Question

You’ve been assigned the task of using a shaft encoder a device that measures the angle of a shaft or axle and provides a signal to a computer to analyze the rotation of an engine crankshaft under certain conditions. The table lists the crankshaft’s angles over a $0.6\mathrm{s}$interval.

Is the crankshaft rotating with uniform circular motion? If so, what is its angular velocity in rpm? If not, is the angular acceleration positive or negative?

Short answer

The crankshaft is not rotating with uniform circular motion and it doesn't have any angular velocity. The angular acceleration is negative.

Step-by-step solution

Given information

We are given with the table of time in second and angle in radian.

We have to check weather the crankshaft is rotating with uniform circular motion? If so, what is its angular velocity in rpm? If not, is the angular acceleration positive or negative?

Graphical representation

The Graph between angle and time is shown below:

As we can check from the graph that the data is not fall along straight line, so the crankshaft is not rotating with uniform circular motion. It does not have angular velocity.

Slope is:

$\mathrm{m}=\frac{7.0-0}{{(0.6-0)}^2}$

The angular acceleration is:

$$\begin{gathered} \mathrm{\alpha }=-2\mathrm{m} \\ \mathrm{\alpha }=-2\times 19.4 \\ \mathrm{\alpha }=-38.9\mathrm{rad}/{\mathrm{s}}^2 \end{gathered}$$

The angular acceleration is negative.