(UCM)

motion along a circular path at constant speed.
Characteristic of UCM
1.
The speed is constant.
2.
The direction of motion is continually or uniformly changing.
3.
A constant in magnitude acceleration is present.
This acceleration is always directed at the center
of the circular path and is known as radial acceleration or centripetal central acceleration.
Mathematically;
r
v
A
cp
2
=
Where
cp
A
= centripetal acceleration
v
= tangential velocity
r
= radius of the circle
Principle of circle
Relationship between s, r,
θ
↑↓
↑↓
θ
s
α
s
r
s
=
Linear quantities
s
= linear displacement (cm, m)
v
= linear velocity (cm/s, m/s)
a
= linear acceleration (cm/s
2
, m/s
2
)
Angular quantities
= angular displacement (rad)
ϖ
= angular velocity (rad/s)
= angular acceleration (rad/s
2
)
Relationship between
v
and
(
29
t
r
s
1
=
(s = r
θ
) /t
r
Consider a moving body along a circular path with angular displacement of very very small rads or
θ
approaches 0.
1
st
characteristics
1
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 Spring '11
 darp
 Acceleration, Circular Motion, Force, Velocity, circular path

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