A disk and a ring of the same mass and radius are rolling down an incline. Which one will have a greater translational speed at the bottom?

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Q: A disk and a ring of the same mass and radius are rolling down an incline. Which one will have a greater translational speed at the bottom?

Solution: The disk has a lower moment of inertia than the ring, allowing it to convert more potential energy into translational kinetic energy.

Steps: 6

Step 1: Understand that both the disk and the ring have the same mass and radius.
Step 2: Know that when they roll down the incline, they convert potential energy into kinetic energy.
Step 3: Recognize that kinetic energy has two parts: translational kinetic energy (movement) and rotational kinetic energy (spinning).
Step 4: Learn about moment of inertia, which is a measure of how difficult it is to change the rotation of an object. The disk has a lower moment of inertia than the ring.
Step 5: Since the disk has a lower moment of inertia, it can convert more of its potential energy into translational kinetic energy compared to the ring.
Step 6: Conclude that the disk will have a greater translational speed at the bottom of the incline than the ring.