The planes of two rigid discs are perpendicul | vedclass

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(C) Angular velocity is a vector quantity. Let the angular velocity of the first disc be $\vec{\omega}_1 = 3 \hat{i} \, rad/s$ and the angular velocit

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$5$

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(C) Angular velocity is a vector quantity. Let the angular velocity of the first disc be $\vec{\omega}_1 = 3 \hat{i} \, rad/s$ and the angular velocity of the second disc be $\vec{\omega}_2 = 4 \hat{j} \, rad/s$.Since the planes of the discs are perpendicular,their axes of rotation are also perpendicular.The resultant angular velocity $\vec{\omega}_{res}$ is given by the vector sum of the two individual angular velocities:$\vec{\omega}_{res} = \vec{\omega}_1 + \vec{\omega}_2$.The magnitude of the resultant angular velocity is given by:$|\vec{\omega}_{res}| = \sqrt{\omega_1^2 + \omega_2^2}$.Substituting the given values:$|\vec{\omega}_{res}| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, rad/s$.

The planes of two rigid discs are perpendicular to each other. They are rotating about their axes. If their angular velocities are $3 \, rad/s$ and $4 \, rad/s$ respectively,then the resultant angular velocity of the system would be ........ $rad/s$.

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