Sir Isaac Newton first presented his three
laws of motion
in the "Principia Mathematica Philosophiae Naturalis"
in 1686. His first law states that every object will remain at rest
or in uniform motion in a straight line unless compelled to change
its state by the action of an external force.
When an external force F is applied,
the object is
in the direction
of the force with a magnitude directly proportional to the force and inversely
proportional to the mass m of the object. This is a restatement of Newton's
second law of motion:
a = F / m
On this page we show two examples of the motion of an object which is
subjected to a single external side force.
In both cases, we are viewing the motion from above. An object, represented
by a black circle, enters the domain from the bottom while moving
at a constant initial velocity V.
The small black circles
represent the position of the object as time passes; the red
line is the path, or trajectory, of the object's motion.
There is initially
no external force acting on the object, so in keeping with Newton's
the object moves upward at a constant velocity. The object is then
subjected to a side force F.
Trajectory A - Instantaneous Force
On the left side of the figure, the force F
is directed to the right of the path
and is instantaneously applied to the object.
This type of force application occurs if the object experiences
a collision with another object moving to the right.
In response to Newton's second law,
the object receives an instantaneous acceleration to the right;
the velocity to the right
is changed from zero to some new value.
Remember that forces, accelerations, and velocities are
having both a magnitude and a direction and that the acceleration of an
object in response to an external force is in the direction of the force.
Since the force is instantly removed, the object
continues in a straight line motion as described by the first law. The
object now has an additional
of velocity (to the right) which
remains until some future external force acts on the object.
Trajectory B - Continuous Force
On the right side of the figure, the force F is directed to the right of the path
and is continuously applied to the object.
This type of force application occurs if the object is subjected to an
side force which is perpendicular to the flight direction, such as the
banking turn of an aircraft, or a thrown,
If the force remains constant, and is applied perpendicular to the motion,
the resulting path is a circular arc. The radius of the circle is called
the radius of curvature - R and it depends on the relative magnitude
of the velocity V and the acceleration a generated by the side force.
R = V ^2 / a
When the force is removed
(banked aircraft brought to wings level)
the object continues in a straight line motion as described by the first law.
A continuous force applied perpendicular to the motion is called a
centralized force since it produces a circular motion about some
Forces, Torques and Motion:
- Beginner's Guide Home Page