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Friction: Static, Kinetic and Rolling

Classical Mechanics

Friction is the force that opposes motion whenever two surfaces slide or try to slide over each other. It is why you can walk without slipping, why cars can brake, and also why machines wear out and waste energy as heat. Understanding the different kinds of friction, and the simple formula that describes them, explains a surprising amount of everyday physics.

What friction is

Friction arises from the tiny roughness of surfaces: even a surface that looks smooth has microscopic bumps that catch on each other. When two surfaces press together, these bumps interlock and resist sliding. Friction always acts parallel to the surfaces and in the direction opposite to the motion, or opposite to the attempted motion. It depends on how hard the surfaces are pressed together and on the nature of the surfaces, rubber on dry asphalt grips far more than ice on steel, but, for most school problems, it does not depend on the area of contact.

Static, kinetic and rolling friction

Static friction acts when surfaces are not moving relative to each other. It adjusts itself to match the applied force, up to a maximum value, which is why a heavy box stays put until you push hard enough. Once the box starts moving, kinetic friction takes over; it is usually smaller than maximum static friction and roughly constant, which is why a box is easier to keep moving than to start. Rolling friction, for a wheel or ball rolling on a surface, is much smaller still, which is why wheels, ball bearings and rollers are used to move heavy loads.

The friction formula

The size of friction is described by **F = μ N**, where N is the normal force pressing the surfaces together and μ (mu) is the **coefficient of friction**, a number that depends on the two materials. For maximum static friction, μ is the static coefficient μ_s; for sliding, it is the kinetic coefficient μ_k, usually smaller. On a flat surface, N equals the weight mg, so a heavier object has more friction. This formula explains why a car needs more braking force when fully loaded, and why wet or icy roads, with a much smaller μ, make stopping distances far longer.

Common mistakes

• Thinking friction always slows things down. Correction: friction can also drive motion, it is what lets your shoes push backward on the ground so you can walk forward.
• Using weight instead of the normal force on a slope. Correction: on a slope, N = mg cos θ, which is less than the weight, so friction is smaller too.
• Assuming a bigger contact area means more friction. Correction: for most dry surfaces, friction depends on the normal force and the materials, not on the contact area.

Practice questions

1. A 20 kg box sits on a flat floor with μ_s = 0.5. What push is needed to start it moving? Use g = 9.81 m/s².
   Show answer

   N = 20 x 9.81 = 196.2 N. Maximum static friction = 0.5 x 196.2 = 98.1 N, so a push just over 98.1 N is needed.

2. Why is it easier to keep a box sliding than to start it sliding?
   Show answer

   Kinetic friction is usually smaller than maximum static friction, so less force is needed once motion has started.

3. Why do car tyres have treads?
   Show answer

   Treads increase grip by channelling water away and biting into the road surface, keeping the coefficient of friction high, especially in the wet.

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