A system consists of two identical small balls of mass $2 k g$ each connected to the two ends of a $1 m$ long light rod. The system is rotating about a fixed axis through the centre of the rod and perpendicular to it at an angular speed of $9 r a d / s$ . An impulsive force of average magnitude $10 N$ acts on one of the masses in the direction of its velocity for $0.20 s$ . Calculate the new angular velocity of the system.

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Solution

$I (w_{f} - w_{i}) = F S Δ t 2 (\frac{1}{12}) (w_{f} - 9) = 10 \times 0.2 \times \frac{1}{2} \frac{w_{f}}{9} - \frac{9}{6} = 1 (w_{f} - 9) = 6 (w_{f}) = 15 w_{f} = 15 r a d / s e c$

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I(wf−wi)=FSΔt2(112)(wf−9)=10×0.2×12wf9−96=1(wf−9)=6(wf)=15wf=15rad/sec

$I (w_{f} - w_{i}) = F S Δ t 2 (\frac{1}{12}) (w_{f} - 9) = 10 \times 0.2 \times \frac{1}{2} \frac{w_{f}}{9} - \frac{9}{6} = 1 (w_{f} - 9) = 6 (w_{f}) = 15 w_{f} = 15 r a d / s e c$