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a. A turbine spinning with angular velocity ?0 rad/s comes
Chapter 4, Problem 64P(choose chapter or problem)
Problem 64P
a. A turbine spinning with angular velocity ω0 rad/s comes to a halt in T seconds. Find an expression for the angle ∆θ through which the turbine turns while stopping.
b. A turbine is spinning at 3800 rpm. Friction in the bearings is so low that it takes 10 min to coast to a slop. How many revolutions does the turbine make while stopping?
Questions & Answers
QUESTION:
Problem 64P
a. A turbine spinning with angular velocity ω0 rad/s comes to a halt in T seconds. Find an expression for the angle ∆θ through which the turbine turns while stopping.
b. A turbine is spinning at 3800 rpm. Friction in the bearings is so low that it takes 10 min to coast to a slop. How many revolutions does the turbine make while stopping?
ANSWER:
Step 1 of 3
Part (a)
The angular velocity of the spinning turbine is \(\omega_{0} \mathrm{rad} / \mathrm{s}\) and it comes to rest in \(\mathrm{T}\) seconds. We are going to find the angular displacement made by the turbine \(\Delta \theta\) when it stops.
The turbine must have constant acceleration \(a\) as it comes to rest. From the equation of motion, the final angular speed of the turbine is
\(\omega_{f}=\omega_{0}+\alpha T\)
The final angular velocity will be zero, therefore
\(0=\omega_{0}+\alpha T\)
Solving for a
\(\alpha=\frac{-\omega_{0}}{T}---(1)\)
The negative sign indicates that the angular velocity is decreasing.