Instantaneous centre (IC) of rotation — construction rule: For a moving rigid member with known directions of motion at its two ends, the instantaneous centre lies at the intersection of lines drawn at each end that are inclined at which angle to the local direction of motion?

Introduction / Context:
The instantaneous centre (IC) of rotation is a kinematics concept used to analyze planar motion of rigid bodies. Locating the IC allows velocities to be obtained quickly without full vector calculus, which is valuable in mechanisms and machine theory.

Given Data / Assumptions:

• Planar motion of a rigid member.
• Directions of velocity (tangents to paths) at two distinct points on the member are known.
• No constraints beyond planar rigidity.

Concept / Approach:

At any instant, the velocity at a point is perpendicular to the radius from the IC to that point. Hence, drawing through each known point a line perpendicular (normal) to the velocity direction gives two lines that must pass through the IC. Their intersection is the instantaneous centre.

Step-by-Step Solution:

Verification / Alternative check:

With the IC known, compute velocity of any point as V = ω * r, where r is the distance from the IC. Cross-check with the original known velocities to confirm consistency.

Why Other Options Are Wrong:

30°, 45°, and 60° (a–c) do not satisfy the orthogonality condition between velocity and radius to the IC. 0° (e) would place the line along the velocity direction, which cannot pass through the IC.

Common Pitfalls:

Drawing lines along the velocity direction instead of the normal; mixing up normal and tangent; using approximate sketches that miss the true intersection.

Final Answer:

90°