To start the derivation first let us bring the moment of inertia of a circle. Where again R is the radius of the circle and I is the moment of inertia Derivationīefore starting the derivation of the moment of inertia of a quarter circle let us make a diagram of a quarter circle to understand the annotations and other parameters.Ĭonsider a quarter circle having its centre of mass at location c and a radius r. We should also learn about the moment of inertia of a circle which is given by the equation, Where R is the radius of the quarter circle and I is the moment of inertia.

In a circle, the MOI of it about the x-axis is similar to that of the y-axis.īefore deriving the formula let us first have a look at the moment of inertia of a quarter circle which is given by the equation, The procedure for deriving the moment of inertia of a quarter circle is to find the moment of inertia of a circle and divide the result by two. To find the moment of inertia of a quarter circle about its centroid is similar to finding the moment of inertia of a circle. It is defined as the product of the particle’s mass in the object and its length’s square from the rotational axis. Indeed, the correct meaning of the angular momentum or the MOI is the tendency of an object to resist angular momentum. Whenever an object begins to rotate along a fixed axis, each component in the object moves in a circle with constant speed, indicating that each particle moves with rotational movement. It may be deduced that inertia is proportional to a body’s mass. First and foremost, let us define the idea of the moment of inertia in simple words.

Moment of inertia of circle derivation