a bob of mass mm is tied by a massless string whose other end is wound on a flywheel (disc) of radius rr and mass mm

As shown in the figure, a bob of mass mm is tied by a massless string whose other end is wound on a flywheel (disc) of radius rr and mass mm. When released from rest, the bob starts falling vertically. When it has covered a distance hh, what will be the angular speed of the wheel?

Solution:

Step 1: Energy Conservation

The total mechanical energy remains conserved as there is no energy loss due to non-conservative forces (like friction).

Step 2: Relating Linear and Angular Velocities

The bob and the flywheel are connected via a string. So, the linear velocity of the bob, vvv, is related to the angular velocity of the wheel, ω\omegaω, by:

v=rω

Step 3: Energy Conservation Equation

The total energy equation is:

Step 4: Solve for ω

Conclusion:

This question beautifully illustrates the interplay of translational and rotational mechanics. By understanding energy conservation and the relationship between linear and angular velocities, you can solve such problems with ease.

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