Question

A non uniform rod OA of linear mass density lamda= lamda x is suspended from ceiling with hinge joint O & light string as shown. Find the angular acceleration of rod just after the string is cut?

Answer 1

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linear mass density of the rod is given by

now we have

integrate both sides

so above is the total mass of rod

now by the formula of center of mass

now plug in value of mass of rod

so above is the position of center of mass of rod.