Problem: A 1.24 m diameter flywheel which is initially rotating at 1200 rpm is braked to a stop in 13.5 seconds. Find the angular acceleration, tangential acceleration, angular displacement, and the distance a point on the periphery turns through.
Solution: The equations work only for standard units; i.e., rad. So the 1200 rpm must be converted to rad/s:
(You should make units conversions in this way - it's called the "factor analysis" method.)
Since we have the initial and final angular velocities, and the time,
The tangential acceleration is r times this:
Notice that "rad" is discarded when we "feel like it"; it's not a unit (as explained previously).
To get the angular displacement, we use:
Finally, we use a "connection equation" to get the linear distance turned through:
If you don't get quite the same answers I do, check your work! You may be rounding off in the middle of the problem. For example, while I write the rounded value of 848 rad, I use the unrounded value in further calculations (I store it in the calculator's memory).