Question

Consider a rod that is 0.220 cm in diameter and 1.50 m long, with a mass...

Consider a rod that is 0.220 cm in diameter and 1.50 m long, with a mass of 0.0400 kg.

1. Find the moment of inertia about an axis perpendicular to the rod and passing through one end.(kg*m^2 units please)

2. Find the moment of inertia about an axis along the length of the rod.

Express your answer in kilogram meters squared.

Homework Answers

Answer #1

Solution:

Given:

Diameter (d) = 0.22 cm = 2.2 x 10-3 m

Thus : r = 1.1 x 10-3 m

Length (L) = 1.50 m

Mass (m) = 0.04 kg

the moment of inertia about an axis perpendicular to the rod and passing through its center = IC = (1/2) ML2

Thus : Ic = (0.5)(0.04)(1.50)2 = 0.045 kg m2

Now : using parallel axis theorem :

the moment of inertia about an axis perpendicular to the rod and passing through one end (Iend) = IC + m d2

Iend = (0.045) + M (L/2)2

Iend = (0.045) + (0.04) (1.50/2)2

Iend = 0.0675 kg m2

the moment of inertia about an axis along the length of the rod = (1/2) m r2 = (0.5)(0.04)(1.1 x 10-3 m)2 = 2.42 x 10-8 kg m2

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