I have a simple question, can you spin a conical pendulum fast enough so that it rotates at 90 degrees?
The equation is $\tan(\theta)=v^2/rg$ , but at 90 degrees, $\tan(\theta)=\infty$ ... so what does this mean? Please provide supporting data.
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Firstly, $tan(\theta) = \frac{v^2}{rg}$ means that as you increase the centrepital velocity, $v$, of the pendulum, the angle between the rope and the vertical increases. Now as the pendulum gets faster and faster, the angle gets larger and larger but never exceeds 90 degrees. I will not provide supporting data, as the above equation is all the data you need. |
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The frequency or the angular velocity will help with understanding how the pendulum moves as its The number of complete cycles of a periodic process occurring per unit time. Meaning how the angle and velocity together affect the pendulum. To find ω we know from basic physics V= ωr. We can compute this into the force equations from Newtons second law F=ma. We also know that r/l=Sin(θ). So if we combine this information we generate a formula of ω^2=1/(lCos(θ)) . To really help see what this means, we can say ω=infinity then Cos(θ) must =0 so θ=π/2. This means no matter how fast we try to make the velocity the pendulum will never be perfectly horizontal as we can never reach an infinite speed. |
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