Acceleration of rolling body on incline (a = g sinθ/(1 + k²/R²))
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a = g sinθ/(1 + k²/R²)
What each symbol means
| Symbol | What it stands for |
|---|---|
| R | Radius of the rolling body (m) |
| a | Linear acceleration down the incline (m/s²) |
| g | Acceleration due to gravity (m/s²) |
| k | Radius of gyration of the body (m) |
| θ | Angle of incline with horizontal |
When to use this
Pure rolling (no slipping). k²/R² values: solid sphere = 2/5, hollow sphere = 2/3, solid cylinder/disc = 1/2, hollow cylinder/ring = 1. Larger k²/R² → slower acceleration. Time to reach bottom ∝ √(1+k²/R²).