Part of a series on
Classical mechanics
${\displaystyle {\textbf {F))={\frac {d}{dt))(m{\textbf {v)))}$ Second law of motion
History Timeline Textbooks
Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical mechanics
Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Koopman–von Neumann mechanics
Core topics Damping Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational frequency Angular acceleration / displacement / frequency / velocity
Scientists Kepler Galileo Huygens Newton Horrocks Halley Maupertuis Daniel Bernoulli Johann Bernoulli Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Cauchy Routh Liouville Appell Gibbs Koopman von Neumann
Physics portal  Category
v t e

Sliding is a type of motion between two surfaces in contact. This can be contrasted to rolling motion. Both types of motion may occur in bearings.

The relative motion or tendency toward such motion between two surfaces is resisted by friction. Friction may damage or "wear" the surfaces in contact. However, wear can be reduced by lubrication. The science and technology of friction, lubrication, and wear is known as tribology.

Sliding may occur between two objects of arbitrary shape, whereas rolling friction is the frictional force associated with the rotational movement of a somewhat disclike or other circular object along a surface. Generally, the frictional force of rolling friction is less than that associated with sliding kinetic friction.^[1] Typical values for the coefficient of rolling friction are less than that of sliding friction.^[2] Correspondingly sliding friction typically produces greater sound and thermal bi-products. One of the most common examples of sliding friction is the movement of braking motor vehicle tires on a roadway, a process which generates considerable heat and sound, and is typically taken into account in assessing the magnitude of roadway noise pollution.^[3]

Sliding friction

Sliding friction (also called kinetic friction) is a contact force that resists the sliding motion of two objects or an object and a surface. Sliding friction is almost always less than that of static friction; this is why it is easier to move an object once it starts moving rather than to get the object to begin moving from a rest position.

${\displaystyle F_{k}=\mu _{k}\cdot N}$

Where F_k, is the force of kinetic friction. μ_k is the coefficient of kinetic friction, and N is the normal force.

Examples of sliding friction

• Sledding
• Pushing an object across a surface
• Rubbing one's hands together (The friction force generates heat.)
• A car sliding on ice
• A car skidding as it turns a corner
• Opening a window
• Almost any motion where there is contact between an object and a surface
• Falling down a bowling lane

Motion of sliding friction

The motion of sliding friction can be modelled (in simple systems of motion) by Newton's Second Law

${\displaystyle \sum F=ma}$

${\displaystyle F_{E}-F_{k}=ma}$

Where ${\displaystyle F_{E))$ is the external force.

• Acceleration occurs when the external force is greater than the force of kinetic friction.
• Slowing Down (or Stopping) occurs when the force of kinetic friction is greater than that of the external force.
  • This also follows Newton's first law of motion as there exists a net force on the object.
• Constant Velocity occurs when there is no net force on the object, that is the external force is equal to force of kinetic friction.

Motion on an planed plane

A common problem presented in introductory physics classes is a block subject to friction as it slides up or down an inclined plane. This is shown in the free body diagram to the right.

The component of the force of gravity in the direction of the incline is given by:^[4]

${\displaystyle F_{g}=mg\sin {\theta ))$

The normal force (perpendicular to the surface) is given by:

${\displaystyle N=mg\cos {\theta ))$

Therefore, since the force of friction opposes the motion of the block,

${\displaystyle F_{k}=\mu _{k}\cdot mg\cos {\theta ))$

To find the coefficient of kinetic friction on an inclined plane, one must find the moment where the force parallel to the plane is equal to the force perpendicular; this occurs when the block is moving at a constant velocity at some angle ${\displaystyle \theta }$

${\displaystyle \sum F=ma=0}$

${\displaystyle F_{k}=F_{g))$ or ${\displaystyle \mu _{k}mg\cos {\theta }=mg\sin {\theta ))$

Here it is found that:

${\displaystyle \mu _{k}={\frac {mg\sin {\theta )){mg\cos {\theta ))}=\tan {\theta ))$ where ${\displaystyle \theta }$ is the angle at which the block begins moving at a constant velocity^[5]