Question

The instantaneous centre of rotation of a rigid thin disc rolling on a plane rigid surface is located at:

• A. Centre of the disc
• B. An infinite distance on the plane surface
• C. The point of contact
• D. The point on the circumference situated vertically opposite to the contact point

Hint:

In rolling motion, the point on the rolling object that is in contact with the surface is momentarily at rest. The velocity of all other points on the object is a combination of translational and rotational velocities. The instantaneous centre of rotation is a crucial concept in analyzing such motions.

Answer 1

The Correct Option is D

When a rigid thin disc rolls on a plane surface, it experiences pure rolling motion. In this case, the instantaneous centre of rotation is the point on the circumference of the disc that is vertically opposite to the point of contact. This point is stationary relative to the surface during rolling, while every other point on the disc has a combination of translational and rotational motion.
The instantaneous centre of rotation is critical in understanding how the disc rotates about this point. This is known as the instantaneous centre of velocity, and its location is dependent on the radius of the disc and the point of contact with the surface.
This point also helps in understanding the kinematics of rolling motion and can be useful in solving problems related to dynamics and velocity analysis.