Download Newton`s Laws

Newton’s Laws
Newton I:
A moving object will continue to move with constant velocity, until acted upon by an
external force. If at rest an object will remain at rest until an external force is applied.
→ this is an extension of Galileo’s Law of Inertia.
You should remember that this applies to both linear forces: those in straight lines, and to
the rotational equivalents like torque.
Newton II:
The rate of change of momentum of an object is equal to the external force acting
upon it:
When the mass of the object is constant,
, and we have:
Newton III:
At a point of contact between two bodies the action and reaction are equal and
opposite:
where
the force on the ith body from the jth body:
Conservation Laws
There are two laws we will use in mechanics that you should be familiar with: the
conservation of momentum, and the conservation of energy.
Strictly when we say the conservation of momentum, we mean the conservation of linear
momentum (
), the momentum in straight lines. Angular momentum (
) is also
conserved, but separately from linear momentum. These laws are empirical: they are
relationships we have seen in experiments always to be the case. For example, for a
system involving bodies, labelled
The total momentum before an event must equal the total momentum after the event for an
isolated system.
where the
and
refer to initial and final states respectively.
The law of conservation of energy is also an empirical law. It states that energy may be
converted into different forms, but that overall the total of all the forms of energy in a closed
system must be constant. For example, for a ball that is repeatedly thrown up and caught, its
kinetic energy and gravitational potential energy is transferred from one form to another all
the time, but the SUM is constant:
These two laws are some of the most useful tools we have for solving problems in
mechanics, and in wide areas of physics in general.
Newton’s Laws and the Conservation Laws are useful tools. When dealing with things that
are moving the equations can become quite complicated and so we sometimes also use
what is called a Galilean Transformation, which is introduced on the Kinematics page.