A disk and a ring of the same mass and radius are rolling without slipping. Whic

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Question: A disk and a ring of the same mass and radius are rolling without slipping. Which one will reach the bottom of an incline first?

Options:

Correct Answer: Disk

Solution:

The disk will reach the bottom first because it has a smaller moment of inertia compared to the ring.

A disk and a ring of the same mass and radius are rolling without slipping. Which one will reach the bottom of an incline first?

A disk and a ring of the same mass and radius are rolling without slipping. Which one will reach the bottom of an incline first?

Step 1: Understand that both the disk and the ring have the same mass and radius.
Step 2: Know that when objects roll down an incline, they convert potential energy into kinetic energy.
Step 3: Recognize that kinetic energy has two parts: translational (moving forward) and rotational (spinning).
Step 4: Learn about moment of inertia, which is a measure of how mass is distributed in an object. A smaller moment of inertia means the object can spin more easily.
Step 5: The disk has a smaller moment of inertia compared to the ring, meaning it can convert more of its potential energy into translational kinetic energy.
Step 6: Since the disk can move forward faster than the ring, it will reach the bottom of the incline first.

Moment of Inertia – The distribution of mass in an object affects its rotational motion; a lower moment of inertia allows for faster acceleration down an incline.
Rolling Motion – Objects rolling without slipping convert potential energy into both translational and rotational kinetic energy.
Energy Conservation – The total mechanical energy (potential + kinetic) is conserved, influencing how quickly objects reach the bottom of an incline.