A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom-most point and sticks to it. The angular speed (in rad/s) of the ro…

Question

A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom-most point and sticks to it. The angular speed (in rad/s) of the rod immediately after the collision will be .

Accepted Answer

20. The suspension exerts a force during the impact, so linear momentum is not conserved — but angular momentum about the suspension point is. Before: the particle travels horizontally at the bottom of the rod, a distance ℓ=1 m from the pivot. L=mvℓ=(0.1)(80)(1)=8 kg m² s⁻¹. After, the rod and the stuck particle turn together about the pivot. I=(Mℓ²)/3+mℓ²=(0.9)/3+0.1=0.3+0.1=0.4 kg m². ω=L/I=8/(0.4). ω=20 rad/s.

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