Question

The Parallel-Axis Theorem allows one to find the moment of inertia of an object if the moment of inertia through the center of mass (c.o.m.) is known and the second axis is parallel to the axis through the c.o.m.. The equation is given by I= I_com +md², where I_com is the moment of inertia about an axis through the c.o.m., m is the mass of the object, d is the perpendicular distance from the axis through the c.o.m. to the new axis which is parallel to the first, and I is the new moment of inertia.

(a) Starting with a thin rod of mass m and length l, and the moment of inertia through the c.o.m. and perpendicular to the length of the rod is (1/12)ml², use the parallel-axis theorem to solve for I for an axis parallel to the first but passing through the end of the rod.

(b) The moment of inertia of a planet revolving around a star is treated like a point mass. Using the parallel-axis theorem show that this is a reasonable technique.

Explain the concepts and fundamental equations used.

Answer 1