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Thermodynamics

# An arbitrary shaped object is rotated about any axis of rotation $\;'w_{0} '$ . If the temperature is increased , then the new value of angular speed $\;w^{'}\;$ depends upon -

$(a)\;the\;dimensions\;of\;the\;object\qquad(b)\;the\;position\;of\;the\;axis\;of\;rotation\qquad(c)\;Coefficient\;of\;linear\;expansion\;of\;material\qquad(d)\;All\;of\;these$

Can you answer this question?

Answer : Coefficient of linear expansion of material
Explanation :
Suppose the moment of inertia of object is $\;I_{0}\;$ & linear dimension is $\;'l_{0}'\;$ . Since the angular momentum of the system is conserved
$I_{0}w_{0}=I^{'}w^{'}$
Since $\;I_{0} \alpha l_{0}^2\;$ and $\;l=l_{0}(1+\alpha \bigtriangleup t)$
$\large\frac{I^{'}}{I_{0}}$$=(2 \alpha \bigtriangleup t +1)$
Therefore , $\;w^{'}=\large\frac{w_{0}}{(1+2 \alpha \bigtriangleup t)}$
answered Mar 13, 2014 by
edited Mar 25, 2014