The apparatus is a wheel spinning with an accelerometer attached to the outer edge of it. As the apparatus spins the accelerometer records the linear acceleration of the wheel.
As a class we recorded the time it took the wheel to spin 4 times at various speeds and the accelerometer the acceleration for each trail composing this data set:
Using this data we were able to equate it in the equation for centripetal acceleration as well the period.
The angular velocity is defined as:
w = 2π/ T
T = Period = time / 1 revolution
Since we recorded the time it took to complete 4 revolutions, in order to use our times, we must multiple the period by 4 to receive its value.
The centripetal acceleration is defined as
F = mr(w^2)
The mass here would cancel out giving us:
a = r(w^2)
Since we are trying to find the angular velocity we would isolate w^2.
w^2 = a/r
After finding this expression we input the data to logger pro in order to find the w^2 giving us the results below.
The value of w using the period and the centripetal acceleration is almost identical meaning that the experiment was successful
To conclude it is clear to see the relationship between the angular velocity and period and its accuracy in this experiment. Although the values were very close it is much more accurate to calculate the angular velocity using the centripetal acceleration for it does not require round recorded times
No comments:
Post a Comment