![]() If the system of rigid bodies is divided into an infinite number of particles, then its mass, ‘dm’ and distance of mass from the axis of rotation is ‘r’. The moment of inertia of rigid bodies can be calculated by integrating. Mi = Mass of ith the particle Moment of inertia of rigid bodies Ri = ith particle perpendicular distance from the axis. The Moment of inertia of a system of particles can be described as a, Moment of inertia, I = ∑mi ri2 Moment of Inertia of a system of particles ![]() Moment of inertia remains constant for rigid frame and rotation in specific axes. It can also be measured as the body’s resistance by changing its rotational motion. The mass of inertia plays the same role as the mass of linear motion. Value of distance from the rotating axis = rĪnd the dimensional formula for the moment of inertia can be described as an M1 L2 T0 The moment of inertia is the value due to the resisting angular acceleration and is the summation of the product of the mass of each particle with the distance squared. In simpler words, it can be said it’s the quantity that decides the amount of torque required for acceleration. It is the sum of the product of the mass of every particle of the body and the square of the distance at which the object is placed from the rotating axis. The moment of inertia is the resistance to the change in angular acceleration of the body. For a body with regular shape and homogenous density, they are calculated using dimension, shape, and total mass. The moment of inertia of an extended rigid body is just the sum of all the little pieces of mass multiplied by the square of their distances from the rotating axis. Although, in rigid bodies, a moment of inertia is the summation of small quantities of mass multiplied by the square of the distance (distance from the axis). Rotational motion depends on the distribution of mass around the axis of rotation, which changes by changing the axis. ![]() The moment of inertia is also used to find out the kinetic energy, momentum, and Newton’s laws of motion for a rigid body. It plays a significant role in rotational kinematics and linear kinetics. It is commonly used in problems related to mass in rotational motion and for calculating angular momentum. Moment of inertia is a particular topic utilized in various physics fields. ![]()
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