NCERT Class 11 Physics Solutions: Chapter 7 – System of Particles and Rotation Motion-Part 10

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Question 7.25:

Two discs of moments of inertia and about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds and are brought into contact face to face with their axes of rotation coincident.

(a) What is the angular speed of the two-disc system?

(b) Show that the kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs. How do account for this loss in energy?

Take

Answer:

(a) The angular speed of the two-disc system:

Moment of inertia of disc

Angular speed of disc

Angular speed of disc

Angular momentum of disc

Angular momentum of disc

Angular momentum of disc

Total initial angular speed of the system ,

When the two discs are joined together, their moments of inertia get added up.

Let be the angular speed of the system.

Total final angular momentum,

Using the law of conservation of angular momentum,

Angular momemntum and its relation between the I and ω shown …

Figure Shown the Angular Momemntum

Loading image

We have:

(b) The kinetic energy of the combined system is less than the sum of the initial kinetic energies of the two discs:

Kinetic energy of disc

Kinetic energy of disc

Total initial kinetic energy,

When the discs are joined, their moments of inertia get added up.

Moment of inertia of the system,

Angular speed of the system

Final kinetic energy

All the quantities on RHS are Positive.

The loss of can be attributed to the frictional force that comes into play when the two discs come in contact with each other.