# Derive a relation between Torque and Moment of Inertia?

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Feb 9, 2018

#### Answer:

$I = {\tau}_{\text{net}} / \alpha$

#### Explanation:

Momentum of inertia is similar to mass in Newton's 2nd Law.

Mass is the inertia of an object in response to an unbalanced (net) force that causes the object to accelerate translationally.

$m = {F}_{\text{net}} / a$

Momentum of the inertia is the rotational inertia in response to an unbalanced (net) torque that causes the object to accelerate its rotation on an axis (i.e., angular acceleration).

$I = {\tau}_{\text{net}} / \alpha$

So it fact, it's like Newton's 2nd law for angular motion.

${F}_{\text{net}} = m a - -$ Newton's Second Law for translational motions.

${\tau}_{\text{net}} = I \alpha - -$Newton's Second Law for angular motions.

However, $I$ is more complex, it depends on mass of the object and the geometric shape rotating on its axis of rotation.

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