Stars and Pulsars

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Earth, Moon, Sun and Stars

Earth, moon, sun and stars

Stars and pulsars

Angular momentum calculation

Let's start with the situation where you are holding the bottles out at arm's length. Suppose you do 3 revolutions on the spinning chair, before friction begins to slow you down appreciably, and that it takes 90 seconds for these. You can work out your angular momentum like this:

\begin{displaymath}angular momentum = mass x speed x radius \end{displaymath}



\begin{displaymath}angular momentum = mass x \frac{distance}{time} x radius \end{displaymath}


So

$ angular momentum = m x (2\pi r / t) x n x r $ kg m2 /s

If your mass is 40kg, and you can hold the bottles 0.7m from the centre of your body, you can calculate your angular momentum like this:

\begin{displaymath}angular momentum = 40 x (2 x \pi x 0.7 / 90) x 3 x 0.7 \end{displaymath}



which works out to about 4.1 kg m2 /s. (There is no point giving the answer to any greater number of decimal places than this, since you are unlikely to have measured the radius, your mass or the time to more than 2 significant figures).

Now compare this with what happens when you hold you the bottles close to your chest. Say you do 8 revolutions in 20 seconds like this before slowing down appreciably, and you are now holding the bottles 0.2m from your centre.

\begin{displaymath}angular momentum = 40 x (2 x \pi x 0.2 / 20) x 8 x 0.2 \end{displaymath}



This comes to about 40 kg m2 /2. If you get answers as close as this that will be very good!

Discrepancies will occur for various reasons. It is hard to judge precisely the point at which friction is having an impact on your speed, and the calculations above don't take friction into account. It will help if you decide to measure just one or two revolutions in each case, and get as accurate a time as you can for these. What is important is that the students realise how much faster they
can go with their arms close to their bodies than with them stretched out. This is the principle skaters use when spinning: they can vary their speed by stretching their arms out, or holding them close to their bodies.