First slide

Angular momentum

Question

A circular disc of mass m and radius R rests flat on a horizontal frictionless surface. A bullet, also of mass m and moving with a velocity v, strikes the disc and gets embedded in it. If the disc is free to rotate about a fixed axis passing through its center then the angular velocity
with which the system rotates after the bullet strikes the hoop is

Moderate

Solution

Conservation of angular momentum about the axis of rotation
$\begin{array}{l} m v R = I_{t o t a l} ω \\ = [m {(R)}^{2} + \frac{1}{2} m R^{2}] ω = \frac{3 m R^{2}}{2} ω \\ ∴ ω = \frac{2 v}{3 R} \end{array}$

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