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A system contains 2 identical small bobs of mass 2kg each connected to the ends of 1m long light rod. The system is rotating about a fixed axis through centre of the rod and perpendicular to it at an angular speed of 9 rad/s. An impulsive force of average magnitude 10 N acts on one of the masses in the direction of its velocity for 0.2s. calculate new angular velocity of system

A system contains 2 identical small bobs of mass 2kg each connected to the ends of 1m long light rod. The system is rotating about a fixed axis through centre of the rod and perpendicular to it at an angular speed of 9 rad/s. An impulsive force of average magnitude 10 N acts on one of the masses in the direction of its velocity for 0.2s. calculate new angular velocity of system

Grade:12

1 Answers

Sanju
106 Points
6 years ago
The impulse is provided by the force F = 10N in the direction of velocity which is perpendicular to the rod as the mass is moving in circular motion.
Therefore, the torque, T = rF = 0.5m * 10N = 5 Nm
Moment of inertia of the system abt the line passing thru its center & perpendicular to it is given by:
I = 2 * 2kg * (0.5m)2 = 1 kg m2 
We have, T = I * α
where α is the angular acceleration
Therefore, α = T / I = 5/1 = 5 rad/s2
 
So, the new angular velocity, w = w0 +αt   
w = w0 +αt = 9 + (5*0.2) = 10 rad/s

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