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## Homework Statement:

- A triangular plate of a mass of 150kg is shown as below. Calculate the angular velocity of the plate when CM is directly below the pivot.

## Relevant Equations:

- -

So first of all, I will have to find the centre of mass.

##X_{cm} = \frac{1}{M}\int x dm##

likewise for Y.

##M## =150kg

From the above-given points, I can find the equation of a line to be

## y =-\frac{3}{4}x +3## .

Area density = ##150kg/(0.5*4*3) = 25kg/m^2##

##X_{cm} = \frac{1}{M}\int x dm = \frac{1}{150}\int x \mu y dx = \frac{1}{150}\int x (25) (-\frac{3}{4}x+3) dx =\frac{1}{150}\int_{0}^{4} x (25) (-\frac{3}{4}x+3) dx = 4/3##

##Y_{cm} = \frac{1}{M}\int y dm = \frac{1}{150}\int y \mu x dy = \frac{1}{150}\int y (25) (-\frac{4}{3}y+4) dy =\frac{1}{150}\int_{0}^{3} y(25) (-\frac{4}{3}y+4) dy = 1##

After getting the coordinates, what concepts should I apply next? Moment of inertia/rotational motion? Not sure what formulas/theories to apply here, any guidance will be appreciated. Thanks