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Find the moment of inertia of the rod AB...


Find the moment of inertia of the rod AB about an axis yy as shown in figure. Mass of the rod is m and length is l.

Text Solution

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Consider a small element `dx` of the rod which is at a distance `x` from the end `P` if `theta` is the inclination of rod w.r.t the axis of rotation, the radius of the circle in which the element rotates is given by `sin theta=r/xrArrr=x sin theta`

`M.I.` of the element about the axis of rotation is `dI=dm.r^(2)`
where `dm `is the mass of element `dm =m/L dx`
`dI=m/Ldx(x sin theta)^(2).` Total `M.I.` of the rod is given by `I=int dI=int_(0)^(L)m/Lsin^(2) thetax^(2)dx, I=(mL^(2))/3 sin^(2) theta`
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