape but not the kinematic category; the question stresses a fixed axis.
• Translatory as well as rotatry: Misspelt and inapplicable to a single particle about a fixed axis.
• Oscillatory: Back-and-forth motion about an equilibrium, not continuous rotation.

Common Pitfalls:
Equating any circular path to the term 'circular' without considering whether the axis-based definition (rotational) is being tested.

Final Answer:
rotary