Open Question
The four masses shown in FIGURE EX12.13 are connected by massless, rigid rods. (b) Find the moment of inertia about a diagonal axis that passes through masses B and D.
13. Rotational Inertia & Energy
Intro to Moment of Inertia
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A solid disc 4 m in diameter has a moment of inertia equal to 30 kg m2 about an axis through the disc, perpendicular to its face. The disc spins at a constant 120 RPM. Calculate the mass of the disc.
A
1.88 kg
B
3.75 kg
C
7.5 kg
D
15 kg
Verified step by step guidance1
Start by understanding the formula for the moment of inertia of a solid disc about an axis perpendicular to its face: \( I = \frac{1}{2} m r^2 \), where \( I \) is the moment of inertia, \( m \) is the mass, and \( r \) is the radius of the disc.
Given that the moment of inertia \( I \) is 30 kg m² and the diameter of the disc is 4 m, calculate the radius \( r \) by dividing the diameter by 2: \( r = \frac{4}{2} = 2 \) m.
Substitute the known values into the moment of inertia formula: \( 30 = \frac{1}{2} m (2)^2 \).
Simplify the equation: \( 30 = 2m \).
Solve for \( m \) by dividing both sides of the equation by 2: \( m = \frac{30}{2} \).
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