Question

Find momentum of inertia​

Answer 1

Answer:

The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass, the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr2

Explanation:

Answer 2

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Given :

4 particles in the form of square

Distance = a

mass = m

To find :

Moment of inertia

Solution :

I = Σ m¡r¡²

where

I → momentum of inertia

m¡→mass of particles

r¡ → distance between particles

Σ → summation (addition of all particles)

Momentum of Inertia at particle A is due to particles B, C and D

where mass of B = mass of C = mass of D = m

and AB = AD = a, AC = √2a

Formula used :

$\tt \red{\: I = m_1r_1 {}^{2} + m_2r_2 {}^{2} + m_3r_3 {}^{2}}$

where,

$\tt m_1$ =$\tt m_2$ = $\tt m_3$ =m

$\tt r_1$ = $\tt r_2$ = a

$\tt r_3$ =√2a

• Inserting values,

$\tt\ I = ma {}^{2} + ma {}^{2} + m { (\sqrt{2}a) }^{2}$

$\tt\ I = 2ma {}^{2} + m2 {a}^{2}$

$\tt\ I = 2ma {}^{2} + 2ma {}^{2}$

$\tt\ I = 4ma {}^{2}$