{"id":179,"date":"2022-03-24T02:14:10","date_gmt":"2022-03-23T20:14:10","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=179"},"modified":"2022-04-18T12:53:18","modified_gmt":"2022-04-18T06:53:18","slug":"angular-momentum","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/angular-momentum\/","title":{"rendered":"\u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 | Angular Momentum"},"content":{"rendered":"\r\n

\u09b8\u0982\u099c\u09cd\u099e\u09be :<\/strong><\/h2>\r\n

\u0998\u09c2\u09b0\u09cd\u09a3\u09a8\u09b0\u09a4 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0<\/strong> \u0993 \u09b0\u09c8\u0996\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 <\/strong>\u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u0995\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997<\/strong> (Angular Momentum) \u09ac\u09b2\u09c7\u0964<\/p>\r\n\r\n

 <\/p>\r\n\r\n

\r\n
\r\n
\"angular-momentum\"

\u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 \u099a\u09bf\u09a4\u09cd\u09b0<\/p><\/div>\r\n<\/figure>\r\n<\/div>\r\n\r\n\r\n\r\n

\u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be<\/strong> :<\/h3>\r\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf\u00a0 ?\u00a0 =\u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u098f\u09ac\u0982\u00a0 ? = \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b0\u09c8\u0996\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997\u0964 \u0985\u09a4\u098f\u09ac, \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 ? = ? \u00d7 ?\u00a0<\/p>\r\n\r\n\r\n\r\n

\u098f\u099f\u09bf \u098f\u0995\u099f\u09bf \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09b0\u09be\u09b6\u09bf\u0964<\/p>\r\n\r\n\r\n\r\n

\u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 :<\/strong><\/h3>\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a8, ? = ??????<\/p>\r\n\r\n\r\n\r\n

\u098f\u0996\u09be\u09a8\u09c7 ? \u09b9\u099a\u09cd\u099b\u09c7\u00a0 ?\u00a0 \u0993\u00a0 ?\u00a0 \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u0995\u09cb\u09a3 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09c7\u0996\u09be\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b9\u099a\u09cd\u099b\u09c7 ????? \u0964 \u0985\u09a4\u098f\u09ac, \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ad\u09b0\u09ac\u09c7\u0997 \u0993 \u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u09b0\u09c7\u0996\u09be\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u0997\u09c2\u09a3\u09ab\u09b2 \u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u00a0?\u00a0 \u0993\u00a0 ?\u00a0 \u09af\u09c7 \u09a4\u09b2\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4\u00a0 ?\u00a0 \u098f\u09b0 \u09a6\u09bf\u0995 \u09b9\u09ac\u09c7 \u0990 \u09a4\u09b2\u09c7\u09b0 \u09b2\u09ae\u09cd\u09ac \u09ac\u09b0\u09be\u09ac\u09b0\u0964 \u0995\u09cd\u09b0\u09b8 \u0997\u09c1\u09a3\u09a8\u09c7\u09b0 \u09a8\u09bf\u09af\u09bc\u09ae \u09a6\u09cd\u09ac\u09be\u09b0\u09be\u00a0 ? -\u098f\u09b0 \u09a6\u09bf\u0995 \u09a8\u09bf\u09b0\u09cd\u09a7\u09be\u09b0\u09bf\u09a4 \u09b9\u09ac\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u0985\u09a8\u09c1\u09b8\u09bf\u09a6\u09cd\u09a7\u09be\u09a8\u09cd\u09a4:<\/strong><\/h3>\r\n

\u0995\u09a3\u09be\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u09aa\u09a5\u09c7 \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b9\u09b2\u09c7,\u00a0 ?\u00a0 \u0993\u00a0 ?\u00a0 \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u0995\u09cb\u09a3 ? = 90\u00b0\u0964 \u09b8\u09c7\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7,<\/p>\r\n\r\n\r\n\r\n L = r P \\sin \\theta = r(mv) = mr(r \\omega) = m r^{2} \\omega <\/span>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 (Angular Momentum)<\/h2>\r\n\r\n\r\n\r\n

\u098f\u0995\u0995 \u0993 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 :<\/strong><\/h3>\r\n

\u098f\u09ae. \u0995\u09c7. \u098f\u09b8. \u0993 \u098f\u09b8. \u0986\u0987. \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u09a4\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 \u098f\u0995\u0995 \u09b9\u099a\u09cd\u099b\u09c7\u00a0 kg\u00a0m^{2}\u00a0s^{-1} <\/span> \u098f\u09ac\u0982 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/p>\r\n\r\n\r\n\r\n [L] = [ \u09ad\u09b0\u09ac\u09c7\u0997 \\times \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac ] = [MLT^{-1}L] = [ML^{2}T^{-1}]<\/span>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 \u098f\u09ac\u0982 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 (Relation between angular momentum and angular velocity)<\/h3>\r\n\r\n\r\n\r\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 ? \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7 \u098f\u0995\u099f\u09bf \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u099a\u09be\u09b0\u09bf\u09a6\u09bf\u0995\u09c7 \u0998\u09c1\u09b0\u099b\u09c7\u0964 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf \u0985\u09a8\u09c7\u0995\u0997\u09c1\u09b2\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09b8\u09ae\u09b7\u09cd\u099f\u09bf \u09b9\u09b2\u09c7 \u0986\u09ae\u09b0\u09be \u09b2\u09bf\u0996\u09a4\u09c7 \u09aa\u09be\u09b0\u09bf,<\/p>\r\n\r\n\r\n\r\n

[\u098f\u0996\u09be\u09a8\u09c7\u00a0 l_1 , l_2 , \\cdot \\cdot \\cdot , l_n <\/span> \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09b8\u09ae\u09be\u09a8\u09cd\u09a4\u09b0\u09be\u09b2 ]<\/p>\r\n\r\n\r\n\r\n L= l_1 + l_2 + \\cdot \\cdot \\cdot + l_n<\/span>\r\n\r\n\r\n\r\nL= r_1 P_1 + r_2 P_2 + \\cdot \\cdot \\cdot + r_n P_n<\/span>\r\n\r\n\r\n\r\n

= r_1 m_1 v_1 + r_2 m_2 v_2 + \\cdot \\cdot \\cdot + r_n m_n v_n <\/span>
= r_1 m_1 \\omega r_1 + r_2 m_2 \\omega r_2 + \\cdot \\cdot \\cdot <\/span><\/p>\r\n\r\n\r\n\r\n = m_1 r_1^{2} + m_2 r_2^{2} + \\cdot \\cdot \\cdot\n= \\sum m r^{2} <\/span>\r\n\r\n\r\n\r\n =\\omega \\sum m r^{2} <\/span>\r\n\r\n\r\n\r\n = I \\omega <\/span>\r\n\r\n\r\n\r\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce,\u00a0 L = L = I \\omega <\/span><\/p>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 \u09b8\u0982\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be (Terms Related to Angular Momentum)<\/h3>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3 (Angular displacement)<\/h3>\r\n\r\n\r\n\r\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0987 \u09ac\u0987\u09af\u09bc\u09c7\u09b0 \u09aa\u09be\u09a4\u09be\u09b0 \u09ae\u09a4\u09cb \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09b8\u09ae\u09a4\u09b2\u09c7\u09b0 \u0989\u09aa\u09b0 \u098f\u0995\u099f\u09bf \u0995\u09a3\u09be \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 ? \u098f\u09b0 \u099a\u09be\u09b0\u09bf\u09a6\u09bf\u0995\u09c7 \u09ac\u09c3\u09a4\u09cd\u09a4 \u09aa\u09a5\u09c7 \u0998\u09c1\u09b0\u099b\u09c7\u0964 \u098f\u0996\u09be\u09a8\u09c7 \u0998\u09c2\u09b0\u09cd\u09a3\u09be\u0995\u09cd\u09b7 \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 ? \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09a6\u09bf\u09af\u09bc\u09c7 \u09af\u09be\u09ac\u09c7 \u098f\u09ac\u0982 \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09a4\u09b2\u09c7\u09b0 \u09b8\u0999\u09cd\u0997\u09c7 \u09b2\u09ae\u09cd\u09ac \u09b9\u09ac\u09c7\u0964 \u0995\u09cb\u09a3\u0995\u09c7 \u0995\u09a3\u09be\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3 (angular displacement) \u09ac\u09b2\u09c7\u0964 ?? \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0\u0964<\/strong><\/p>\r\n\r\n\r\n\r\n

\u09b8\u0982\u099c\u09cd\u099e\u09be <\/strong>: \u09ac\u09c3\u09a4\u09cd\u09a4\u09c0\u09af\u09bc \u0997\u09a4\u09bf\u09a4\u09c7 \u09b8\u099a\u09b2 \u0995\u09a3\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09ac\u0995\u09be\u09b6\u09c7 \u09af\u09c7 \u0995\u09cb\u09a3\u09c7 \u09b8\u09b0\u09c7 \u09af\u09be\u09af\u09bc, \u09a4\u09be\u0995\u09c7 \u0990 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09ac\u0995\u09be\u09b6\u09c7 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0995\u09a3\u09be\u099f\u09bf\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3(Angular displacement)<\/strong> \u09ac\u09b2\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u09b0\u09c7\u09a1\u09bf\u09af\u09bc\u09be\u09a8 \u098f\u0995\u0995\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09b2\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3 ? \u098f\u09b0 \u09b8\u0999\u09cd\u0997\u09c7 \u09b8\u0982\u09b6\u09cd\u09b2\u09bf\u09b7\u09cd\u099f \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u099a\u09be\u09aa ?-\u098f\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u0996\u09c1\u09ac\u0987 \u09b8\u09b0\u09b2 \u09b9\u09af\u09bc\u0964<\/p>\r\n\r\n\r\n\r\n

\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 r \u09b9\u09b2\u09c7 \u09b2\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc, \\theta = \\frac{s}{r} <\/span>\u00a0<\/p>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 (Angular Velocity)<\/h3>\r\n\r\n\r\n\r\n

\u09b0\u09c8\u0996\u09bf\u0995 \u0997\u09a4\u09bf\u09b0 \u09ae\u09a4\u09cb \u0995\u09cc\u09a3\u09bf\u0995 \u0997\u09a4\u09bf\u0993 \u09b8\u09ae \u09ac\u09be \u0985\u09b8\u09ae (\u09a4\u09cd\u09ac\u09b0\u09bf\u09a4) \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u0995\u09cc\u09a3\u09bf\u0995 \u0997\u09a4\u09bf \u0985\u09b8\u09ae \u09b9\u09b2\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3 \u098f\u09ac\u0982 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u0995\u09c7 \u0995\u09a3\u09be\u09b0 \u0997\u09a1\u09bc \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 (average angular velocity)<\/strong> \u09ac\u09b2\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u098f\u0995\u09c7 ? \u0985\u0995\u09cd\u09b7\u09b0 \u09a6\u09bf\u09af\u09bc\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u0995\u09cc\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3\u09c7\u09b0 \u09ae\u09a4\u09cb \u098f\u0995\u0987 \u09b0\u09c0\u09a4\u09bf \u098f\u0996\u09be\u09a8\u09c7 \u0985\u09a8\u09c1\u09b8\u09b0\u09a3 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964<\/p>\r\n\r\n

 <\/p>\r\n\r\n

\r\n
\"angular-velocity\"<\/figure>\r\n<\/div>\r\n\r\n

 <\/p>\r\n\r\n

\u0985\u09a4\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09ac\u0995\u09be\u09b6 \u0394? \u09a4\u09c7 \u0995\u09a3\u09be\u09b0 \u09b8\u09b0\u09a3 \u0394? \u09b9\u09b2\u09c7 [\u099a\u09bf\u09a4\u09cd\u09b0] \u0990 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09ac\u0995\u09be\u09b6\u09c7 \u0995\u09a3\u09be\u09b0 \u0997\u09a1\u09bc \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 \u09b9\u09ac\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b8\u09cd\u09a5\u09bf\u09b0 \u09a5\u09be\u0995\u09b2\u09c7 \u09ac\u09c3\u09a4\u09cd\u09a4\u09c0\u09af\u09bc \u0997\u09a4\u09bf\u0995\u09c7 \u09b8\u09ae\u09ac\u09c3\u09a4\u09cd\u09a4\u09c0\u09af\u09bc \u0997\u09a4\u09bf(uniform circular motion)<\/strong> \u09ac\u09b2\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u09b8\u09ae\u09ac\u09c3\u09a4\u09cd\u09a4\u09c0\u09af\u09bc \u0997\u09a4\u09bf\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0 t \u09b8\u09ae\u09af\u09bc\u09c7\u00a0 \u0995\u09cc\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3 ? \u09b9\u09b2\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a8 \u09b9\u09af\u09bc \\omega = \\frac{\\theta}{t} <\/span>\u00a0 \u0985\u09a5\u09ac\u09be ? = ??\u00a0<\/p>\r\n\r\n\r\n\r\n

\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u09b8\u09ae\u09b0\u09c8\u0996\u09bf\u0995 \u0997\u09a4\u09bf\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 ? = ?? \u098f\u09b0 \u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u0964<\/p>\r\n\r\n\r\n\r\n

\u098f\u0995\u0995 :<\/strong> \u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u0995\u09c7 \u09b0\u09c7\u09a1\u09bf\u09af\u09bc\u09be\u09a8\/\u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1 ( ??????\/sec<\/span>\u2061 \u09ac\u09be \u09b8\u0982\u0995\u09cd\u09b7\u09c7\u09aa\u09c7 ???\/ ?) \u098f\u0995\u0995\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u09af\u09a8\u09cd\u09a4\u09cd\u09b0\u09ac\u09bf\u09a6\u09cd\u09af\u09be \u09ac\u09be \u0987\u099e\u09cd\u099c\u09bf\u09a8\u09bf\u09af\u09bc\u09be\u09b0\u09bf\u0982-\u098f \u0986\u09b0\u09c7\u0995\u099f\u09bf \u098f\u0995\u0995\u09c7 \u09aa\u09cd\u09b0\u099a\u09b2\u09bf\u09a4 \u0986\u099b\u09c7\u0964 \u098f\u09b0 \u09a8\u09be\u09ae \u0986\u09ac\u09b0\u09cd\u09a4\u09a8\/\u09ae\u09bf\u09a8\u09bf\u099f ( revolution per minute, \u09b8\u0982\u0995\u09cd\u09b7\u09c7\u09aa\u09c7 ???)<\/p>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be :\u00a0<\/strong> [\\omega] = [\\frac{\u09b0\u09c8\u0996\u09bf\u0995 \u09ac\u09c7\u0997}{\u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7}] = \\frac{[LT^{-1}]}{[L]} = [T^{-1}] <\/span><\/p>\r\n\r\n\r\n\r\n

\u098f\u0995\u09ac\u09be\u09b0 \u09aa\u09c2\u09b0\u09cd\u09a3 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u09a4\u09c7 \u0995\u09a3\u09be\u09b0 \u09af\u09c7 \u09b8\u09ae\u09af\u09bc \u09b2\u09be\u0997\u09c7 \u09a4\u09be\u0995\u09c7 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u0995\u09be\u09b2 (time period) \u09ac\u09b2\u09c7\u0964\u098f\u0995\u099f\u09bf \u09aa\u09c2\u09b0\u09cd\u09a3 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8 \u09ac\u09b2\u09a4\u09c7 2\u03c0 \u09b0\u09c7\u09a1\u09bf\u09af\u09bc\u09be\u09a8 \u0995\u09cb\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3 \u09ac\u09cb\u099d\u09be\u09af\u09bc\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09aa\u09b0\u09cd\u09af\u09be\u09af\u09bc\u0995\u09be\u09b2 T <\/span> \u09b9\u09b2\u09c7 (4.25) \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u0985\u09a8\u09c1\u09af\u09be\u09af\u09bc\u09c0<\/p>\r\n\r\n\r\n\r\n \\omega = \\frac{2 \\pi}{T} <\/span>\r\n\r\n\r\n\r\n

\\frac{1}{T}<\/span>\u00a0 \u098f\u0995\u0995 \u09b8\u09ae\u09af\u09bc\u09c7 \u09aa\u09c2\u09b0\u09cd\u09a3 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be \u09ac\u09cb\u099d\u09be\u09af\u09bc\u0964 \u098f\u0995\u09c7 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995 (frequency)<\/strong> \u09ac\u09b2\u09c7\u0964 \u0995\u09ae\u09cd\u09aa\u09be\u0999\u09cd\u0995\u0995\u09c7 \u2018?\u2019 \u09a6\u09bf\u09af\u09bc\u09c7 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09b2\u09c7 \u0986\u09ae\u09be\u09b0\u09be \u09aa\u09be\u0987, \\omega = 2 \\pi n <\/span>\u00a0<\/p>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 \u0993 \u09b0\u09c8\u0996\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 (Relation between angular velocity and linear velocity)<\/h3>\r\n\r\n\r\n\r\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, \u09b0\u09c8\u0996\u09bf\u0995 \u09aa\u09a5\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a6\u09bf\u0995\u09c7 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf \u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1\u09c7\u09b0 \u09b0\u09c8\u0996\u09bf\u0995 \u09b8\u09b0\u09a3\u0987 \u09b0\u09c8\u0996\u09bf\u0995 \u09ac\u09c7\u0997<\/strong> \u098f\u09ac\u0982 \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u09aa\u09a5\u09c7 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf \u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1\u09c7\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09b8\u09b0\u09a3\u0987 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 (angular velocity)<\/strong>\u0964 \u09b0\u09c8\u0996\u09bf\u0995 \u09ac\u09c7\u0997\u0995\u09c7 ? \u098f\u09ac\u0982 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u0995\u09c7 ? \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964 \u09b0\u09c8\u0996\u09bf\u0995 \u09ac\u09c7\u0997 \u098f\u09ac\u0982 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u099c\u09a8\u09bf\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u099f\u09bf \u098f\u0996\u09a8 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09be \u09b9\u09ac\u09c7\u0964<\/p>\r\n\r\n

 <\/p>\r\n\r\n

\r\n
\"angular-velocity-and-linear-velocity\"<\/figure>\r\n<\/div>\r\n\r\n

 <\/p>\r\n\r\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be ? \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09aa\u09b0\u09bf\u09a7\u09bf \u09ac\u09b0\u09be\u09ac\u09b0 ? \u09b8\u09ae\u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7 \u0998\u09c1\u09b0\u099b\u09c7 [ \u099a\u09bf\u09a4\u09cd\u09b0] \u0964 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/p>\r\n\r\n\r\n\r\n

\\omega <\/span> =\u00a0 \u0995\u09cc\u09a3\u09bf\u0995 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \/ \u09b8\u09ae\u09af\u09bc = \\frac{2 \\pi}{T} <\/span><\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be, T = 2 \\pi \\omega <\/span> \u2026\u2026\u2026\u2026\u2026.\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026(4.28)<\/p>\r\n\r\n\r\n\r\n

\u098f\u0996\u09a8 \u09af\u09a6\u09bf \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u09aa\u09a5\u09c7 \u09a8\u09be \u0998\u09c1\u09b0\u09c7 \u0995\u09a3\u09be\u099f\u09bf ? \u09ac\u09c7\u0997\u09c7 \u098f\u0995\u0987 \u09b8\u09ae\u09af\u09bc\u09c7 \u09b8\u09b0\u09b2\u09b0\u09c7\u0996\u09be\u09af\u09bc \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09aa\u09b0\u09bf\u09a7\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8 \u09aa\u09a5 ? \u09b8\u09ae\u09af\u09bc\u09c7 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09c7, \u09a4\u09ac\u09c7 ?=\u00a0\u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09aa\u09b0\u09bf\u09a7\u09bf \/ \u09aa\u09b0\u09bf\u09a7\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u09a4\u09c7 \u09b8\u09ae\u09af\u09bc = \u00a0\\frac{2 \\pi r}{T} <\/span>\u00a0<\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be, ?= \\frac{2 \\pi r}{v} <\/span>\u00a0<\/p>\r\n\r\n\r\n\r\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3(4.28) \u098f\u09ac\u0982 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (4.29) \u09b9\u09a4\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/p>\r\n\r\n\r\n\r\n ?= \\frac{2 \\pi}{\\omega} = \\frac{2 \\pi r}{v} <\/span>\r\n\r\n\r\n\r\n

\u09ac\u09be,\u00a0 \\frac{1}{\\omega} = \\frac{r}{v}<\/span><\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be, ? = \\omega ?<\/span><\/p>\r\n\r\n\r\n\r\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce, \u09b0\u09c8\u0996\u09bf\u0995 \u09ac\u09c7\u0997 = \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 \u00d7 \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7<\/strong><\/p>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 (Angular acceleration)<\/h3>\r\n\r\n\r\n\r\n

\u0985\u09a8\u09c7\u0995 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8\u09b0\u09a4 \u0995\u09a3\u09be\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 \u09ac\u09be\u09a1\u09bc\u09c7 \u09ac\u09be \u0995\u09ae\u09c7\u0964 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09b2\u09c7 \u09ac\u09cb\u099d\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7 \u0995\u09a3\u09be\u099f\u09bf \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09a8\u09bf\u09af\u09bc\u09c7 \u099a\u09b2\u099b\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u0986\u09ac\u09b0\u09cd\u09a4\u09a8\u09b0\u09a4 \u0995\u09a3\u09be\u09b0 \u0997\u09a1\u09bc \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 (average angular acceleration) <\/strong>\u09ac\u09b2\u09a4\u09c7 \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09ac\u0995\u09be\u09b6\u09c7 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09b8\u0999\u09cd\u0997\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u09b9\u09be\u09b0 \u09ac\u09cb\u099d\u09be\u09af\u09bc\u0964<\/p>\r\n\r\n\r\n\r\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u0985\u09a4\u09bf \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09ac\u0995\u09be\u09b6 \u0394? – \u09a4\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u0394? \u09b9\u09b2\u09c7 \u0990 \u0985\u09ac\u0995\u09be\u09b6\u09c7 \u0997\u09a1\u09bc \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09b9\u09ac\u09c7,<\/p>\r\n\r\n\r\n\r\n\\lim_{\\Delta t \\to 0} \\frac{\\Delta \\omega}{\\Delta t}\u2005\u2005\u2005\u2005 \u09ac\u09be, \u03b1=\\frac{d\\omega}{dt}= \\frac{d}{dt} \\frac{d \\theta}{dt}=\\frac{d^{2} \\theta}{dt^{2}}<\/span>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09ac\u09b2\u09a4\u09c7 \u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 \u09a4\u09be\u09ce\u0995\u09cd\u09b7\u09a3\u09bf\u0995 \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09ac\u09cb\u099d\u09be\u09af\u09bc\u0964 \u098f\u09b0 \u098f\u0995\u0995 \u09b0\u09c7\u09a1\u09bf\u09af\u09bc\u09be\u09a8 \u09aa\u09cd\u09b0\u09a4\u09bf \u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1 \u09aa\u09cd\u09b0\u09a4\u09bf \u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b0\u09c7\u09a1\u09bf\u09af\u09bc\u09be\u09a8\/\u09b8\u09c7\u0995\u09c7\u09a8\u09cd\u09a1 ^2 (??? ?^{\u22122} ) <\/span> \u0964<\/p>\r\n\r\n\r\n\r\n

\u0986\u09ac\u09b0\u09cd\u09a4\u09a8\u09b0\u09a4 \u0995\u09a3\u09be\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995 \u09b9\u09b2\u09c7 \u09a4\u09be\u09ce\u0995\u09cd\u09b7\u09a3\u09bf\u0995 \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09ac\u0995\u09be\u09b6\u09c7 \u0997\u09a1\u09bc \u0995\u09cb\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09af\u09bc\u0964 \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 ? \u09b8\u09ae\u09af\u09bc\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf ? \u09b9\u09b2\u09c7, \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3, \\alpha = \\frac{\\omega}{t} <\/span><\/p>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be, [\\alpha] = \\frac{[\\omega]}{[T]} = \\frac{[T^{-1}]}{[T]} = [T^{-2}]\u00a0<\/span><\/p>\r\n\r\n\r\n\r\n

\u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 \u0993 \u09b0\u09c8\u0996\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 (Relation between angular acceleration and linear acceleration)<\/h3>\r\n\r\n

 <\/p>\r\n\r\n

\r\n
\"angular-acceleration-and-linear-acceleration\"<\/figure>\r\n<\/div>\r\n\r\n

 <\/p>\r\n\r\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be ? \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f [ \u099a\u09bf\u09a4\u09cd\u09b0 ] \u09ac\u09c3\u09a4\u09cd\u09a4\u09c7\u09b0 \u09aa\u09b0\u09bf\u09a7\u09bf \u09ac\u09b0\u09be\u09ac\u09b0 \u0985\u09b8\u09ae \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u0997\u09a4\u09bf\u09a4\u09c7 \u0986\u09ac\u09b0\u09cd\u09a4\u09a8 \u0995\u09b0\u099b\u09c7\u0964 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u099f\u09bf\u09b0 t \u09b8\u09ae\u09af\u09bc\u09c7 \u09b0\u09c8\u0996\u09bf\u0995 \u09ac\u09c7\u0997 = ?, \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u0997 = ?, \u09b0\u09c8\u0996\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 = ? \u098f\u09ac\u0982 \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 = ?\u0964<\/p>\r\n\r\n\r\n\r\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, v = \\omega r <\/span><\/p>\r\n\r\n\r\n\r\n \\alpha = \\frac{d \\omega}{dt} <\/span>\r\n\r\n\r\n\r\n

\u098f\u09ac\u0982\u00a0 ?= \\frac{dv}{dt} <\/span><\/p>\r\n\r\n\r\n\r\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 4.33- \u098f\u09b0 \u0989\u09ad\u09af\u09bc \u09aa\u0995\u09cd\u09b7\u0995\u09c7 ?\u2212 \u098f\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09ac\u09cd\u09af\u09ac\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,<\/p>\r\n\r\n\r\n\r\n

\\frac{dv}{dt}= \\omega \\frac{dr}{dt}+ \\frac{d\\omega}{dt}r=r \\frac{d\\omega}{dt}<\/span>\u00a0\u00a0 [ \u2235 r =\u00a0\u00a0 \u00a0\u09a7\u09cd\u09b0\u09c1\u09ac\u0995 ]<\/p>\r\n\r\n\r\n\r\n

\u09ac\u09be, a = \\alpha r , [\\because \\frac{d\\omega}{dt} = \\alpha]<\/span><\/p>\r\n\r\n\r\n\r\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u00a0 \u09b0\u09c8\u0996\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 = \u0995\u09cc\u09a3\u09bf\u0995 \u09a4\u09cd\u09ac\u09b0\u09a3 \u00d7 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7<\/strong><\/p>\r\n\r\n\r\n\r\n

\u099f\u09b0\u09cd\u0995 \u09ac\u09be \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995<\/a> (Torque or Moment of a force)<\/h3>\r\n\r\n\r\n\r\n

\u0995\u09cb\u09a8 \u09a6\u09c3\u09a2\u09bc \u09ac\u09b8\u09cd\u09a4\u09c1 \u098f\u0995\u099f\u09bf \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u0995\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u09b0\u09c7 \u0998\u09c1\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u09af\u09c7\u09ae\u09a8 \u09a6\u09c7\u09af\u09bc\u09be\u09b2\u09c7 \u099d\u09c1\u09b2\u09be\u09a8\u09cb \u09ab\u099f\u09cb \u09aa\u09c7\u09b0\u09c7\u0995 \u0993 \u09b8\u09c1\u09a4\u09be\u09b0 \u09b8\u0982\u09af\u09cb\u0997 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0998\u09c1\u09b0\u09a4\u09c7 \u09a5\u09be\u0995\u09c7; \u0986\u09ac\u09be\u09b0 \u0997\u09be\u09a1\u09bc\u09bf\u09b0 \u099a\u09be\u0995\u09be \u09a4\u09be\u09b0 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0998\u09c1\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u0995\u09cb\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u099a\u09be\u09b0\u09a6\u09bf\u0995\u09c7 \u0998\u09c1\u09b0\u09cd\u09a3\u09be\u09af\u09bc\u09ae\u09be\u09a8 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09a4\u09c7 \u09a4\u09cd\u09ac\u09b0\u09a3 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09a6\u09cd\u09ac\u09a8\u09cd\u09a6\u09cd\u09ac\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u0995\u09c7 \u099f\u09b0\u09cd\u0995 \u09ac\u09be \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 \u09ac\u09b2\u09c7\u0964 \u098f\u0995\u09c7 ? (\u099f\u09be\u0989) \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964<\/p>\r\n\r\n

 <\/p>\r\n\r\n

\r\n
\"torque\"<\/figure>\r\n<\/div>\r\n\r\n

 <\/p>\r\n\r\n

\u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be<\/strong>: \u09a7\u09b0\u09be \u09af\u09be\u0995, ? \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u0995\u099f\u09bf \u09aa\u09be\u09a4\u09b2\u09be \u09aa\u09be\u09a4 \u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995 \u0985\u09ac\u09b8\u09cd\u09a5\u09cd\u09af\u09be \u098f\u09ae\u09a8\u09ad\u09be\u09ac\u09c7 \u0986\u099b\u09c7 \u09af\u09c7 \u09a4\u09be \u0989\u09b2\u09ae\u09cd\u09ac \u0985\u0995\u09cd\u09b7 ???-\u098f\u09b0 \u099a\u09a4\u09c1\u09b0\u09cd\u09a6\u09bf\u0995\u09c7 ?-\u0995\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u0995\u09b0\u09c7 \u0998\u09c1\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u09aa\u09be\u09a4\u099f\u09bf\u0995\u09c7 \u09a4\u09be\u09b0 \u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 ?-\u09a4\u09c7 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7 \u0998\u09c1\u09b0\u09be\u09b2\u09c7 \u09af\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7,<\/p>\r\n\r\n\r\n\r\n

(\u09e7) \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09af\u09a4 \u09ac\u09c7\u09b6\u09bf \u09b9\u09ac\u09c7, \u09a4\u09be\u09b0 \u0998\u09c1\u09b0\u09cd\u09a3\u09a8 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf\u09b0 \u0995\u09cd\u09b7\u09ae\u09a4\u09be\u0993 \u09a4\u09a4 \u09ac\u09c7\u09b6\u09bf \u09b9\u09ac\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

(\u09e8) ? \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2 ?-\u098f\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac ? \u09af\u09a4 \u09ac\u09c7\u09b6\u09bf \u09b9\u09ac\u09c7, \u0990 \u09ac\u09b2\u09c7 \u0998\u09c1\u09b0\u09cd\u09a3\u09a8 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf\u09b0 \u0995\u09cd\u09b7\u09ae\u09a4\u09be\u0993 \u09a4\u09a4 \u09ac\u09c7\u09b6\u09bf \u09b9\u09ac\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

(\u09e9) \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09ae\u09c1\u0996 ? \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0985\u09ad\u09bf\u09ae\u09c1\u0996\u09c0 \u09b9\u09b2\u09c7, \u09aa\u09be\u09a4\u099f\u09bf\u09a4\u09c7 \u0995\u09cb\u09a8\u09cb \u0998\u09c1\u09b0\u09cd\u09a3\u09a8 \u09b9\u09ac\u09c7 \u09a8\u09be\u0964<\/p>\r\n\r\n\r\n\r\n

\u0989\u09aa\u09b0\u09bf\u0989\u0995\u09cd\u09a4 \u0995\u09be\u09b0\u09a3\u09c7 \u0995\u09cb\u09a8\u09cb \u0985\u0995\u09cd\u09b7 \u09ac\u09be \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u09c7\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b2\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0993 \u0985\u0995\u09cd\u09b7 \u09b9\u09a4\u09c7 \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u09b0\u09c7\u0996\u09be\u09b0 \u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac ?-\u098f\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09b9\u09af\u09bc\u0964<\/p>\r\n\r\n\r\n\r\n\\tau = d \\times F<\/span>\r\n\r\n\r\n\r\n

\u09ac\u09be, \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 \u09ac\u09be \u099f\u09b0\u09cd\u0995 =\u09ac\u09b2\u00d7\u09b2\u09ae\u09cd\u09ac \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/strong><\/p>\r\n\r\n\r\n\r\n

\u099a\u09bf\u09a4\u09cd\u09b0 \u09ea.\u09e8\u09eb-\u098f O \u09b9\u09a4\u09c7 F \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 C-\u098f\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac = r \u0993 F \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b0\u09c7\u0996\u09be NC-\u098f\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac = d \u098f\u09ac\u0982 \u2220???=? \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u09c7\u099b\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u0995\u09be\u099c\u09c7\u0987, ?? = ? = r sin \\theta <\/span><\/p>\r\n\r\n\r\n\r\n

\u2234 \\tau = d \\times F = ? ? sin \\theta <\/span><\/p>\r\n\r\n\r\n\r\n

\u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u09ac\u09c0\u099c\u0997\u09a3\u09bf\u09a4\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 ?-\u0995\u09c7 \u09a8\u09bf\u09ae\u09cd\u09a8 \u0989\u09aa\u09be\u09af\u09bc\u09c7 \u09b2\u09c7\u0996\u09be \u09b9\u09af\u09bc,<\/p>\r\n\r\n\r\n\r\n \\tau = r \\times F <\/span>\r\n\r\n\r\n\r\n

\u09b8\u0982\u099c\u09cd\u099e\u09be:<\/strong> \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0998\u09c1\u09b0\u09cd\u09a3\u09a8\u09b0\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u09af\u09c7 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09b2 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2 \u0990 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0993 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2\u09c7\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u0995\u09c7 \u099f\u09b0\u09cd\u0995<\/strong> \u09ac\u09b2\u09c7\u0964<\/p>\r\n\r\n\r\n\r\n

\u099f\u09b0\u09cd\u0995 \u09ac\u09be \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u09c7\u09b0 \u098f\u0995\u0995 (Unit of torque or moment of a force)<\/h3>\r\n\r\n\r\n\r\n

\u098f\u09b8. \u0986\u0987. \u09aa\u09a6\u09cd\u09a7\u09a4\u09bf\u09a4\u09c7 \u099f\u09b0\u09cd\u0995 \u09ac\u09be \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u09c7\u09b0 \u098f\u0995\u0995 \u09a8\u09bf\u0989\u099f\u09a8-\u09ae\u09bf\u099f\u09be\u09b0 (?\u2212?) <\/span>\u0964<\/p>\r\n\r\n\r\n\r\n

\u099f\u09b0\u09cd\u0995 \u09ac\u09be \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u09c7\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (Dimension of torque or moment of a force)<\/h3>\r\n\r\n\r\n\r\n

\u099f\u09b0\u09cd\u0995 \u09ac\u09be \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u09c7\u09b0 \u09b8\u0982\u099c\u09cd\u099e\u09be \u09b9\u09a4\u09c7 \u098f\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09aa\u09cd\u09b0\u09a4\u09bf\u09aa\u09be\u09a6\u09a8 \u0995\u09b0\u09be \u09af\u09be\u09af\u09bc\u0964 \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995\u09c7\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u09b8\u09ae\u09c0\u0995\u09b0\u09a3,\u00a0 \u099f\u09b0\u09cd\u0995 \u09ac\u09be \u09ac\u09b2\u09c7\u09b0 \u09ad\u09cd\u09b0\u09be\u09ae\u0995 = \u09ac\u09b2\u00d7\u09a6\u09c2\u09b0\u09a4\u09cd\u09ac = [MLT^{-2} \\times L] = [ML^{2}T^{-2}] <\/span><\/p>\r\n","protected":false},"excerpt":{"rendered":"

\u09b8\u0982\u099c\u09cd\u099e\u09be : \u0998\u09c2\u09b0\u09cd\u09a3\u09a8\u09b0\u09a4 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0993 \u09b0\u09c8\u0996\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u0997\u09c1\u09a3\u09ab\u09b2\u0995\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997 (Angular Momentum) \u09ac\u09b2\u09c7\u0964   \u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be : \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf\u00a0 ?\u00a0 =\u0998\u09c2\u09b0\u09cd\u09a3\u09a8 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ad\u09c7\u0995\u09cd\u099f\u09b0 \u098f\u09ac\u0982\u00a0 ? = \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b0\u09c8\u0996\u09bf\u0995 \u09ad\u09b0\u09ac\u09c7\u0997\u0964 \u0985\u09a4\u098f\u09ac, \u09b8\u0982\u099c\u09cd\u099e\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0995\u09cc\u09a3\u09bf\u0995<\/p>\n

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