In 1687 Isaac Newton presented three laws on the motion of a
particle. It is these laws which in his Royal Institution lecture Eric
Laithwaite claimed only applied to motion in straight lines and where
there
is no net acceleration.

Newton's Laws of motion can be stated as:

*First Law:*
A
particle at
rest, or moving in a straight line will remain in this state provided
the particle is not subject to an unbalanced force.

*Second Law:*
A particle acted upon by an unbalanced force F experiences an
acceleration a
that has same direction as the force and a magnitude that is directly
proportional to the force (this can be interpreted as 'F=ma' where m is the
mass of the particle).

Third Law:
The mutual forces of action and reaction between two particles are
equal, opposite and collinear.

## Newton's laws of motion
applied to a body

Newton's Laws are related to the motion of a particle,
however, in the context of gyroscopic
motion such as that demonstrated in Laithwaite's lecture the motion of
whole bodies is dealt with. Any 'body' is a collection of particles,
therefore, by summing over all the particles in a body we can see

how Newton's Laws relate to bodies.

The key result of this
analysis is that 'F=ma' holds for any

rigid body provided
it is applied to the center of mass

## Newton's
laws of motion applied to circular
motion

A gyroscope is essentially a mass that spins at a high rate about its
axis of symmetry, mounted so this axis of rotation can change.
Therefore,
an analysis of a general body can be carried out which takes account of

angular
motion in 3D. The following result is found:

This
is derived from Newton's Second Law and applies to angular motion
of 3-D rigid bodies. This result is used in the repetition and
analysis of

Laithwaite's videos,
and can be seen to hold for all cases. Laithwaite claimed that Newton's
Laws of motion do not hold for circular motion, but there is some other
force acting. This is not the case, Newton's Second Law, which applies
to the motion of a particle can be used to obtain the above formula
which holds for circular motion.