Parallel and Perpendicular Axis Theorems
Parallel axis: I = Icm + Md2. Perpendicular axis (planar bodies only): Iz = Ix + Iy.
What is Parallel and Perpendicular Axis Theorems?
Parallel axis: I = Icm + Md2. Perpendicular axis (planar bodies only): Iz = Ix + Iy.
Key formula / rule: Parallel axis needs the axis through the centre of mass as reference.
Key points
- Apply the parallel axis theorem to shifted axes.
- Justify the restriction of the perpendicular axis theorem to laminae.
Common exam trap
Applying the perpendicular axis theorem to three-dimensional bodies.
Definitions
- Term
Parallel and Perpendicular Axis Theorems
- Meaning
Parallel axis: I = Icm + Md2. Perpendicular axis (planar bodies only): Iz = Ix + Iy.
- Term
Parallel and Perpendicular Axis Theorems — explanation
- Meaning
These two theorems generate almost every moment of inertia needed in an exam from a small table of standard results.
Learning objectives
Apply the parallel axis theorem to shifted axes.
Justify the restriction of the perpendicular axis theorem to laminae.
Formulae
- Key point
Parallel axis needs the axis through the centre of mass as reference.
- Key point
Perpendicular axis applies only to plane laminae.
- Key point
I is minimum about an axis through the centre of mass.
Prerequisites
PHY-U2-ROT-T1-S1-C2
Common mistakes
Applying the perpendicular axis theorem to three-dimensional bodies.
Using an axis other than the centre-of-mass axis as Icm.
Keywords
Parallel
Perpendicular
Theorems
Practice preview
The perpendicular axis theorem is applicable only for which type of rigid bodies?…
easy
A uniform disc of mass M and radius R has a moment of inertia (I_z) of (1/2)MR^2 about an axis passing through its center and perpendicular to its plane. What is its moment of inertia about one of its diameters?…
medium
A uniform ring of mass M and radius R has a moment of inertia (I_cm) of MR^2 about an axis passing through its center and perpendicular to its plane. What is its moment of inertia about a tangent in its plane?…
medium