First slide

Toppling

Question

A cubical block of side a is moving with velocity v on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits O is

Moderate

A

$\frac{3 v}{(4 a)}$
B

$\frac{3 v}{(2 a)}$
C

$\frac{\sqrt{3 v}}{\sqrt{2 a}}$
D

zero

Solution

Apply conservation of angular momentum about O
$Mv \frac{a}{2} = [\frac{{Ma}^{2}}{6} + M {(\frac{a}{\sqrt{2}})}^{2}] ω$
$\Rightarrow ω = \frac{3 v}{4 a}$

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