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Physics

Mechanics

Easy

Question

$text Two discs of moments of inertia end text I subscript 1 text and end text I subscript 2 text about their respective axes, rotating with angular end text text frequencies, end text omega subscript 1 text and end text omega subscript 2 text respectively, are brought into contact face to face with their axes of end text text rotation coincident. The angular frequency of the composite disc will be A end text$

$\frac{I_{1} ω_{1} + I_{2} ω_{2}}{I_{1} + I_{2}}$
$\frac{I_{2} ω_{1} + I_{1} ω_{2}}{I_{1} + I_{2}}$
$\frac{I_{1} ω_{1} + I_{2} ω_{2}}{I_{1} - I_{2}}$
$\frac{I_{2} ω_{1} + I_{1} ω_{2}}{I_{1} - I_{2}}$

The correct answer is: $fraction numerator I subscript 1 omega subscript 1 plus I subscript 2 omega subscript 2 over denominator I subscript 1 plus I subscript 2 end fraction$

$L subscript i equals I subscript 1 omega subscript 1 plus I subscript 2 omega subscript 2 text i.e., end text I equals I subscript 1 plus I subscript 2 L subscript f equals I omega equals open parentheses I subscript 1 plus I subscript 2 close parentheses omega L subscript i equals L subscript f I subscript i omega subscript 1 plus I subscript 2 omega subscript 2 equals open parentheses I subscript 1 plus I subscript 2 close parentheses omega omega equals fraction numerator I subscript 1 omega subscript 1 plus I subscript 2 omega subscript 2 over denominator I subscript 1 plus I subscript 2 end fraction$

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