A solid cylinder and a hollow cylinder of the same mass and radius are rolling d

A solid cylinder and a hollow cylinder of the same mass and radius are rolling down an incline. Which one reaches the bottom first? (2023)

A solid cylinder and a hollow cylinder of the same mass and radius are rolling down an incline. Which one reaches the bottom first? (2023)

Step 1: Understand that both cylinders have the same mass and radius.
Step 2: Know that when objects roll down an incline, they have both translational (moving down) and rotational (spinning) motion.
Step 3: Learn about moment of inertia, which is a measure of how difficult it is to change an object's rotation. A solid cylinder has a smaller moment of inertia than a hollow cylinder.
Step 4: Realize that a smaller moment of inertia means the solid cylinder can convert more of its potential energy into translational kinetic energy (moving down) rather than rotational kinetic energy (spinning).
Step 5: Conclude that since the solid cylinder accelerates faster due to its smaller moment of inertia, it will reach the bottom of the incline before the hollow cylinder.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation. A solid cylinder has a lower moment of inertia compared to a hollow cylinder of the same mass and radius.
Rolling Motion – Rolling motion involves both translational and rotational motion. The acceleration of rolling objects depends on their moment of inertia.
Acceleration on Incline – The acceleration of an object rolling down an incline is influenced by its moment of inertia, affecting how quickly it reaches the bottom.