A uniform circular disc of mass m is set rolling on a smooth horizontal table with a uniform linear velocity v. Find the total K.E. of the disc.

Explanation

To find the total kinetic energy (K.E.) of a uniform circular disc of mass \( m \) that is rolling on a smooth horizontal table with a uniform linear velocity \( v \), we need to consider both the translational kinetic energy and the rotational kinetic energy of the disc.

### Step-by-Step Solution:

1. **Identify the Types of Kinetic Energy**:
- The total kinetic energy (K.E.) of the disc consists of two components:
- Translational K.E. due to its linear motion.
- Rotational K.E. due to its rotation about its own axis.
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