Curvilinear
Motion: Introduction
In the last few lessons, we studied Rectilinear (Straight Line) motion, where the key feature was that the acceleration is always collinear with the velocity.
Today, and in the next few classes, we will investigate Curvilinear Motion.
Key Features of Curvilinear Motion (refer to the picture above):
1.
Velocity,
v,
is always tangent to the path. See
velocities
, v1,
v2,
and v3 in the figure above. Notice
that the lengths (speed) of these velocity vectors vary
( v3 >
v2
> v1
)due to the tangential acceleration.
2.
In general, the total
acceleration a
is not
tangent to the path; it acts
toward the concave side.
3.
The tangential
acceleration,
at,
like velocity, always acts tangent to the curve.
It changes the length of the velocity vector.
It may act in the opposite direction of v,
slowing the particle along the path (as it does at position 3), or in the
direction of
v, increasing the
particle’s speed along the path (in positions 1 and 2).
4.
The normal
acceleration,
an,
always acts toward the concave side of the path.
Normal acceleration changes the direction of the velocity vector.