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A dumb-bell consists of two identical small balls of mass 12 kg each connected to the two ends of a 50 cm long light rod. The dumb-bell is rotating about a fixed axis through the centre of the rod and perpendicular to it at an angular speed of 10 rad/s. An impulsive force of average magnitude 5.0 N acts on one of the masses in the direction of its velocity for 0.10 s. Find the new angular velocity of the system.


Solution

τ=Ia

F×r=(mr2+mr2)α

5×0.25=2mr2×α

α=1.252×0.5×0.025×0.25

= 20

ω0=10 rad/s

t=0.10 sec

ω=ω0+αt

ω=10+0.10×20

=10+2=12 rad/s

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