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

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

Infinity Learn · Accepted Answer

Conservation of angular momentum about the axis of $$rotationmvR=Itotal$$ω                     $$=mR2+12mR2$$ω$$=3mR22$$ω∴ω$$=2v3R$$

Angular momentum

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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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Angular momentum

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Conservation of angular momentum about the axis of rotationmvR=Itotalω =mR2+12mR2ω=3mR22ω∴ω=2v3R

Ready to Test Your Skills?

free study material

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