Final answer:
The moment of inertia of a rectangle with a base of 3.5 inches, a height of 2.5 inches, and a mass of 12 kg is calculated to be approximately 0.995 kg·m².
Step-by-step explanation:
The moment of inertia (I) of a rectangular object with respect to an axis through its center, perpendicular to the plane of the object, is given by I = (1/12)M(L₂ + W₂), where M is the mass, L is the length (or height), and W is the width (or base). Considering the rectangle shown, if the mass (M) is 12 kg, the base (b) is 3.5 in (converted to meters), and the height (h) is 2.5 in (converted to meters), we can calculate the moment of inertia.
First, we convert the base and height from inches to meters: 3.5 in = 0.0889 m and 2.5 in = 0.0635 m. Then, substitute the values into the equation:
I = (1/12) × 12 kg × (0.0889 m² + 0.0635 m²)
Compute the squares and the sum:
I = (1/12) × 12 kg × (0.00790641 m² + 0.00403225 m²)
Adding the squares:
I = (1/12) × 12 kg × 0.01193866 m²
Multiplying through gives us the moment of inertia:
I = 0.995 kg · m²
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