therefore, the statement that the object’s velocity is constant is a statement that both
its speed and the direction of its motion are constant.
The first law can be stated mathematically, when the mass is a nonzero constant,
as
F ¼ 0,
dv
dt
¼ 0
where F is the total net force acting on the system and
dv
dt is the time derivative of
velocity. Consequently, an object that is at rest will stay at rest unless a force acts
upon it. An object that is in motion will not change its velocity unless a force acts
upon it. This is known as uniform motion. An object continues to do whatever it
happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a
state of rest (demonstrated when a tablecloth is skillfully whipped from under dishes
on a tabletop and the dishes remain in their initial state of rest), where the inertia of
dishes balances the force exerted by the tablecloth. If an object is moving, it
continues to move without turning or changing its speed. This is evident in space
probes that continuously move in outer space. Changes in motion must be imposed
against the tendency of an object to retain its state of motion. In the absence of net
forces, a moving object tends to move along a straight-line path indefinitely.
Newton placed the first law of motion to establish frame of reference for which
the other laws are applicable. The first law of motion postulates the existence of at
least one frame of reference called a Newtonian or inertial reference frame, relative
to which the motion of a particle not subject to forces is a straight line at a constant
speed (Newton 1999; Anon 2020). Newton’s first law is often referred to as the law
of inertia. Thus, a condition necessary for the uniform motion of a particle relative to
an inertial reference frame is that the total net force acting on it is zero. In this sense,
the first law can be restated as:
“In every material universe, the motion of a particle in a preferential reference frame X is
determined by the action of forces whose total vanished for all times when and only when the
velocity of the particle is constant in X. That is, a particle initially at rest or in uniform
motion in the preferential frame X continues in that state unless compelled by forces to
change it.” [Motte’s 1729 translation]
“Newton’s first and second laws are valid only in an inertial reference frame. Any reference
frame that is in uniform motion with respect to an inertial frame is also an inertial frame,
i.e. Galilean invariance or the principle of Newtonian relativity” (Resnick and Halliday
1977). If someone is kicking a ball on a moving train car, the acceleration the ball will gain
will be with respect to the train not with respect to the ground.
2.1.2 Second Universal Law of Motion
Newton’s original Latin text reads:
2.1 Newton’s Universal Laws of Motion
7
its speed and the direction of its motion are constant.
The first law can be stated mathematically, when the mass is a nonzero constant,
as
F ¼ 0,
dv
dt
¼ 0
where F is the total net force acting on the system and
dv
dt is the time derivative of
velocity. Consequently, an object that is at rest will stay at rest unless a force acts
upon it. An object that is in motion will not change its velocity unless a force acts
upon it. This is known as uniform motion. An object continues to do whatever it
happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a
state of rest (demonstrated when a tablecloth is skillfully whipped from under dishes
on a tabletop and the dishes remain in their initial state of rest), where the inertia of
dishes balances the force exerted by the tablecloth. If an object is moving, it
continues to move without turning or changing its speed. This is evident in space
probes that continuously move in outer space. Changes in motion must be imposed
against the tendency of an object to retain its state of motion. In the absence of net
forces, a moving object tends to move along a straight-line path indefinitely.
Newton placed the first law of motion to establish frame of reference for which
the other laws are applicable. The first law of motion postulates the existence of at
least one frame of reference called a Newtonian or inertial reference frame, relative
to which the motion of a particle not subject to forces is a straight line at a constant
speed (Newton 1999; Anon 2020). Newton’s first law is often referred to as the law
of inertia. Thus, a condition necessary for the uniform motion of a particle relative to
an inertial reference frame is that the total net force acting on it is zero. In this sense,
the first law can be restated as:
“In every material universe, the motion of a particle in a preferential reference frame X is
determined by the action of forces whose total vanished for all times when and only when the
velocity of the particle is constant in X. That is, a particle initially at rest or in uniform
motion in the preferential frame X continues in that state unless compelled by forces to
change it.” [Motte’s 1729 translation]
“Newton’s first and second laws are valid only in an inertial reference frame. Any reference
frame that is in uniform motion with respect to an inertial frame is also an inertial frame,
i.e. Galilean invariance or the principle of Newtonian relativity” (Resnick and Halliday
1977). If someone is kicking a ball on a moving train car, the acceleration the ball will gain
will be with respect to the train not with respect to the ground.
2.1.2 Second Universal Law of Motion
Newton’s original Latin text reads:
2.1 Newton’s Universal Laws of Motion
7