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

A rod AB of length l is pivoted at an end A and freely rotated in a ho

1.	A rod AB of length l is pivoted at an end A and freely rotated in a horizontal plane at an angular speed co about a vertical axis passing through A.If coefficient of linear expansion of materiol of rod is alpha , find the percenlllge change in its angular velocity if temperature of system is increased by DeltaT.
Answer» Solution :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 AAND 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`%