Finding volumes of revolution using centroids

[Towk667]

In my Cal II, we're discussing finding volumes of revolution using centroids, which we find using moments of x or y. Can someone explain to me what a moment is?

 

[Dr.D]

If you think of a function f(x) defined over the interval from a to b, then the moment of this function with respect to the origin is

M = int( x*f(x) dx) from a to b

 

[Towk667]

No, thanks though, I know how to solve for a moment over an interval, I'd like know what a moment actually is.

 

[Dr.D]

A moment is just that quantity. If you know the definition, then you know what a moment is.

It has a physical interpretation also, but that is not likely be be a part of a calc class. If f(x) represents a force per unit length, then the moment represents the tendency of that force distribution to cause a rotation about the reference point.

 

[Feldoh]

Moment is essentially a vector quantity that tells you about an objects ability to rotate about a point by some given force at some given distance. If you know what a torque is they're pretty much the same.