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## Homework Statement

A uniform thin rod of mass m and length l is standing upright on a table, then given a tiny kick so it tips over. The lower end is fixed. Find angular velocity when it hits the table.

## Homework Equations

## The Attempt at a Solution

So I applied conservation of energy.

Ei=Ef (1)

Ei=mgl/2

Ef=1/2mv

_{cm}

^{2}+1/2Iω

^{2}

where v

_{cm}is the linear velocity of the CM and ω is the angular velocity of the rod when it hits the floor.

**v**

_{cm}=ωl/2For a thin rod that rotates about one end

**I=ml**

^{2}/3So substituting in equation (1) i get

mgl/2=1/2(ωl/2)

^{2}+ 1/6m(lω)

^{2}

which leads to

**ω**

^{2}=12/7g/lBut i 've checked the answer and it turns out is ω

^{2}=3g/l

where am i wrong?

thanks in advance for your help

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