First slide

Rotational motion

Question

A solid cube ABCD of side a and mass M is placed on a rough horizontal surface. A bullet of mass m and speed v is shot at the top of the cube so that cube rotates about
point D. The bullet sticks to the cube, m << M. Find the angular velocity of the cube.

Moderate

A

$\frac{6 m v}{4 M a}$
B

$\frac{3 M v}{2 m a}$
C

$\frac{2 M v}{3 m a}$
D

$\frac{2 m v}{3 M a}$

Solution

Angular momentum about point D is conserved.
$\begin{array}{l} m v a = I_{D} ω \\ But I_{D} = \frac{4}{6} M a^{2} . So, ω = \frac{6 m v}{4 M a} \end{array}$

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