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)
Practice Questions
1 question
Q1
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)
Solid cylinder
Hollow cylinder
Both reach at the same time
Depends on the angle of incline
The solid cylinder has a smaller moment of inertia compared to the hollow cylinder, thus it accelerates faster and reaches the bottom first.
Questions & Step-by-step Solutions
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Q
Q: 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)
Solution: The solid cylinder has a smaller moment of inertia compared to the hollow cylinder, thus it accelerates faster and reaches the bottom first.
Steps: 5
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.
