#9 relationship between angular speed and angle of the string above the vertical for a particular rotating apparatus.

Relationship between angular speed (ω) and angle of
the string above the vertical (θ) for a particular rotating
apparatus.

introduction:

After we do the activity about the relationship between the angle speed and the centripetal acceleration, we are able to find the relationship between the angle and the angle speed by the function and define. 

Setting:

give the unknown 

Thesis:

the total R we have is r=d+lsinθ

Tension*cosθ=mg

Tension*sinθ=ma(centripetal acceleration)

centripetal acceleration=g tanθ=w^2*r=w^2(d+lsinθ)

we can find that w=[gtanθ/(d+lsinθ)]^1/2

use this formula to find the e=relationship

and compare with the w we find from time

Date and calculate

I use Excel to help me calculate those date and this is what I got 

 I make the graph

Conclusion: 

from my graph, we can say that the w from T is close to the w we found by angle are almost the same.

it means that we prove that  the w^2r = centripetal acceleration