{"id":287,"date":"2022-03-24T02:09:06","date_gmt":"2022-03-24T02:09:06","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=287"},"modified":"2022-03-30T18:35:42","modified_gmt":"2022-03-30T12:35:42","slug":"moment-of-inertia-radius-of-gyration","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/moment-of-inertia-radius-of-gyration\/","title":{"rendered":"\u0995\u09df\u09c7\u0995\u099f\u09bf \u09ac\u09bf\u09b6\u09c7\u09b7 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u099c\u09dc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 \u0993 \u099a\u0995\u09cd\u09b0\u0997\u09a4\u09bf\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09a8\u09bf\u09b0\u09cd\u09a3\u09df\u0964 Determination of moment of inertia and radius of gyration for some special cases"},"content":{"rendered":"\r\n

(\u09e7) \u09b8\u09b0\u09c1 \u0993 \u09b8\u09c1\u09b7\u09ae \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09bf\u09af\u09bc\u09c7 \u0993 \u09a4\u09be\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0998\u09c2\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u09ae\u09be\u09a8 \u0990 \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 (Moment of Inertia)<\/h2>\r\n\r\n\r\n\r\n

\u09a7\u09b0\u09bf ? \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u0993 ? \u09ad\u09b0\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09b8\u09c1\u09b7\u09ae \u09b8\u09b0\u09c1 \u09a6\u09a3\u09cd\u09a1 ??-\u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 ? \u09a6\u09bf\u09af\u09bc\u09c7 \u0993 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u0985\u0995\u09cd\u09b7 ??-\u098f\u09b0 \u099a\u09a4\u09c1\u09b0\u09cd\u09a6\u09bf\u0995\u09c7 \u0998\u09c1\u09b0\u099b\u09c7 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u098f\u0987 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09a4\u09be\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995<\/a> \u0993 \u099a\u0995\u09cd\u09b0\u0997\u09a4\u09bf\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u09a6\u09a3\u09cd\u09a1\u099f\u09bf \u09b8\u09c1\u09b7\u09ae \u09b9\u09c7\u09a4\u09c1 \u09a4\u09be\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf \u098f\u0995\u0995 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u09ad\u09b0 = \\frac{M}{l}<\/span>\u0964 \u0995\u09be\u099c\u09c7\u0987 ?? \u0985\u0995\u09cd\u09b7 \u09b9\u09a4\u09c7 ? \u09a6\u09c2\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 ?? \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u0985\u0982\u09b6\u09c7\u09b0 \u09ad\u09b0 ?? \u09b9\u09b2\u09c7 dM = \\frac{M}{l}dx<\/span>\u0964 ?? \u0985\u0982\u09b6\u099f\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc \u09a4\u09be\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0995\u09a3\u09be ?? \u0985\u0995\u09cd\u09b7 \u09b9\u09a4\u09c7 x \u09a6\u09c2\u09b0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u0997\u09a3\u09cd\u09af \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 ?? \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 ?? \u0985\u0982\u09b6\u09c7\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 =dM\\times x^2 = \\frac{M}{l} \\times dx \\times x^2<\/span> \u098f\u09ac\u0982 \u098f\u0995\u09c7 x = \\frac{l}{2}<\/span> \u098f\u09ac\u0982 x = -\\frac{l}{2}<\/span> \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09b2\u09c7 \u09b8\u09ae\u0997\u09cd\u09b0 \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u099c\u09a1\u09bc\u09a4\u09be \u09ad\u09cd\u09b0\u09be\u09ae\u0995 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09ac\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\r\n
\"moment-of-inertia\"<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n

\u2234?? \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09b8\u09ae\u0997\u09cd\u09b0 \u09a6\u09a3\u09cd\u09a1\u099f\u09bf\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995,<\/p>\r\n\r\n\r\n\r\nI = \\int_{-\\frac{l}{2}}^{\\frac{l}{2}}(\\frac{M}{l})\\times dx \\times x^2 = \\frac{M}{l} \\int_{-\\frac{l}{2}}^{\\frac{l}{2}} x^2 dx = \\frac{M}{l}[\\frac{x^3}{3}]_{-\\frac{l}{2}}^{\\frac{l}{2}}<\/span>\r\n\r\n\r\n\r\n= \\frac{M}{3l} [(\\frac{l}{2})^3-(-\\frac{l}{2})^3] = \\frac{M}{3l} (\\frac{l^3}{8}+\\frac{l^3}{8})<\/span>\r\n\r\n\r\n\r\nI = \\frac{M}{12}l^2<\/span>\r\n\r\n\r\n\r\n

\u09a7\u09b0\u09bf \u099a\u0995\u09cd\u09b0\u0997\u09a4\u09bf\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 ?<\/p>\r\n\r\n\r\n\r\n\\therefore MK^2 = \\frac{M}{12} l^2<\/span>\r\n\r\n\r\n\r\n\\therefore K = \\frac{1}{\\sqrt{12}} = \\frac{1}{2\\sqrt3}<\/span>\r\n\r\n\r\n\r\n

\u09a7\u09b0\u09bf \u098f\u0995\u099f\u09bf \u09b8\u09c1\u09b7\u09ae \u09aa\u09be\u09a4\u09b2\u09be \u0986\u09af\u09bc\u09a4\u09be\u0995\u09be\u09b0 \u09aa\u09be\u09a4 ???? [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u098f\u09b0 \u09ad\u09b0 ?, \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af ?=??=?? \u0993 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5 ?=??=??\u0964 \u09aa\u09be\u09a4\u099f\u09bf \u09a4\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09ac\u09be \u09ad\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 ? \u09a6\u09bf\u09af\u09bc\u09c7 \u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u0985\u0995\u09cd\u09b7 ??? \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0998\u09c1\u09b0\u099b\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\r\n
\"moment-of-inertia-1\"<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n

\u098f\u0996\u09a8 ?? \u0985\u0995\u09cd\u09b7 ? \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u098f\u09ac\u0982 ?? \u09ac\u09be\u09b9\u09c1\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 \u098f\u09ac\u0982 ?? \u0985\u0995\u09cd\u09b7 ? \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0997\u09be\u09ae\u09c0 \u098f\u09ac\u0982 ?? \u09ac\u09be\u09b9\u09c1\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2\u0964 ?? \u098f\u09ac\u0982 ?? \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u0964 ??? \u0985\u0995\u09cd\u09b7 ?? \u0993 ?? \u098f\u09b0 \u0989\u09aa\u09b0 \u09b2\u09ae\u09cd\u09ac\u0964<\/p>\r\n\r\n\r\n\r\n

\u09b2\u09ae\u09cd\u09ac-\u0985\u0995\u09cd\u09b7 \u0989\u09aa\u09aa\u09be\u09a6\u09cd\u09af \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 ??? \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0990 \u09aa\u09be\u09a4\u09c7\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995,<\/p>\r\n\r\n\r\n\r\nI = \\frac{Ml^2}{12} + \\frac{Mb^2}{12}<\/span>\r\n\r\n\r\n\r\n

\u09ac\u09be,I = \\frac{M}{12}(l^2+b^2)<\/span><\/p>\r\n\r\n\r\n\r\n

\u0986\u09ac\u09be\u09b0,I = MK^2<\/span><\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be,\u00a0MK^2 = I = \\frac{M}{12}(l^2+b^2)<\/span><\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be,\u00a0k^2 = \\frac{l^2+b^2}{12}<\/span><\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be, K = \\sqrt{\\frac{l^2+b^2}{12}} = \\frac{1}{2} \\sqrt{\\frac{l^2+b^2}{3}}<\/span><\/p>\r\n\r\n\r\n\r\n

\u2234 \u099a\u0995\u09cd\u09b0\u0997\u09a4\u09bf\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7, K = \\frac{1}{2}<\/span> \u2026\u2026\u2026\u2026(4.41)<\/p>\r\n\r\n\r\n\r\n

(\u09e8) \u09a8\u09bf\u099c \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u099a\u09a4\u09c1\u09b0\u09cd\u09a6\u09bf\u0995\u09c7 \u0998\u09c2\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u09ae\u09be\u09a8 \u098f\u0995\u099f\u09bf \u09a8\u09bf\u09b0\u09c7\u099f \u099a\u09cb\u0999\u09c7\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 \u09ac\u09be \u099a\u0995\u09cd\u09b0\u0997\u09a4\u09bf\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7(determination of moment of inertia and radius of gyration for solid cylinder rotational around own axis)<\/h2>\r\n\r\n\r\n\r\n

\u09a7\u09b0\u09bf \u098f\u0995\u099f\u09bf \u09b8\u09c1\u09b7\u09ae \u09a8\u09bf\u09b0\u09c7\u099f \u099a\u09cb\u0999 ?-\u098f\u09b0 \u09ad\u09b0 ?, \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af ? \u0993 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 ? [\u099a\u09bf\u09a4\u09cd\u09b0 \u09ea.\u09e9\u09e6]\u0964 \u098f\u099f\u09bf \u09a8\u09bf\u099c \u0985\u0995\u09cd\u09b7 ??-\u098f\u09b0 \u099a\u09a4\u09c1\u09b0\u09cd\u09a6\u09bf\u0995\u09c7 \u0998\u09c1\u09b0\u099b\u09c7\u0964 ?? \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u098f\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 (moment of inertia)\/ \u0993 \u099a\u0995\u09cd\u09b0\u0997\u09a4\u09bf\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 (radius of gyration) \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u09ac\u09b0\u09cd\u09a3\u09a8\u09be \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u099a\u09cb\u0999\u099f\u09bf\u09b0 \u0986\u09af\u09bc\u09a4\u09a8 \\pi r^2 \\times l<\/span>\u0964<\/p>\r\n\r\n\r\n\r\n

\u099a\u09cb\u0999\u09c7\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac = \\frac{\u09ad\u09b0}{\u0986\u09df\u09a4\u09a8} = \\frac{M}{\\pi r^2 l}<\/span><\/p>\r\n\r\n\r\n\r\n

PQ-\u098f\u09b0 \u099a\u09a4\u09c1\u09b0\u09cd\u09a6\u09bf\u0995\u09c7 x \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u0993 dx \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09ab\u09be\u0981\u09aa\u09be \u09b8\u09ae\u09be\u0995\u09cd\u09b7\u09c0\u09af\u09bc \u09aa\u09be\u09a4\u09b2\u09be \u099a\u09cb\u0999 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09bf\u0964<\/p>\r\n\r\n\r\n\r\n

\u098f\u0987 \u09aa\u09be\u09a4\u09b2\u09be \u099a\u09cb\u0999\u09c7\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6 = 2 \\pi x dx<\/span>, \u0986\u09af\u09bc\u09a4\u09a8 = 2 \\pi x \\times dx \\times l<\/span><\/p>\r\n\r\n\r\n\r\n

\u09ad\u09b0 = \u0986\u09af\u09bc\u09a4\u09a8 \u00d7 \u0998\u09a8\u09a4\u09cd\u09ac<\/p>\r\n\r\n\r\n\r\n

= 2\\pi x \\times dx \\times l \\times \\frac{M}{\\pi r^2 l}<\/span><\/p>\r\n\r\n\r\n\r\n

= \\frac{2Mxdx}{r^2}<\/span><\/p>\r\n\r\n\r\n\r\n

\r\n
\"moment-of-inertia-and-radius-of-gyration\"<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n

dx \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0\u09c7\u09b0 \u098f\u0987 \u099a\u09cb\u0999\u099f\u09bf \u09aa\u09be\u09a4\u09b2\u09be \u09b9\u09c7\u09a4\u09c1 \u09a4\u09be\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u0995\u09a3\u09be PQ \u09b9\u09a4\u09c7 x \u09a6\u09c2\u09b0\u09c7 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u0995\u09be\u099c\u09c7\u0987 PQ \u09b9\u09a4\u09c7 x \u09a6\u09c2\u09b0\u09c7 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u0995\u09be\u099c\u09c7\u0987 PQ \u098f\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u098f\u0987 \u09aa\u09be\u09a4\u09b2\u09be \u099a\u09cb\u0999\u09c7\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995<\/p>\r\n\r\n\r\n\r\n\\frac{2Mxdx}{r^2} \\times x^2 = \\frac{2M}{r^2} x^3 dx<\/span>\r\n\r\n\r\n\r\n

\u09b8\u09ae\u0997\u09cd\u09b0 \u099a\u09cb\u0999\u099f\u09bf\u0995\u09c7 \u09b8\u09ae\u09be\u0995\u09cd\u09b7\u09c0\u09af\u09bc \u0985\u09a8\u09c1\u09b0\u09c2\u09aa \u0985\u09a8\u09c7\u0995\u0997\u09c1\u09b2\u09cb \u09aa\u09be\u09a4\u09b2\u09be \u09ab\u09be\u0981\u09aa\u09be \u099a\u09cb\u0999\u09c7\u09b0 \u09b8\u09ae\u09a8\u09cd\u09ac\u09cd\u09af\u09c7 \u0997\u09a0\u09bf\u09a4 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964<\/p>\r\n\r\n\r\n\r\n

\u0995\u09be\u099c\u09c7\u0987 x=0 \u0993 x=r \u098f\u0987 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0989\u09aa\u09b0\u09cb\u0995\u09cd\u09a4 \u09ab\u09be\u0981\u09aa\u09be \u099a\u09cb\u0999\u09c7\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u0995\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09b2\u09c7 \u09a8\u09bf\u099c \u0985\u0995\u09cd\u09b7 PQ-\u098f\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09b8\u09ae\u0997\u09cd\u09b0 \u099a\u09cb\u0999\u099f\u09bf\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 I \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09ac\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n\\therefore I = \\int_0^r \\frac{2M}{r^2}x^3 dx = \\frac{2M}{r^2} \\int_0^r x^3 dx = \\frac{2M}{r^2} [\\frac{x^4}{4}]_0^r\\\\\n= \\frac{2M}{4r^2}[r^4-0]\\\\\n\\therefore I = \\frac{1}{2}M<\/span>\r\n\r\n\r\n\r\n

\u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u099a\u0995\u09cd\u09b0\u0997\u09a4\u09bf\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 K \u09b9\u09b2\u09c7,<\/p>\r\n\r\n\r\n\r\nMK^2 = \\frac{1}{2}Mr^2<\/span>\r\n\r\n\r\n\r\n\\therefore K = \\frac{r}{\\sqrt 2}<\/span>\r\n","protected":false},"excerpt":{"rendered":"

(\u09e7) \u09b8\u09b0\u09c1 \u0993 \u09b8\u09c1\u09b7\u09ae \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09bf\u09af\u09bc\u09c7 \u0993 \u09a4\u09be\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u0985\u09ad\u09bf\u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0998\u09c2\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u09ae\u09be\u09a8 \u0990 \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u099c\u09a1\u09bc\u09a4\u09be\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 (Moment of Inertia) \u09a7\u09b0\u09bf ? \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u0993 ? \u09ad\u09b0\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09b8\u09c1\u09b7\u09ae \u09b8\u09b0\u09c1 \u09a6\u09a3\u09cd\u09a1 ??-\u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 ? \u09a6\u09bf\u09af\u09bc\u09c7 \u0993 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac\u09ad\u09be\u09ac\u09c7<\/p>\n

Read More<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4238,3028,50,51],"tags":[902,40,904,903],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/287"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=287"}],"version-history":[{"count":15,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/287\/revisions"}],"predecessor-version":[{"id":12429,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/287\/revisions\/12429"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}