Summary and Main Ideas

Summary

• Acceleration, \(\mathbf{\text{a}}\), is defined as a change in velocity, meaning a change in its magnitude or direction, or both.
• An external force is one acting on a system from outside the system, as opposed to internal forces, which act between components within the system.
• Newton’s second law of motion states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass.
• In equation form, Newton’s second law of motion is \(\mathbf{\text{a}}=\frac{{\mathbf{\text{F}}}_{\text{net}}}{m}\).
• This is often written in the more familiar form: \({\mathbf{\text{F}}}_{\text{net}}=m\mathbf{\text{a}}\).
• The weight \(\mathbf{\text{w}}\) of an object is defined as the force of gravity acting on an object of mass \(m\). The object experiences an acceleration due to gravity \(\mathbf{\text{g}}\):
  \(\mathbf{\text{w}}=m\mathbf{\text{g}}.\)
• If the only force acting on an object is due to gravity, the object is in free fall.
• Friction is a force that opposes the motion past each other of objects that are touching.

Glossary

acceleration

the rate at which an object’s velocity changes over a period of time

free-fall

a situation in which the only force acting on an object is the force due to gravity

friction

a force past each other of objects that are touching; examples include rough surfaces and air resistance

net external force

the vector sum of all external forces acting on an object or system; causes a mass to accelerate

Newton’s second law of motion

the net external force \({\mathbf{\text{F}}}_{\text{net}}\) on an object with mass \(m\) is proportional to and in the same direction as the acceleration of the object, \(\mathbf{\text{a}}\), and inversely proportional to the mass; defined mathematically as \(\mathbf{\text{a}}=\frac{{\mathbf{\text{F}}}_{\text{net}}}{m}\)

system

defined by the boundaries of an object or collection of objects being observed; all forces originating from outside of the system are considered external forces

weight

the force \(\mathbf{\text{w}}\)due to gravity acting on an object of mass \(m\); defined mathematically as: \(\mathbf{\text{w}}=m\mathbf{\text{g}}\), where \(\mathbf{\text{g}}\) is the magnitude and direction of the acceleration due to gravity