जड़त्वाघूर्णों की सूची

यहाँ पर विभिन्न आकार-प्रकार के पिण्डों के जड़त्वाघूर्ण दिये गये हैं। ज। दत्वाघूर्ण की इकाई की विमा द्रव्यमान × लम्बाई² होती है। नीचे दिये गये व्यंजकों की गणना में यह माना गया है कि घनत्व सर्वत्र समान है।

टिप्पणी: जहाँ कहीं भी अलग से न कहा गया हो, यह माना गया है कि घूर्णन-अक्ष द्रव्यमान केन्द्र से जाता है।

वर्णन	जड़त्वाघूर्ण	टिप्पणी
पतला बेलनाकार शेल (shell) जिसके सिरे खुले हैं, त्रिज्या r तथा द्रव्यमान m	$I = m r^{2}$	शेल की मोटाई को नगण्य (शून्य) माना गया है। यह अगले पिण्ड का एक विशेष दशा है जिसमें r₁=r₂.
मोटी दिवार वाली खुले सिरों वाली बेलनाकार नली जिसकी अन्त:त्रिज्या r₁, वाह्य त्रिज्या r₂, लम्बाई h एवं द्रव्यमान m	$I_{z} = \frac{1}{2} m ({r_{1}}^{2} + {r_{2}}^{2})$ ^[१] $I_{x} = I_{y} = \frac{1}{12} m [3 ({r_{2}}^{2} + {r_{1}}^{2}) + h^{2}]$ or when defining the normalized thickness t_n = t/r and letting r = r₂, then $I_{z} = m r^{2} (1 - t_{n} + \frac{1}{2} t_{n}^{2})$	घनत्व ρ और उपरोक्त ज्यामिति के साथ $I_{z} = \frac{1}{2} π ρ h ({r_{2}}^{4} - {r_{1}}^{4})$
r त्रिज्या, h उंचाई, तथा m द्रव्यमान का ठोस बेलन	$I_{z} = \frac{m r^{2}}{2}$ $I_{x} = I_{y} = \frac{1}{12} m (3 r^{2} + h^{2})$	This is a special case of the previous object for r₁=0.
Thin, solid disk of radius r and mass m	$I_{z} = \frac{m r^{2}}{2}$ $I_{x} = I_{y} = \frac{m r^{2}}{4}$	This is a special case of the previous object for h=0.
Thin circular hoop of radius r and mass m	$I_{z} = m r^{2}$ $I_{x} = I_{y} = \frac{m r^{2}}{2}$	This is a special case of a torus for b=0. (See below.)
Solid sphere of radius r and mass m	$I = \frac{2 m r^{2}}{5}$	A sphere can be taken to be made up of a stack of infinitesimal thin, solid discs, where the radius differs from 0 to r.
Hollow sphere of radius r and mass m	$I = \frac{2 m r^{2}}{3}$	Similar to the solid sphere, only this time considering a stack of infinitesimal thin, circular hoops.
Oblate Spheroid of major a, minor b and mass m	$I = \frac{2 m b^{2}}{3}$	—
Right circular cone with radius r, height h and mass m	$I_{z} = \frac{3}{10} m r^{2}$ $I_{x} = I_{y} = \frac{3}{5} m (\frac{r^{2}}{4} + h^{2})$	—
Solid cuboid of height h, width w, and depth d, and mass m	$I_{h} = \frac{1}{12} m (w^{2} + d^{2})$ $I_{w} = \frac{1}{12} m (h^{2} + d^{2})$ $I_{d} = \frac{1}{12} m (h^{2} + w^{2})$	For a similarly oriented cube with sides of length $s$ , $I_{C M} = \frac{m s^{2}}{6}$ .
Thin rectangular plane of height h and of width w and mass m	$I_{c} = \frac{m (h^{2} + w^{2})}{12}$	—
Thin rectangular plane of height h and of width w and mass m (Axis of rotation at the end of the plate)	$I_{e} = \frac{m h^{2}}{3} + \frac{m w^{2}}{12}$	—
Rod of length L and mass m	$I_{c e n t e r} = \frac{m L^{2}}{12}$	This expression assumes that the rod is an infinitely thin (but rigid) wire. This is a special case of the previous object for w=L and h=d=0.
Rod of length L and mass m (Axis of rotation at the end of the rod)	$I_{e n d} = \frac{m L^{2}}{3}$	This expression assumes that the rod is an infinitely thin (but rigid) wire.
Torus of tube radius a, cross-sectional radius b and mass m.	About a diameter: $\frac{1}{8} (4 a^{2} + 5 b^{2}) m$ About the vertical axis: $(a^{2} + \frac{3}{4} b^{2}) m$	—
Plane polygon with vertices ${\vec{P}}_{1}$ , ${\vec{P}}_{2}$ , ${\vec{P}}_{3}$ , ..., ${\vec{P}}_{N}$ and mass $m$ uniformly distributed on its interior, rotating about an axis perpendicular to the plane and passing through the origin.	$I = \frac{m}{6} \frac{\sum_{n = 1}^{N} ‖ {\vec{P}}_{n + 1} \times {\vec{P}}_{n} ‖ ({\vec{P}}_{n + 1}^{2} + {\vec{P}}_{n + 1} \cdot {\vec{P}}_{n} + {\vec{P}}_{n}^{2})}{\sum_{n = 1}^{N} ‖ {\vec{P}}_{n + 1} \times {\vec{P}}_{n} ‖}$	—