I am currently reading through a document Finding Moments of Inertia from MIT, page 4, and I am a little confused as to one of the concepts that they use.
In this document, there is mention of a mass moment. Could someone possibly define this for me please? I can't find anything too clear on the Internet.
Is this synonymous with the first moment of mass?
To TNTCookie and anyone else who may be looking at this post in need of help
I have found the answer. It lies within the definition of a centre of mass:
$$x_{cm} = \frac{\Sigma_{i=1}^{i=N}m_i x_i}{M},$$
where $M$ is the sum of all masses in a system, and the sum in the numerator is the first moment of mass (mass moment).
If we multiply both sides of our equation by $M$, we get:
$$M\times x_{cm} = \Sigma_{i=1}^{i=N}m_i x_i.$$
This works in accordance with the steps in the MIT document as attached. We are summing individual masses multiplied by individual distances from the centre of mass. In the problem in the document, we have to deal with a lack of mass (which can be considered negative mass), and thus we get:
$$M\times |\vec{OC}| = \big(m_{\mbox{cylinder}} \times 0\big) - \big(m_{\mbox{missing cylinder}} \times \frac{R}{2}\big).$$
*Note that the distance from the centre of mass, to the centre of mass of a normal cylinder must be $0$, and the fraction $\frac{R}{2}$ comes from the problem in the attached MIT document.
This is referring to the moment of inertia.
It is similar to how inertia refers to mass, as described in Newton's 1st law, so the tendency of a body to resist acceleration by a force. This is seen as $F=ma$
Now for rotational movements, the physics terms change. The acceleration refers to angular acceleration ($\alpha$), the force to torque ($\tau$), and finally the mass to the moment of inertia ($I$). The equivalent equation is $\tau=I\alpha$.
So in English: the moment of inertia is the tendency of a body to resist angular acceleration, by a torque.
Note: mass moment is not the accepted term. It should be called the moment of inertia and the calculations use it as such.
Mass moment is slightly different from moment of inertia. It is moment of inertia x total Mass
