The Effect of the Radius on Circular Motion Watch

velocitous
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#1
Report Thread starter 4 years ago
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Hi,

I’m quite confused because there are so many formulae which seem to contradict each other?

When you increase the radius, does your speed increases? From v=\frac{2{\pi}r}{T}.

Yet when you increase your radius, your acceleration decreases? From a=\frac{mv^{2}}{r}.

So if I want to increase centripetal acceleration, I would decrease the radius, but so doing, I would be decreasing the speed, which would decrease centripetal acceleration?

Furthermore, in this formula, a=4\pi^{2}rf^{2}, radius and acceleration are proportional to each other? But they were inversely proportional in the previous formula?

I’m confused.
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Actaeon
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When thinking about direct and inverse proportionality with these equations, you need to remember what you're keeping constant in each case. In the first, you need your time period and hence angular velocity to be constant, but in the second you are keeping your linear velocity constant. So both are correct, but not at the same time.
For example, if you reduce radius, while keeping angular velocity constant, linear speed will increase and your first proportionality equation applies. But because linear speed isn't a constant, angular acceleration won't be inversely proportional to the radius, and the second equation doesn't apply
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