Question

The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through O. Its mass moment of inertia is equal to 0.1 kg∙cm2 about O. A point mass of 0.001 kg hits it normally at 200 cm/sat the location shown, and sticks to it. Immediately after the impact, the angular velocity of the rod is ___________ rad/s (in integer).

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Answer :

Correct answer is : 10 rad/s

I = 0.1 kg∙cm2, m = 0.001 kg, v = 200 cm/s, ω = ?

r = 10 cm

Moment of inertia after mass strike rod Ic = 0.1 + 0.001 × 102

Taking rod and mass as a system, by the law of conservation of angular momentum:

angular momentum before striking of mass = angular momentum after striking mass

m × V × r = Ic × ω

0.001 × 200 × 10 = (0.1 + 0.001 × 102) × ω

2 = 0.2 ω

ω = 10 rad/s

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