[<< wikibooks] Physics Course/Motion/Periodic Motion/Circular Motion
== Circular Motion ==

Circular Motion is a motion of an object along a circular path. If the speed of the body remains constant throughout the motion, the object is said to perform a uniform circular motion.
For an object in uniform circular motion along a circular path of radius R and

r
→

{\displaystyle {\vec {r}}}
be the position vector of the object with the center of the path as the and

r
^

{\displaystyle {\hat {r}}}
being the unit vector along it and T be the time taken to traverse the path once (period), the total linear distance covered in one period is (the circumference of the circle)

s
=
2
π
R

{\displaystyle s=2\pi R}
The speed (or linear velocity) is then given by

v
=

s
T

=

2
π
R

T

=
2
π
f
R

…

(

f
=

1
T

=

frequency

)

The linear velocity is a vector quantity whose direction at any given instance is tangential to the circle at that point.
The angular velocity around the circle is

ω
→

=

r
→

×

v
→

|

r
→

|

2

{\displaystyle {\vec {\omega }}={\frac {{\vec {r}}\times {\vec {v}}}{\left|{\vec {r}}\right|^{2}}}}
Due to the vector product, the angular velocity vector is perpendicular to the plane of motion.
With circle of radius R = 1

ω
=
2
π
f

{\displaystyle \omega =2\pi f}