The instantaneous center of rotation (ICR) is a point on a moving body that has zero velocity at a particular instant. For a circular disc rolling on a straight path, the ICR is located at the point of contact between the disc and the straight path.

Explanation:

When a circular disc rolls on a straight path, the bottommost point of the disc is in contact with the straight path, and this point is stationary at any instant. At this point, the velocity of the disc is zero, and hence it is the ICR of the disc.

To understand this concept in detail, we can consider the following points:

1. The motion of a rolling disc:

When a circular disc rolls on a straight path, its motion can be resolved into two components: translation and rotation. The center of mass of the disc moves in a straight line, while the disc rotates about its center.

2. Velocity of the ICR:

At any instant, the velocity of the ICR is zero because it is the point on the disc that is momentarily at rest. The velocity of the other points on the disc can be determined by considering the motion of the disc as a combination of translation and rotation.

3. Location of the ICR:

The location of the ICR depends on the type of motion of the rolling body. For a circular disc rolling on a straight path, the ICR is located at the point of contact between the disc and the straight path. This is because the bottommost point of the disc is stationary, and hence it has zero velocity.

Conclusion:

In conclusion, the instantaneous center of rotation of a circular disc rolling on a straight path is located at the point of contact between the disc and the straight path. This is because the bottommost point of the disc is stationary, and hence it has zero velocity. Understanding the concept of ICR is essential in the study of mechanics and is used in various applications, including robotics and vehicle dynamics.