Which has a greater rotational inertia, a cylinder about its axis or a sphere about a diameter if the two have the same mass and radius?
The shape that has the greater rotational inertia out of the cylinder about its axis or a sphere about a diameter if both have same mass and radius.
Answer to Problem 4A
Cylinder
Explanation of Solution
Introduction:
Rotational inertia of a uniformly distributed mass
Where,
As can be seen from above that the rotational inertia of an object is directly proportional to the mass of the object and to the square of its distance from the axis of rotation..
Now, in the cylinder mass is distributed at a larger distance from its axis as compared to the case in sphere.
Conclusion:
Hence, the cylinder has greater rotational inertia about its axis as compared to the sphere about its diameter.
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