By the theorem of parallel axes:

State the conditions under which the theorem of parallel axes and perpendicular axes are applicable. State the mathematical expression .

According to the theorem of parallel axes I = I_("cm") + Mx^(2) , the graph between I and x will be

According to the theorem of parallel axes I = I_("cm") + Mx^(2) , the graph between I and x will be

Define the theorem of parallel axes and apply it to find the moment of inertia of a uniform rod about an axis passing through one of its ends and perpendicular to its length.

(a) Prove the theorem of perpendicular axes. (Hint : Square of the distance of a point (x, y) in the x-y plane from an axis through the origin perpendicular to the plane is x^(2)+y^(2) ). (b) Prove the theorem of parallel axes. (Hint : If the centre of mass is chosen to be the origin Sigmam_(1)(r_(i)=0) .

(a) Prove the theorem of perpendicular axes. (Hint : Square of the distance of a point (x, y) in the x-y plane from an axis through the origin and perpendicular to the plane is ^(x2)+y^(2)) . (b) Prove the theorem of parallel axes. (Hint : If the centre of mass of a system of n particles is chosen to be the origin summ_(i)r_(i)=0 ).

Prove the theorem of parallel axes.