A rod AB of length l is pivoted at an end A and freely rotated in a horizontal plane at an angular speed `omega` about a vertical axis passing through A. If coefficient of linear expansion of material of rod is `alpha`, find the percentage change in its angular velocity if temperature of system is increased by `DeltaT`.

Explanation

If temperature of surrounding increases by `DeltaT`, the new length of rod becomes l. = `l(1+alphaDeltaT)`
Due to change in length, moment of inertia of rod also changes and moment of inertia about an end A and is given as `I_(A).=(Ml^(2))/3`
As no external force or torque is acting on rod, its angular momentum remains constant during heating.
Thus we have `I_(A)omega=I_(A).omega.` [where omega. is the final angular velocity of rod after heating]
or `(Ml^(2))/3omega=(Ml^(2)(1+alphaDeltaT)^(2))/3omega.`
or `omega.=omega(1-2alphaDeltaT)`
[using binomial expansion for small `alpha`]
Thus percentage change in angular velocity of rod due to heating can be given as
`Deltaomega=(omega-omega)/omegaxx100%=-2alphaDeltaTxx100%`