The topmost and bottommost velocities of a disc are $v_{1}$ and $v_{2} (< v_{1})$ in the same direction.The radius is $R$ . The value of angular velocity $ω = (\frac{v_{1} - v_{2}}{x R})$ . Find $x$ .

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Solution

Consider the bottommost point,
then the relative velocity of uppermost point is ( $v_{1} - v_{2}$ ).
And distance between those two points is 2R.
For a rigid body,
angular velocity ,( $ω) = \frac{Δ v}{d}$
$= \frac{v_{1} - v_{2}}{2 R}$

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Consider the bottommost point,
then the relative velocity of uppermost point is ( $v_{1} - v_{2}$ ).
And distance between those two points is 2R.
For a rigid body,
angular velocity ,( $ω) = \frac{Δ v}{d}$
$= \frac{v_{1} - v_{2}}{2 R}$