{"id":923,"date":"2020-03-23T16:10:19","date_gmt":"2020-03-23T15:10:19","guid":{"rendered":"https:\/\/blogs.ua.es\/jjrr2011\/?p=923"},"modified":"2020-04-18T12:58:16","modified_gmt":"2020-04-18T11:58:16","slug":"chapter-4-iii","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/jjrr2011\/2020\/03\/23\/chapter-4-iii\/","title":{"rendered":"Chapter 4: Rigid bodies (III)"},"content":{"rendered":"

Chapter 4: RIGID BODIES III
\n<\/strong><\/span><\/p>\n

    \n
  1. ROTATION. CIRCULAR MOTION.<\/strong><\/span><\/li>\n
  2. MOMENT OF A FORCE (TORQUE).<\/strong><\/span><\/li>\n
  3. MOMENT ANGULAR CONSERVATION.<\/strong><\/span><\/li>\n<\/ol>\n

    Massachusetts Institute of Technology<\/span><\/strong><\/a> have developed Open Course Wares (OCW)<\/span><\/a> where you can follow a “Classical Mechanics course<\/strong><\/span>” by Internet.<\/p>\n

    One of the most important magnitudes in architecture is the moment of a force<\/strong><\/span> or torque<\/strong><\/span>. And this magnitude will be extremely important in Chapter 5: Equilibrium<\/strong><\/span><\/a>.<\/p>\n

    Linear momentum, i.e. p = <\/strong>m\u00b7v<\/strong>, has a rotational analogue that it is called angular momentum<\/strong>, L<\/strong>. For a symmetrical object rotating about a fixed axis through the centre of mass (CM), the angular momentum is L =<\/strong> I\u00b7\u03c9<\/strong> where I is the moment of inertia and \u03c9<\/strong> is the angular velocity about the axis of rotation. The SI units for L are kg\u00b7m^2\/s<\/strong>, which has no special name.<\/p>\n

    We saw in Chapter 2: Dynamics laws and applications<\/span><\/strong> that Newton’s second law<\/strong> can be written more generally in terms of momentum \u03a3F<\/strong> = \u0394p<\/strong>\/\u0394t. In a similar way, the rotational equivalent of Newton’s second law which is \u03a3\u03c4<\/strong> = I\u00b7\u03b1<\/strong>, can also be written more generally in terms of angular momentum \u03a3\u03c4<\/strong> = \u0394L<\/strong>\/\u0394t where \u03a3\u03c4<\/strong> is the net torque acting to rotate the object and \u0394L<\/strong> is the change in angular momentum in a interval time \u0394t.<\/p>\n

    Angular momentum<\/strong> is an important concept in physics because, under certain conditions<\/strong><\/span>, it is a conserved<\/strong><\/span> quantity. If \u03a3\u03c4<\/strong> = \u0394L<\/strong>\/\u0394t on an object is zero then \u0394L<\/strong> = 0, so L<\/strong> does not change. This is the law of conservation of angular momentum<\/strong><\/span> for a rotating object:<\/p>\n

    The total angular momentum of a rotating object remains constant if the net torque acting on it is zero.<\/strong><\/span><\/p>\n