First slide

Moment of intertia

Question

A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r is made from an iron plate of thickness t/4. The relation between the moments of inertia I_A and I_B is

Moderate

A

I_A > I_B
B

I_A = I_B
C

I_A < I_B
D

Depends on the actual values of t and r.

Solution

For a solid disc ,
I = 1/2 mR²
m = π R² / t ρ , where ρ = Density
.: I = 1/2 (πR² + σ) R²
⇒ I $\large \propto$ t R⁴
.: I_A = I_B = (t / t/4) (r / 4r)⁴ = 1/64
.: I_A < I_B

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