Question

Moment of inertia of rigid body

Answer 1

The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid body is a tensor that determines the torque needed for a desired angular acceleration about a rotational axis. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rotation. It is an extensive (additive) property: the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). One of its definitions is the second moment of mass with respect to distance from an axis r, {\displaystyle I=\int _{Q}r^{2}\mathrm {d} m}, integrating over the entire mass {\displaystyle Q}.

For bodies constrained to rotate in a plane, it is sufficient to consider their moment of inertia about an axis perpendicular to the plane. For bodies free to rotate in three dimensions, their moments can be described by a symmetric 3 × 3 matrix; each body has a set of mutually perpendicular principal axes for which this matrix is diagonal and torques around the axes act independently of each other.

Answer 2

Answer:-

• The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration.
• Moment of Inertia. The moment of inertia is sometimes called and referred to as "angular mass." It is the "amount of resistance" to rotational motion. ... The moment of inertia is commonly used to calculate torque when multiplied by the angular acceleration.
• Moment of inertia about a given axis of rotation resists a change in its rotational motion; it can be regarded as a measure of rotational inertia of the body.
• The formula for moment of inertia is the “sum of the product of mass” of each particle with the “square of its distance from the axis of the rotation”. The formula of Moment of Inertia is expressed as I = Σ MiRi²

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