A rod with a diameter of 1.8 cm is used to make the letter A in an 18 by 12 cm space. If the number were to spin about one the left side of the space calculate the moment of inertia. The rod has a linear mass density of 4.6 kg/m.
duplicate post; already answered
To calculate the moment of inertia of the spinning rod, we need to consider the following steps:
Step 1: Determine the mass of the rod.
First, we need to calculate the mass of the rod. We can do this by multiplying the length of the rod by its linear mass density. The linear mass density of the rod is given as 4.6 kg/m.
Given: Length of the rod = 18 cm = 0.18 m
Mass of the rod = linear mass density × length of the rod
Mass of the rod = 4.6 kg/m × 0.18 m
Mass of the rod = 0.828 kg
Step 2: Find the moment of inertia of the rod.
The moment of inertia of a long, thin rod spinning about an axis perpendicular to its length is given by the formula:
I = (1/3) × Mass × Length²
Given: Length of the rod = 18 cm = 0.18 m
Mass of the rod = 0.828 kg
Moment of inertia of the rod = (1/3) × Mass × Length²
Moment of inertia of the rod = (1/3) × 0.828 kg × (0.18 m)²
Moment of inertia of the rod = 0.018 kg·m²
Therefore, the moment of inertia of the spinning rod is 0.018 kg·m².