Question

Your engineering team has been assigned the task of measuring the properties of a new jet-engine turbine. You’ve previously determined that the turbine’s moment of inertia is 2.6 kg m2. The next job is to measure the frictional torque of the bearings. Your plan is to run the turbine up to a predetermined rotation speed, cut the power, and time how long it takes the turbine to reduce its rotation speed by 50,. Your data are given in the table. Draw an appropriate graph of the data and, from the slope of the best-fit line, determine the frictional torque.

Short answer

Frictional torque = 10.7 Nm.

Step-by-step solution

Given Information

Data is given as below

Explanation

First re-create the table by changing the rpm to rad/sec

Now plot the graph

Find slope using any two data points

$Slope=\frac{(220-157)rad/s)}{(25-19)s}=0.121rad/s^2$

Angular acceleration is calculated as

$$\begin{gathered} \frac{{\omega }_i}{2}={\omega }_i+\alpha t \\ \Rightarrow t=\frac{{\omega }_i}{2\alpha } \end{gathered}$$

It shows that, slope =$-\frac{1}{2\alpha }$

so

$\alpha =-\frac{1}{2\left(slope\right)}$

Substitute the value of slope, we get

localid="1649166916354" $$\begin{gathered} \alpha =-\frac{1}{2(0.121rad/s^2)} \\ \left|\alpha \right|=4.13rad/s^2 \end{gathered}$$

To find the torque now substitute the values in $\tau =I\alpha$, we get

$\tau =(2.6kg{m}^2)(4.13rad/s^2)=10.7Nm$