# Math Help - C.O.M Mechanics question.

1. ## C.O.M Mechanics question.

Okey, sorry for the crap diagram!
Radius of the hemisphere is 6.
The question is:
Find the horizontal distance from the center of mass of the hemisphere to the vertical through O.
Now the distance is:
3/8 x 6 = 2.25.

But then im stuck as to find the horizontal distance. If i assume the angle of the triangle formed is 60 degrees then i could do 2.25Cos60 which is 1.125...but i don't think its right to assume that.

The overall answer is 1.125.

Any help would be appreciated!

Thankyou .

2. If you extend the line from COM to O outwards beyond O you find it is normal (at 90 degrees) to the flat surface of the hemisphere. Since the surface is at 60 degrees to the vertical this means that the angle the line COM to O makes with the vertical must be

90 -60 degrees = 30 degrees.

The horizontal distance is then $\sin 30$ multiplied by the distance you calculated (which is the hypotenuse of the triangle).

Hence the answer is as you said 1.125 cm.

Does that help?