Question

The moment of inertia of a long rod spun around an axis through one end perpendicular to its length is mL^(2/3). Why is this moment of inertia greater than it would be if you spun a point mass m at the location of the center of mass of the rod (at L/2) (that would be mL^(2/4))?

a) The rod has more mass concentrated at the end.
b) The rod has less mass concentrated at the end.
c) The rod's mass distribution affects its moment of inertia.
d) It depends on the length of the rod.

Answer 1

The moment of inertia of a long rod spun around an axis through one end perpendicular to its length is greater than it would be if you spun a point mass at the location of the center of mass of the rod, due to the rod's mass distribution.

Step-by-step explanation:

The moment of inertia of a long rod spun around an axis through one end perpendicular to its length is given by the formula mL2/3. This moment of inertia is greater than it would be if you spun a point mass at the location of the center of mass of the rod, which would be mL2/4. The reason for this is that the rod's mass distribution affects its moment of inertia.