A uniform rod of mass m and lengh I makes a constant angle `theta` with an axis of rotation which passes through one end of therod. Find the moment of inertia about this axis.

Explanation

Moment of I of uniform rod about an axis passing through one end of the rod is
`I=M/lint_(0)^(l)x^(2)dx`
`=M/l[(x^(3))/3]_(0)^(l)=M/l[(l^(3))/3]`
`=1/3 Ml^(2)`
Since the rod makes a constant angle `theta` with the axis of rotation is
`I=1/3Mr^(2)`
But `r=l sin theta`
MI about the axis
`I=1/3(Ml sin theta)^(2)=1/3Ml^(2)sin^(2) theta`