Lesson 32: Measuring Circular Motion
Velocity
There should be a way to come up with a basic formula that relates velocity in a circle to some of the
basic properties of a circle.
●
Let’s try starting off with a formula that we know from the beginning of the course.
v
=
d
t
●
Since we are looking at something going around in a circle, the distance it covers each
revolution is equal to the circumference of the circle.
C
=
2
r
●
We will substitute this into the first formula where the distance the object travels (“d”) equals
the circumference (“C”)...
v
=
2
r
t
The last thing we need to change is the time “t” on the bottom.
●
We're only interested in how much time it takes for the
object to go around that circumference once, so what
we really need to measure is the
period
of the motion,
not its time.
●
This gives us a slightly different looking formula...
v
=
2
r
T
v = velocity (m/s)
π = pi, use 3.14 in your calculations
r = radius of the circle (m)
T = period (s)
Example 1
:
Determine
the length of a student’s arm if she can swing a pail around five times in a
circle at 2.72m/s in 7.5s.
Period is the time it takes to do something once, so...
T
=
7.5s
5
revs
=
1.5
s
Then we can calculate the radius...
v
=
2
r
T
r
=
vT
2
r
=
2.72
1.5
2
3.14
r
=
0.65m
7/22/2008
© studyphysics.ca
Page 1 of 5 / Section 5.2
Did You Know?
The word
period
is also used in other
sciences, such as the "Periodic Table
of the Elements" in chemistry. It is
named this way because
periodically
the elements repeat the same
characteristics.
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Centripetal Acceleration
We already know that the centripetal acceleration points in towards the centre of the circle.
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 Fall '08
 Staff
 Circular Motion, Force, 0.65M

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