A disk and a ring of the same mass and radius are released from rest at the same

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Question: A disk and a ring of the same mass and radius are released from rest at the same height. Which one reaches the ground first?

Options:

Correct Answer: Disk

Solution:

The disk has a lower moment of inertia compared to the ring, thus it reaches the ground first.

A disk and a ring of the same mass and radius are released from rest at the same height. Which one reaches the ground first?

A disk and a ring of the same mass and radius are released from rest at the same height. Which one reaches the ground first?

Step 1: Understand that both the disk and the ring have the same mass and radius.
Step 2: Know that when they are released from the same height, they will both start to fall due to gravity.
Step 3: Learn about moment of inertia, which is a measure of how difficult it is to change the rotation of an object.
Step 4: Realize that the disk has a lower moment of inertia compared to the ring, meaning it can rotate more easily.
Step 5: Understand that because the disk rotates more easily, it will convert more of its potential energy into kinetic energy as it falls.
Step 6: Conclude that the disk will reach the ground before the ring because it has a lower moment of inertia.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation. The disk has a lower moment of inertia than the ring, which affects how quickly it can accelerate when rolling.
Rolling Motion – When objects roll down an incline, both translational and rotational motion must be considered. The distribution of mass affects the acceleration of the object.
Energy Conservation – The total mechanical energy (potential + kinetic) is conserved. The way this energy is converted into translational and rotational kinetic energy differs between the disk and the ring.