First slide

Rotational motion

Question

Two discs, each having moment of inertia 5 kg m² about its central axis, rotating with speeds 10 rad s^-1 and 20 rad s^-1 are brought in contact face to face with their axes
of rotation coincided. The loss of kinetic energy in the process is

Moderate

A

2 J
B

5 J
C

125 J
D

0 J

Solution

When brought in contact , due to kinetic friction , both acquire common velocities.
Applying conservation of angular momentum,
$\begin{array}{l} (5 + 5) ω' = 5 \times 10 + 5 \times 20 = 150 \\ \Rightarrow ω' = 15 {rads}^{- 1} \end{array}$
Initial kinetic energy
$\begin{array}{l} = \frac{1}{2} \times 5 \times 10 \times 10 + \frac{1}{2} \times 5 \times 20 \times 20 \\ = 250 + 1000 = 1250 J \end{array}$
Final kinetic energy $= \frac{1}{2} \times 10 \times 15 \times 15 = 1125 J$
Loss of kinetic energy $= (1250 - 1125) J = 125 J$

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