Corrections to Review Problems Rotational Dynamics, Harmonic Motion, and Waves

Several students in my Honors Physics class complained that in two cases of problem 6 I had created problems that reflected inappropriate situations, i.e the maximum angles of displacement for the pendulum did not make much sense for the 3 and 4 kg cases. They are correct. For the 3 kg case its a bit too large for accuracy; for the 4kg case it is too large for pendulum motion at all.

I would like to point out that the only reason they had difficulties with this problem is because of their defective eyesight. Apparently these poor students have trouble seeing the decimal points in numbers just because I neglected to put them in. A pretty lame excuse if you ask me.

The difficulties for the 3 kg case arise from the energy being 50 J instead of the 5.0 J it should have been. This results in a maximum displacement angle of 1.05 radians. While this is physically okay ( its about 60 degrees from vertical), it violates the small angle approximation that allowed us to say phi = sin phi in deriving the equation for omega for a pedulum. Thus the equation we used is not valid for the situation we analyze here.

The 4 kg case is even worse, since the 15m/s ( it should have been 1.5 m/s) vmax yields a maximum angle of 2.5 radians. While at 143 degrees from straight down, this is still less than straight up, with an angle like this all bets are off since the mass would tend to fall straight down rather than describe an arc the way all well bred pendulums do.

In any case, I am going to post the sheet with a revised table for Problem 6 for these nitpickers who insist on reading numbers as I typed them instead of as I should have typed them. The corrections are use 5J for the 3 kg case and 1.5 m/s for the 4 kg case. Just to show there are no hard feelings I will even post the solutions to the corrected problem.

Here is the revised problem sheet with just the changes I mentioned:

RevProbRotandHarmR2.doc

and here are the solutions for the corrected problems. SolnsforRevProbRotHarWaves.xls

Again, the difference is that energies ,velocities, and the phi max are now more reasonable for the 3 and 4 kg cases for problem 6.