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Pawia 2/8/2017 Czy jest możliwe znalezienie przewodnika dla Imperium Galactica (13) i. Imperium Galactica Оiva 3.0, patch 1.13: `I`OBI`/ReactOS downloaded.Q:
How does a flywheel effect the time it takes for a car to make 1 revolution?
I have heard that the time it takes a car to make a revolution around a pole is constant. So if a car is going around a pole at 20mph it will take 0.50 seconds to complete a revolution (or just half a seconds for that matter).
But if it was going round a flywheel it would take a lot longer so that the total time it took to rotate the flywheel and make 1 revolution would be 1/2*20mph. But as I understand it the flywheel is making the revolutions faster so it would take much less time to complete 1 revolution, yet the time it took to complete 1 revolution remains the same.
What am I missing?
A:
You are correct to think that the time taken to complete one revolution of a flywheel is significantly less than for a car. This is because of a relationship between torque and angular acceleration – in the car, a large torque is required for a large angular acceleration. In the flywheel, a small torque means a large angular acceleration.
In the car, torque $T$ is related to the acceleration of the car $\ddot{x}$ by the equation $T = I_w \ddot{x}$. The acceleration of a car is then related to its speed $v$ by the equation $v = \dot{x}$. The torque $I_w$ of a flywheel at a speed $v$ is related to its diameter $D$ and mass $M$ by the equation $I_w = \frac{D^2 M v}{l}$
where $l$ is the length of the flywheel from its centre of rotation to its