Dynamics Lecture 23: Rigid body planar motion -- Translation

- [Instructor] With this
video, we start the study

of rigid body planar kinematics.

By kinematics, if you
recall, we mean that for now,

we only focus on the
geometric aspects of motion.

Rigid body motion by nature

is more complicated than particle motion

because it involves not only translation,

but rotation as well.

For now, we only focus
on plainer motion instead

of a three-dimensional motion,

which means that during motion,

the path of any given
particle in this rigid body

is limited in a plane,

and these planes are
parallel to each other.

And also, each plane is always parallel

to a fixed plane,

and it remains at the same
distance to this fixed plane.

There are three types of
rigid body plane motion:

translation, rotation about a fixed axis,

and lastly, the general plane motion,

which is simply when the rigid body

is undergoing both translation
and rotation simultaneously.

During translation, the path
could be a straight line,

which is called rectilinear translation,

or the path could be a curve,

and this is known as
curvilinear translation.

Either way, during translation,

for any two points on this rigid body,

their paths are identical.

Now let's analyze translation
using relative motion.

Let's say there are two arbitrary
points on this rigid body,

point A and point B.

Initially, there's a fixed
X, Y, Z coordinate system

with the origin at point A.

Then we define another X prime, Y prime,

Z prime rectangular coordinate system

that will always have
the origin at point A

and will translate with point A.

Therefore, at any given
time during motion,

vector rA represents the absolute position

of point A measured from a fixed origin.

rB represents the absolute
position of point B.

And rBA represents the relative position

of point B relative to point
A, and we already learned

that this relative position
equals to rB minus rA.

During translation,

this relative position
vector remains the same.

Its time derivative is zero,
which means that the position

of point B is always the
same relative to point A,

and the relative velocity
of point B is also zero.

The relative acceleration
of point B is also zero.

This means that for any
two arbitrary points

on the rigid body undergoing
translation, the two points

will always have the same
velocity and acceleration.

You can also say that during translation,

all the particles in the
rigid body will always move

at the same velocity, same
acceleration at all time.