Question

A thin rod has mass 1.2 kg and length 4m. Find its moment
of inertia about a transverse axis passing through a point
at a distance of 1m from the centre of mass of the rod..​

Answer 1

Solution:

Concept to be known: Parallel Axis Theorem

Formula:

→ MOI at any point P = MOI at COM + MR²

where, R is the distance between the point P and COM.

According to the question,

Mass = 1.2 kg

Length = 4m

Distance of P from COM is 1 m

Therefore MOI at point P is given as:

→ MOI ( at P ) = MOI at COM + M (1)²   ...(1)

MOI at COM of uniform rod is given as 1/12 (ML²)

→ MOI at COM = 1/12 × 1.2 × 4

→ MOI at COM = 0.4 Kg.m²   ... (2)

Using (2) in (1) we get:

→ MOI ( at P ) = 0.4 Kg.m² + 1.2 (1)²

→ MOI ( at P ) = 0.4 + 1.2 = 1.6 Kg.m²

Hence Moment of Inertia (MOI) about a transverse axis passing through a point at a distance of 1 m from the Centre of Mass (COM) is 1.6 Kg.m²

Answer 2

Answer:

Let us assume a transverse axis AB passing through COM.Now, assume another axis 90°

to AB.Say it I_y.

When θ = 45 °

Ix=Iy(symmetry

From perpendicular axis theorem,

Iz=lx+ly

Iz=21x=ml²

12

lx=ml² = 1.2*4² = 0.8 kg-m²

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