I guess everyone hates doing proof questions.
Need help on two proof questions I hope you guys can help!
There is alot on the internet but it's hard the way they explain it.
1) Prove that the centre of mass of a uniform wire in the form of a semi-circle of radius r is at a distance 2r/pie (sorry don't know how to insert symbol) from the centre.
2) Prove that the centre of mass of a uniform semi-circular laminar of radius r is at a distance 4r/3pie from the centre.
Thanks
Originally Posted by dadon
The centre of mass is the average position of the mass of a body.
In the case of the semi-circle of , the total
mass is .
Introduce as in the diagram, then an element of the wire
has length and the centre of mass is:
.
I'm sure you can complete the problem from here.
RonL
Hello,Originally Posted by dadon
to 1) Put the semicircle into a coordinate system, so that the diameter lies on the x-Axis and the centre of the semicircle is the origin. Then the semicircle is described by:
The centroid of a homogenous plane area, which has a graph of a function and the x-axis as boundaries, can be calculated in this problem here by:
and
Using the substitution method on the integral of the numerator, you'll get the value 0 (zero). So the x-coordinate of the centroid is 0, which could be expected.
you'll get:
I'm awfully sorry, but I'm a little bit in hurry. I hope this was of some help.
Greetings
EB