Moment of Inertia
The rotational analogue of mass, I = sum mi ri^2, depending on both the mass and the axis chosen.
What is Moment of Inertia?
The rotational analogue of mass, I = sum mi ri^2, depending on both the mass and the axis chosen.
Key formula / rule: I = sum m r2, units kg m2.
Key points
- Compute moment of inertia for point-mass systems and standard bodies.
- Compare moment of inertia with mass as a measure of inertia.
Common exam trap
Using a standard I with the wrong axis.
Definitions
- Term
Moment of Inertia
- Meaning
The rotational analogue of mass, I = sum mi ri^2, depending on both the mass and the axis chosen.
- Term
Moment of Inertia — explanation
- Meaning
Unlike mass, moment of inertia is not a property of the body alone; moving the axis changes it. Standard results such as MR2/2 for a disc and 2MR2/5 for a solid sphere should be recalled rather than re-derived under exam pressure.
Learning objectives
Compute moment of inertia for point-mass systems and standard bodies.
Compare moment of inertia with mass as a measure of inertia.
Formulae
- Key point
I = sum m r2, units kg m2.
- Key point
Depends on the axis; larger radius distribution means larger I.
- Key point
Radius of gyration k satisfies I = Mk2.
Prerequisites
PHY-U2-ROT-T1-S1-C1
Common mistakes
Using a standard I with the wrong axis.
Adding moments of inertia about different axes.
Keywords
Moment
Inertia
Practice preview
The Moment of Inertia of a uniform thin rod of mass M and length L about an axis passing through its centre and perpendicular to its length is given by:…
easy
A point mass m is at a distance r from an axis of rotation. If the distance is doubled, the moment of inertia becomes:…
easy
The ratio of the radii of gyration of a circular disc and a circular ring of the same mass and radius about their respective geometric axes is:…
medium