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If two circular disks of the same weight and thickness are made from metals having different densities, which disk, if either, will have the larger rotational inertia about its symmetry axis?

If two circular disks of the same weight and thickness are made from metals having different densities, which disk, if either, will have the larger rotational inertia about its symmetry axis?

Grade:11

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
The rotational inertia is the distribution of mass around the axis of rotation, therefore even if the objects have same weight they can different rotational inertia. Given that the weight of the disk is equal, the mass of the disks must also be the same for constant acceleration due to gravity. Also, since the disk have different densities, but same mass, the volume in which the mass is contained must be different.
Therefore the disk with larger radius will have a bigger volume as compared to the disk having lower volume. The disk with larger volume will contain mass farther from the axis of rotation relative to the disk with smaller volume. From the definition of rotational inertia, the farther spread of mass about the axis of rotation will increase the rotational inertia of the disk, and therefore the disk with larger volume will have large rotational inertia.

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