Two discs of moments of inertia I1 and I2 about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds ω1 and ω2 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 you account for this loss in energy? Take ω1 ≠ ω2.

Asked by Abhisek | 1 year ago |  61

1 Answer

Solution :-

(a) Let I1 and I2 be the moments of inertia of two discs having angular speeds w1, and w2 respectively. When they are brought in contact, the moment of inertia of the two-disc system will be I1 + I2. Let the system now have an angular speed w. From the law of conservation of angular momentum, we know that
NCERT Solutions for Class 11 Physics Chapter 7 System of Particles and Rotational Motion Q25
Now, (w1 – w2)2 will be positive whether w1 is greater or smaller than w2.
Also,I1I2/2(I1+ I2) is also positive because I1 and I2 are positive.
Thus, k1– k2 is a positive quantity.
k1 = k2 + a positive quantity or k1 > k2
The kinetic energy of the combined system ( k2) is less than the sum of the kinetic energies of the two dies.The loss of energy on combining the two discs is due to the energy being used up because of the frictional forces between the surfaces of the two discs. These forces, in fact, bring about a common angular speed of the two discs on combining.

Answered by Pragya Singh | 1 year ago

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