# Torque equals rate of change of angular momentum

By Marcus Wilson 27/03/2012

Another day, another New Zealand batting collapse.  But while Kane is still there, there’s hope.

Not what I wanted to blog about. Halogen lights. You know the ones, the little light bulbs that are all the fashion. You fit lots of them snuggly into your ceiling to provide a nice even illumination of the room without obtrusive cables and fittings hanging from the ceiling.

They are nasty things, for three reasons. First, they ain’t energy efficient. They might look hi-tec, but they rack up your electricity bill as fast as a few incandescent bulbs will – especially when you have lots of them.

Second, fitting snuggly into the ceiling means that you have further to reach to change them. Whereas I could do a hanging light fitting without even getting a chair (oh, the advantages of being tall) a chair is the minimum I need in our new house. For many of them, a step ladder is called for. Indeed, we have one light in the most stupidly located position imaginable. It is where the ceiling is the highest, on the upstairs landing right at the top of the stairs. To get to it, I need to put a step ladder at the top of the stairs and go to the top of the ladder and reach upwards. ACC would cringe at the prospect (and so do I). This light bulb is remaining unchanged.

And third, once you finally reach them, they are SO difficult to get in and out of the fitting. With a conventional bulb, you could grasp it and turn; but with this there is nowhere to grasp. To generate a torque on the bulb, which is what you need to do to turn it in the fitting, you need to use friction between your fingers and the bulb. But to stop your fingers sliding across the bulb, you need to press really hard. But also, because the bulb is small, you can generate very little torque. The torque, which is the total ‘strength’ of the turn, is given by the force you exert, times the radius of the circle that is being turned.  A small radius means that you need apply a lot of  force, which isn’t easy to do through friction alone. You can experience a similar thing with opening jam jars. There are a variety of inventions to cope with stiff lids – mostly they work by making the lid effectively bigger – e.g. by gripping the lid and providing you with something larger to turn. That means the radius of the turning circle is bigger, so the force you need to exert to give the same torque is lower.

A couple of days ago I changed a couple of bulbs in a friend’s house – he’s unable to do them himself. One of them, in particular, took an age to get out of the socket. I left with skin missing from my fingertips, because of the friction involved. People with arthritis would have no chance.

I feel like I need to invent a device to grip these things and let you remove them more easily – unless of course someone’s already invented it.