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 iricreases by `Delta T,` the new length of rod becomes l. = l `(1 + alpha Delta T)`
Due .io 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))/(3) omega = (Ml^(2) (1 + alpha Delta T )^(2))/( 3 ) omega . `
or `omega. = omega (1 - 2 alpha Delta T )`
[u sing binomial expansion for small `alpha` ]
Thus percentage change in angular velocity of rod due to heating can be given as `
Delta omega = (omega - omega )/(omega) xx 100% = - 2 alpha Delta T xx 100`%