Multiple Cholce Questlon Gear C shown in the figure weighs 9 lb and has a radius of gyration of 4.3 in . Determine the moment of inertia of gear $$ C $$. O $$ 11.646 imes 10^{-3} \mathrm{lb} \cdot \mathrm{s}^{2} \cdot \mathrm{ft} $$ $$ 8.1432 imes 10^{-3} \mathrm{lb} \cdot \mathrm{s}^{2} \cdot \mathrm{ft} $$ $$ 0.36448 imes 10^{-3} \mathrm{lb} \cdot \mathrm{s}^{2} \cdot \mathrm{ft} $$ $$ 35.889 imes 10^{-3} \mathrm{lb} \cdot \mathrm{s}^{2} \cdot \mathrm{ft} $$

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Multiple Cholce Questlon Gear C shown in the figure weighs 9 lb and has a radius of gyration of 4.3 in . Determine the moment of inertia of gear $$ C $$. O $$ 11.646 	imes 10^{-3} \mathrm{lb} \cdot \mathrm{s}^{2} \cdot \mathrm{ft} $$ $$ 8.1432 	imes 10^{-3} \mathrm{lb} \cdot \mathrm{s}^{2} \cdot \mathrm{ft} $$ $$ 0.36448 	imes 10^{-3} \mathrm{lb} \cdot \mathrm{s}^{2} \cdot \mathrm{ft} $$ $$ 35.889 	imes 10^{-3} \mathrm{lb} \cdot \mathrm{s}^{2} \cdot \mathrm{ft} $$

UpStudy AI · Accepted Answer

We are given that gear C weighs W = 9 lb and has a radius of gyration, k = 4.3 inches. The moment of inertia I about the center of mass is given by

I = m · k²

where m is the mass (in slugs) and k must be in feet.

Step 1. Convert the radius of gyration to feet:

k = 4.3 in × (1 ft / 12 in) = 4.3/12 ft ≈ 0.35833 ft

Step 2. Determine the mass in slugs:

Mass, m = Weight/g, with g ≈ 32.2 ft/s²
  m = 9 lb / 32.2 ft/s² ≈ 0.2795 slugs

Step 3. Compute the moment of inertia:

I = m · k² 
  I ≈ 0.2795 slugs × (0.35833 ft)²

First, calculate k²:

(0.35833)² ≈ 0.12833 ft²

Now, multiply:

I ≈ 0.2795 × 0.12833 ≈ 0.03588 slug·ft²

Since 1 slug·ft² is equivalent to 1 lb·s²·ft, we have:

I ≈ 0.03588 lb·s²·ft

Expressed in scientific notation (x10⁻³ lb·s²·ft):

I ≈ 35.88 × 10⁻³ lb·s²·ft

Looking at the choices provided, the option that matches this value is:

35.889 × 10⁻3 lb·s²·ft

Thus, the correct moment of inertia of gear C is 35.889 × 10⁻³ lb·s²·ft.
The moment of inertia of gear C is $$ 35.889 	imes 10^{-3} \, 	ext{lb} \cdot 	ext{s}^{2} \cdot 	ext{ft} $$.

Multiple Cholce Questlon
Gear C shown in the figure weighs 9 lb and has a radius of gyration of 4.3 in .
Determine the moment of inertia of gear .
O

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Multiple Cholce Questlon Gear C shown in the figure weighs 9 lb and has a radius of gyration of 4.3 in . Determine the moment of inertia of gear . O