# Rotational Dynamics: Turbine Spins 3600 RPM to Coast

• novicephysics
In summary, for an electric-generator turbine spinning at 3600 rpm with minimal friction, it takes 10.0 minutes to come to a stop. To find the number of revolutions it makes while stopping, you can use the rotational versions of linear equations, with angular velocity for v, angular acceleration for a, and initial angular velocity for Vi. The equation d=1/2at^2-Vi*t can be used, with the total angle traveled in radians as d.
novicephysics
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?

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)

Based on the given information, we can calculate the number of revolutions the turbine makes while coasting to a stop using the equation ω = ω0 + αt, where ω is the final angular velocity, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time.

Since the turbine spins at 3600 rpm initially and comes to a stop after 10.0 min, we can convert the initial angular velocity to rad/s by multiplying it by 2π/60, which gives us ω0 = 120π rad/s. We also know that the final angular velocity is 0 rad/s. Therefore, the angular acceleration can be calculated as α = ω/t = (0 - 120π)/600 s = -0.2π rad/s^2.

Now, using the equation ω = ω0 + αt, we can solve for the time it takes for the turbine to come to a stop, which is t = (ω - ω0)/α = (0 - 120π)/(-0.2π) = 600 s.

Since we are looking for the number of revolutions the turbine makes while stopping, we can use the formula N = ω0t + 1/2αt^2, where N is the number of revolutions. Substituting the known values, we get N = 120π(600) + 1/2(-0.2π)(600)^2 = 36000π - 360000π = -324000π.

Therefore, while coasting to a stop, the turbine makes approximately 324000π revolutions. This value may seem negative, but it simply indicates that the turbine rotates in the opposite direction while slowing down.

## 1. How does a turbine spin at 3600 RPM?

A turbine spins at 3600 RPM due to the rotational dynamics involved in its design. The turbine is connected to a source of energy, such as steam or wind, which causes the blades of the turbine to rotate. This rotation is then transferred to the rotor, which is connected to a shaft that rotates at a speed of 3600 RPM.

## 2. What factors affect the speed of a turbine?

The speed of a turbine is affected by various factors, including the size and shape of the blades, the type of energy source, and the design of the rotor and shaft. The efficiency of the turbine also plays a role in determining its speed.

## 3. How is the speed of a turbine measured?

The speed of a turbine is typically measured in revolutions per minute (RPM). This is calculated by counting the number of rotations the turbine makes in one minute. Advanced sensors and instruments can also be used to measure the speed of a turbine with more accuracy.

## 4. What is the purpose of a turbine spinning at 3600 RPM to coast?

When a turbine spins at 3600 RPM to coast, it is essentially slowing down to a stop. This is often done for maintenance purposes, as it allows technicians to safely access and work on the turbine without it being in full operation. It also helps to conserve energy when the turbine is not needed to generate electricity.

## 5. How does rotational dynamics play a role in turbine operation?

Rotational dynamics is the study of how objects rotate and the forces and torques acting on them. In the case of a turbine, rotational dynamics is crucial in understanding how the blades, rotor, and shaft work together to generate rotational motion and convert it into energy. It also helps engineers design and optimize turbines for maximum efficiency and performance.

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