Newton's first law

Newton's first law is also called the law of inertia. It states that if the vector sum of all forces (that is, the net force) acting on an object is zero, then the acceleration of the object is zero and its velocity is constant. Consequently:

• An object that is at rest will stay at rest until an unbalanced force acts upon it.
• An object that is in motion will not change its velocity until an unbalanced force acts upon it.

In the first point, the phrase unbalanced force refers to a set of forces which do not have a zero sum (net force zero) or whose torques about the center of mass of the object do not have a zero sum. Indeed, without the torque requirement, a net force of zero will not accelerate the center of mass of an extended object, but may cause the object to rotate.

The second point seems to violate everyday experience. For example, a hockey puck sliding along ice does not move forever; rather, it slows and eventually comes to a stop. According to Newton's first law, the puck comes to a stop because of a net external force applied in the direction opposite to its motion. This net external force is due to a frictional force between the puck and the ice, as well as a frictional force between the puck and the air. If the ice were frictionless and the puck were traveling in a vacuum, the net external force on the puck would be zero and it would travel with constant velocity so long as its path were unobstructed.

Implicit in the discussion of Newton's first law is the concept of an inertial reference frame, which for the purposes of Newtonian mechanics is defined to be a reference frame in which Newton's first law holds true.

There is a class of frames of reference (called inertial frames) relative to which the motion of a particle not subject to forces is a straight line.^[10]

Newton placed the law of inertia first to establish frames of reference for which the other laws are applicable.^[10][11] To understand why the laws are restricted to inertial frames, consider a ball at rest inside an airplane on a runway. From the perspective of an observer within the airplane (that is, from the airplane's frame of reference) the ball will appear to move backward as the plane accelerates forward. This motion appears to contradict Newton's second law (F = ma), since, from the point of view of the passengers, there appears to be no force acting on the ball that would cause it to move. However, Newton's first law does not apply: the stationary ball does not remain stationary in the absence of external force. Thus the reference frame of the airplane is not inertial, and Newton's second law does not hold in the form F = ma.