Summary and Main Ideas

Summary

• When objects rest on a surface, the surface applies a force to the object that supports the weight of the object. This supporting force acts perpendicular to and away from the surface. It is called a normal force, \(\mathbf{\text{N}}\).
• When objects rest on a non-accelerating horizontal surface, the magnitude of the normal force is equal to the weight of the object:
  \(N=\text{mg}.\)
• When objects rest on an inclined plane that makes an angle \(\theta \) with the horizontal surface, the weight of the object can be resolved into components that act perpendicular (\({\mathbf{\text{w}}}_{\perp }\)) and parallel (\({\mathbf{\text{w}}}_{\parallel }\)) to the surface of the plane. These components can be calculated using:
  \({w}_{\parallel }=w\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\left(\theta \right)=\text{mg}\phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\left(\theta \right)\)
  \({w}_{\perp }=w\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\left(\theta \right)=\text{mg}\phantom{\rule{0.25em}{0ex}}\text{cos}\phantom{\rule{0.25em}{0ex}}\left(\theta \right).\)
• The pulling force that acts along a stretched flexible connector, such as a rope or cable, is called tension, \(\mathbf{\text{T}}\). When a rope supports the weight of an object that is at rest, the tension in the rope is equal to the weight of the object:
  \(T=\text{mg}.\)
• In any inertial frame of reference (one that is not accelerated or rotated), Newton’s laws have the simple forms given in this tutorial and all forces are real forces having a physical origin.

Glossary

inertial frame of reference

a coordinate system that is not accelerating; all forces acting in an inertial frame of reference are real forces, as opposed to fictitious forces that are observed due to an accelerating frame of reference

normal force

the force that a surface applies to an object to support the weight of the object; acts perpendicular to the surface on which the object rests

tension

the pulling force that acts along a medium, especially a stretched flexible connector, such as a rope or cable; when a rope supports the weight of an object, the force on the object due to the rope is called a tension force