## Monday, May 09, 2016

### SATs are harder than you think

How’s your classical mechanics? Mine’s a bit crap. That’s why I’m having trouble working out the following question.

You have a cylinder that rotates around a horizontal axis, like the sort used to pull up buckets from wells. Around the cylinder is wrapped a rope attached to a weight. As the weight falls and the rope unwinds, you measure the time it takes to descend a certain distance.

Now you increase the mass of the cylinder – say, it’s made from iron, not wood (but of the same size). Does the weight fall more slowly? At risk of embarrassment, I’ll say that I think it does. The torque on the cylinder is the same in both cases, but what changes is the cylinder’s moment of inertia, and thereby (via torque = moment of inertia times angular acceleration) the angular acceleration. So the weight takes longer to descend the same distance when attached to the iron cylinder because the angular acceleration is less.

Also, the greater mass of the cylinder means, via Amonton’s Law, that the friction with the axis is greater in the latter case.

Am I right? Or do I need (it is quite possible) to go back to my A-level mechanics?

The reason I ask is that I am trying to understand a question in the SATs science test (now dropped, by the way) for Year 6, i.e. 11-year-olds.

You might wonder why 11-year-olds are having to grapple with torques and so forth. So am I. But they come up in this question:

Now, I suspect that the answer the pupils are expected to give is that the bigger piece of card incurs more air resistance. That is true. But it is not the only influence at play, since the card obviously adds to the rotor’s mass. So this is a rather complicated question in mechanics.

You might think I’m overthinking the problem. But I can’t see how it is ever a good idea to choose a question for which a little more knowledge makes the problem harder. Or am I just wrong here about the answer?

Elsewhere in the SATs papers you find difficulties that seem to be the result purely of bad questioning. Take this one, from an English Reading and Comprehension test. Pupils have to read the following passage: