A solid cylinder and a thin-walled hollow cylinder of identical mass and radius roll down an inclined plane from rest without slipping. Which reaches the bottom first?
Answer and explanation
Correct answer: D. The solid cylinder, because it has a smaller moment of inertia
- Step 1: Acceleration down an incline: a = g sin(theta) / (1 + I / (mr^2)). Step 2. For a solid cylinder, I = (1/2) m r^2, so a = (2/3) g sin(theta) = 0.67 g sin(theta). Step 3. For a hollow cylinder, I = m r^2, so a = (1/2) g sin(theta) = 0.50 g sin(theta). Step 4. The solid cylinder has greater linear acceleration and reaches the bottom first. Answer: The solid cylinder, because it has a smaller moment of inertia. Why not the others:* Greater moment of inertia diverts more energy into rotation, slowing linear descent.
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