- Friction is a contact force between systems that opposes the motion or attempted motion between them. Simple friction is proportional to the normal force pushing the systems together. (A normal force is always perpendicular to the contact surface between systems.) Friction depends on both of the materials involved. The magnitude of static friction between systems stationary relative to one another is given by where is the coefficient of static friction, which depends on both of the materials.
- The kinetic friction force between systems moving relative to one another is given by
- Drag forces acting on an object moving in a fluid oppose the motion. For larger objects (such as a baseball) moving at a velocity in air, the drag force is given by where is the drag coefficient (typical values are given in Table 5.2), is the area of the object facing the fluid, and is the fluid density.
- For small objects (such as a bacterium) moving in a denser medium (such as water), the drag force is given by Stokes' law, where is the radius of the object, is the fluid viscosity, and is the object's velocity.
- Hooke's law is given by
where is the amount of deformation (the change in length), is the applied force, and is a proportionality constant that depends on the shape and composition of the object and the direction of the force. The relationship between the deformation and the applied force can also be written as
where is Young's modulus, which depends on the substance, is the cross-sectional area, and is the original length.
- The ratio of force to area, , is defined as stress, measured in N/m2.
- The ratio of the change in length to length, , is defined as strain (a unitless quantity). In other words,
- The expression for shear deformation is
where is the shear modulus and is the force applied perpendicular to and parallel to the cross-sectional area .
- The relationship of the change in volume to other physical quantities is given by
where is the bulk modulus, is the original volume, and is the force per unit area applied uniformly inward on all surfaces.