Rotational Dynamics: Turbine Spins 3600 RPM to Coast

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An electric-generator turbine spinning at 3600 RPM takes 10 minutes to coast to a stop due to minimal friction. To calculate the total revolutions made while stopping, the rotational equations analogous to linear motion can be applied. The relevant variables include angular displacement (theta), angular acceleration (a), and initial angular velocity (Vi). The problem can be approached by determining the angular acceleration first, then using it to find the total angular displacement in radians. Ultimately, the total angle traveled can be converted to revolutions for the final answer.
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An electric-generator turbine spins at 3600 rpm. Friction is so small that it takes the turbine 10.0 min to coast to a stop. How many revolutions does it make wile stopping?
 
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For these problems you can use the rotational versions of all your linear equations you've been using

So instead of d, you have theta, instead of v, angular velocity, and so on.

So the equation d=1/2at^2-Vi*t can be used but with the angle traveled in radians for d, angular acceleration for a, and initial angular velocity for Vi. That's not the particular equation you should use here though. This is similar to a problem where you know initial velocity and time, and want to find a. Then you can find d(which in this case is the total angle traveled in radians, so for example if it were like 6pi, the answer would be 3 revolutions)
 

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