Consider a uniform rod of mass M = 4m and length ℓ pivoted about its centre. A mass m moving with velocity v making angle to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:

Engineering

Physics

Collision

Angular Momentum and Conservation of Angular Momentum

Question

Consider a uniform rod of mass M = 4m and length ℓ pivoted about its centre. A mass m moving with velocity v making angle $θ = \frac{π}{4}$ to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:

$\frac{3}{7 \sqrt{2}} \frac{v}{ℓ}$

$\frac{4}{7} \frac{v}{ℓ}$

$\frac{3}{7} \frac{v}{ℓ}$

$\frac{3 \sqrt{2}}{7} \frac{v}{ℓ}$

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L_oi = L_of

_{$\frac{mv}{\sqrt{2}} \times \frac{ℓ}{2} = [\frac{4 {mℓ}^{2}}{12} + \frac{{mℓ}^{2}}{4}] \times ω$}

_{$ω = \frac{6 v}{7 \sqrt{2} ℓ} = \frac{3 \sqrt{2} v}{7 ℓ}$}