# Coefficient of kinetic friction

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## Definition

Given two surfaces, the coefficient of kinetic friction or coefficient of dynamic friction between them is the constant $\mu_k$ such that, for small speeds of slipping of two bodies with these two as the surfaces of contact, the kinetic friction between the two bodies is $\mu_k$ times the normal force between the two bodies.

The coefficient of kinetic friction is usually slightly, but not much, smaller than the limiting coefficient of static friction.

## Units and dimensions

The coefficient of kinetic friction is a dimensionless scalar and does not need units.

## Range of values

First surface Second surface Condition $\mu_s$ $\mu_k$ $\tan^{-1}(\mu_s)$ (radians) $\tan^{-1}( \mu_s)$ (degrees) $\tan^{-1}(\mu_k)$ (radians) $\tan^{-1}(\mu_k)$ (degrees)
Aluminimum Mild steel Dry and clean $0.61$ $0.47$ $0.55$ $31$ $0.44$ $25$
Aluminimum Aluminimum Dry and clean $1.05 - 1.35$ $1.4$ $0.81 - 0.93$ $46 - 53$ $0.95$ $54$
Copper Steel Dry and clean $0.53$ $0.36$ $0.49$ $28$ $0.35$ $20$
Copper Copper Dry and clean $1.0$  ? $0.79$ $45$  ?  ?
Wood Concrete Dry and clean $0.62$  ? $0.55$ $32$  ?  ?
Wood Metal Dry and clean $0.2 - 0.6$  ? $0.2 - 0.54$ $11.3 - 31$  ?  ?
Wood Metal Wet $0.2$  ? $0.2$ $11.3$
Wood Wood Dry and clean $0.25 - 0.5$  ? $0.24 - 0.46$ $14 - 26$  ?  ?
Wood Wood Wet $0.2$  ? $0.2$ $11$  ?  ?
Mild steel Mild steel Dry and clean $0.74$ $0.57$ $0.64$ $37$ $0.52$ $30$
Hard steel Hard steel Dry and clean $0.78$ $0.42$ $0.66$ $38$ $0.40$ $23$

For more, see The Engineer's Handbook and Engineering Toolbox.