A bar of mass M and length L is in pure translatory motion with its centre of mass velocity V. it collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2L). The angular velocity of the composite bar will be 3V/xL counter clockwise where ‘x’ is

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A bar of mass M and length L is in pure translatory motion with its centre of mass velocity V. it collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2L). The angular velocity of the composite bar will be 3V/xL counter clockwise where ‘x’ is

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Detailed Solution

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In this case the total angular momentum is conserved about the point P(Since the net torque of all the forces will be zero)

$L_{i} = MV \frac{L}{2}$

finally the moment of inertia of the combined mass will be $\frac{2 M {(2 L)}^{2}}{12} = \frac{2 {ML}^{2}}{3}$

So, $MV \frac{L}{2} = (\frac{2 {ML}^{2}}{3}) ω \Rightarrow ω = \frac{3 V}{4 L}$

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