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The linear density (lamda) of a thin rod varies with position x as (lamda)=lamda0(x^3/L^3). The rod...

The linear density (lamda) of a thin rod varies with position x as (lamda)=lamda0(x^3/L^3). The rod lies along the X axis. If M is the mass of the rod and L is the total length, then,

a) Find lamda0 in terms of M and L

b)Find the position of the centre of mass

c)Find the moment of inertia around the centre of mass.

d) Now imagine the same thin rod is attached to a hinge that is allowed to rotate. The rod is initially held at a position where it makes an angle (theta) above the horizontal. Assuming that it is released from rest, find the magnitude of the rod's angular momentum around the hinge at the instant it is completely horizontal.

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