Equations · equation
Rolling Resistance
Mechanics · 1781
- Equation
- d = v₀² / (2 μ_r g)
- Field
- Mechanics
- Year
- 1781
Symbols
d the distance a rolling ball travels before stopping · v₀ its starting speed · μ_r rolling resistance coefficient — 0.025 on worsted cloth, the figure the shot lab runs on, and 0.002 for a steel wheel on rail · g gravitational acceleration
Significance
A rolling body loses energy slowly, to the deformation of the surface and of the ball, and the deceleration is nearly constant at μ_r g. On a pool table that is about a quarter of a metre per second per second, so a ball at 1 m/s rolls a little over two metres and speed control is a matter of a few percent. Coulomb measured rolling friction in 1781; the work–energy theorem does the rest.
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