Two discs have moments of intertia I 1 and I 2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω 1 and ω 2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in…

Question

Two discs have moments of intertia I 1 and I 2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, &#969; 1 and &#969; 2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:

Aicharya · Accepted Answer

Angular momentum conservation I 1 &#969; 1 + I 2 &#969; 2 = I 1 + I 2 &#969; &#969; = I 1 &#969; 1 + I 2 &#969; 2 I 1 + I 2 Loss = 1 2 I 1 &#969; 1 2 + 1 2 I 2 &#969; 2 2 - 1 2 I 1 + I 2 &#969; 2 = 1 2 I 1 &#969; 1 2 + 1 2 I 2 &#969; 2 2 - 1 2 I 1 + I 2 I 1 &#969; 1 + I 2 &#969; 2 I 1 + I 2 2 = 1 2 I 1 I 2 I 1 + I 2 &#969; 1 - &#969; 2 2 E i - E f = I 1 I 2 &#969; 1 - &#969; 2 2 2 I 1 + I 2

Two discs have moments of intertia I 1 and I 2 about their respective axes perpendicular to the plane and…

Solution