Draw a well levelled diagram to show different trajectories depending upon the tan gential projection speed
Answers
Answer:
Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a propeller spinning at a constant rate is executing uniform circular motion. Other examples are the second, minute, and hour hands of a watch. It is remarkable that points on these rotating objects are actually accelerating, although the rotation rate is a constant. To see this, we must analyze the motion in terms of vectors.
Centripetal Acceleration
In one-dimensional kinematics, objects with a constant speed have zero acceleration. However, in two- and three-dimensional kinematics, even if the speed is a constant, a particle can have acceleration if it moves along a curved trajectory such as a circle. In this case the velocity vector is changing, or
d
→
v
/
d
t
≠
0.
This is shown in (Figure). As the particle moves counterclockwise in time
Δ
t
on the circular path, its position vector moves from
→
r
(
t
)
to
→
r
(
t
+
Δ
t
)
.
The velocity vector has constant magnitude and is tangent to the path as it changes from
→
v
(
t
)
to
→
v
(
t
+
Δ
t
)
,
changing its direction only. Since the velocity vector
→
v
(
t
)
is perpendicular to the position vector
→
r
(
t
)
,
the triangles formed by the position vectors and
Δ
→
r
,
and the velocity vectors and
Δ
→
v
are similar. Furthermore, since
|
→
r
(
t
)
|
=
|
→
r
(
t
+
Δ
t
)
|
and
|
→
v
(
t
)
|
=
|
→
v
(
t
+
Δ
t
)
|
,
the two triangles are isosceles. From these facts we can make the assertion
