Question

A heavy disc with radius R is rolling down hanging on
two non-stretched string wound around the disc very
tightly. The free ends of the string are attached to a fixed
horizontal support. The strings are always tensed during
the motion. At some instant, the angular velocity of the
disc is o, and the angle between the strings is
$\alpha$
. Find the
velocity of centre of mass of the disc at this moment.​

Answer 1

The velocity of centre of mass of the disc at this moment is v = ω R /  cos . α/2

Explanation:

The velocities of point A and B are perpendicular to the strings.

Therefore, the instantaneous axis of rotation must be at D.

Instantaneous point of intersection of the line of the two strings.

Therefore,

V(CM) = ω.OD

          = ω x OB / cos . α/2

          = ω R /  cos . α/2

Thus the velocity of centre of mass of the disc at this moment is v = ω R /  cos . α/2

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A thin uniform rod of length 1 m and mass 1 kg is rotating about an axis passing through its centre and perpendicular to its length. Calculate the moment of inertia and radius of gyration of the rod about an axis passing through a point midway between the centre and its edge, perpendicular to its length.?

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