Module : Rotational Dynamics
Kreshnik Angoni and Kevin Lenton
Worksheet.docx
Worksheet.pdf
Other Resources:
- Haliday & Resnick, Fundamentals of Physics 9.4-11
- Openstax
- Printable version
The Moment of Inertia: the rotational equivalent of mass
A definition of mass comes from Newton's second Law: the mass of an object defines how an object will accelerate given a certain linear net force.
You could say the mass shows you how an object will move. We need an equivalent to describe how an object will rotate, given a net torques. This equivalent is called the The Moment of Intertia, given the symbol I.
The quantity I [Units:kg*m2] is called the moment of inertia of the body with respect to the rotation axis. You can tell from the units that the Moment of Inertia is always a mass times radius squared. The exact
numerical value of I depends on the way that the mass of the body is distributed spatially with respect to
a particular axis. A quick comparison of expression (22) with K = mv2/2 allows to figure out that, in a
rotational motion, I is playing the role of the mass for translational motion. So, we can derive that
The inertia moment is a measure of the resistance a body presents to the change of its rotational
status of motion or in other terms to its existing angular velocity.
You can get a feel for the moment of inertia by trying to rotate a hammer. If you hold it by the wooden end, and try and spin it (the mass is further away from the pivot i.e. bigger moment of inertia ) it is much more difficult to spin
than when holding it by the metallic end (more of the mass is closer to the pivot, smaller r, therefore smaller inertia moment).
- Straight from the definition (23) we may see that the same mass
located at a bigger distance from the axis produces bigger moment
of inertia. So, one may guess that, for the same mass, the inertia
moments versus the central axis of symmetry for a ring, a disk, and
a cylinder (figure 9) are different and Iring >Idisk >Icylinder.
The center of mass CM of the body is a physical concept that
helps a lot to find I-value for any position of rotation axis.
Figure 9