# The parallel axis theorem

The parallel axis theorem relates Icm, the moment of inertia ofan object about an axis passing through its center of mass, to Ip,the moment of inertia of the same object about a parallel axispassing through point p. The mathematical statement of the theoremis Ip=Icm+Md2, where d is the perpendicular distance from thecenter of mass to the axis that passes through point p, and M isthe mass of the object. Part A Suppose a uniform slender rod haslength L and mass m. The moment of inertia of the rod about aboutan axis that is perpendicular to the rod and that passes throughits center of mass is given by Icm=112mL2. Find Iend, the moment ofinertia of the rod with respect to a parallel axis through one endof the rod. Express Iend in terms of m and L. Use fractions ratherthan decimal numbers in your answer. Part B Now consider a cube ofmass m with edges of length a. The moment of inertia Icm of thecube about an axis through its center of mass and perpendicular toone of its faces is given by Icm=16ma2. (Figure 1) Find Iedge, themoment of inertia about an axis p through one of the edges of thecube Express Iedge in terms of m and a. Use fractions rather thandecimal numbers in your answer.

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