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J o = π 64 π 64 d 4 + π 64 π 64 d 4. This is the equation for finding the polar moment of inertia for the circular shaft. The above figure shows the cross-section profile of a hollow circular shaft with an outer diameter (do) and inner diameter (di).
In this subsection, we show how to calculate the moment of inertia for several standard types of objects, as well as how to use known moments of inertia to find the moment of inertia for a shifted axis or for a compound object.
Calculate the moment of inertia for uniformly shaped, rigid bodies; Apply the parallel axis theorem to find the moment of inertia about any axis parallel to one already known; Calculate the moment of inertia for compound objects
In following sections we will use the integral definitions of moment of inertia (10.1.3) to find the moments of inertia of five common shapes: rectangle, triangle, circle, semi-circle, and quarter-circle with respect to a specified axis.
The polar moment of inertia describes the distribution of the area of a body with respect to a point in the plane of the body. Alternately, the point can be considered to be where a perpendicular axis crosses the plane of the body.
Polar Moment of Inertia of a circular hollow shaft can be expressed as. J = π (D 4 - d 4) / 32 (3b) where . d = shaft inside diameter (m, in) Diameter of a Solid Shaft. Diameter of a solid shaft can calculated by the formula. D = 1.72 (T max / τ max ) 1/3 (4)
Polar moment of inertia Moment of inertia is the property of a deformable body that determines the moment needed to obtain a desired curvature about an axis.
