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The problem is asking for the **moment of inertia** of a mass given its weight (14.2 pounds) and its distance from the center of mass (1.25 meters).

The moment of inertia \( I \) is calculated using the formula:
\[
I = m r^2
\]
where:
- \( m \) is the mass in **slugs** (for imperial units),
- \( r \) is the distance from the center of mass in meters.

### Step 1: Convert weight (pounds) to mass (slugs)
Weight (\( W \)) is related to mass (\( m \)) by:
\[
W = m g
\]
where \( g = 32.174 \, \text{ft/s}^2 \).

Rewriting:
\[
m = \frac{W}{g}
\]

Convert 14.2 pounds to slugs:
\[
m = \frac{14.2}{32.174} = 0.4412 \, \text{slugs}.
\]

### Step 2: Calculate the moment of inertia
Substitute \( m = 0.4412 \, \text{slugs} \) and \( r = 1.25 \, \text{m} \) into the formula:
\[
I = m r^2
\]
\[
I = 0.4412 (1.25)^2 = 0.4412 \times 1.5625 = 0.689 \, \text{slug-m}^2.
\]

Convert \( \text{slug-m}^2 \) to \( \text{lb-ft}^2 \):
1 slug-m\(^2\) = 23.730 lb-ft\(^2\).

\[
I = 0.689 \times 23.730 = 16.36 \, \text{lb-ft}^2.
\]

This calculation differs from the answer provided (\( 2218.75 \, \text{lb-m}^2 \)), suggesting the answer might have used incorrect units or assumptions. Let me know if you want me to verify further!

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Would you like a detailed explanation of unit conversions? Here are 5 related questions:

1. What is the difference between the imperial and SI systems for moment of inertia?
2. How do you calculate moments of inertia for irregular objects?
3. Can you explain the significance of \( r^2 \) in the moment of inertia formula?
4. How is the moment of inertia used in rotational dynamics?
5. Can you provide a step-by-step conversion from slug-meters to another unit?

**Tip:** Always confirm the units (slugs, pounds, etc.) when solving physics problems to avoid errors!

Find the moment of inertia of a mass 14.2 pounds moving at a distance of 1.25 m from the center of mass.

Learn how to calculate the moment of inertia of a 14.2-pound mass located 1.25 meters from its center of mass. This solution includes unit conversions and step-by-step explanations using the formula I = m * r^2. Suitable for high school physics and engineering students.

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