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Conservation of angular momentum (view source)
Revision as of 13:25, July 15, 2016
, 13:25, July 15, 2016→Example: Spelling/Grammar Check, typos fixed: the the → the (2)
:<math>\mathbf{U_f}= \mathbf{KE_i}</math>
:<math>\mathbf{U_f}= \mathbf{KE_i}</math>
Now solve the the two sides of the above equation separately:
Now solve the two sides of the above equation separately:
:<math>\mathbf{U_f}= \mathbf{U_{rod}}+\mathbf{U_{block}}</math>
:<math>\mathbf{U_f}= \mathbf{U_{rod}}+\mathbf{U_{block}}</math>
where ''m'' is the mass at each (perpendicular) distance ''r'' from the axis of rotation.
where ''m'' is the mass at each (perpendicular) distance ''r'' from the axis of rotation.
Thus the the moment of inertia ''I'' for a rod of length ''l'' and mass ''M'', with a small block of mass ''m'' at its end is simply this:
Thus the moment of inertia ''I'' for a rod of length ''l'' and mass ''M'', with a small block of mass ''m'' at its end is simply this:
:<math>\mathbf{I}= \frac{M}{3}\times{l^2} + m\times{l^2}</math>
:<math>\mathbf{I}= \frac{M}{3}\times{l^2} + m\times{l^2}</math>