 My name is Amy, and I'm an undergraduate physics student at Lancaster University. We hope you enjoyed our film about Galileo's life, and we hope you learned a bit of science along the way. I'd like to introduce you to Dr Bob Jones, the author of the film, and Dr Christopher Bowdery, a teaching fellow at Lancaster University. They very kindly are going to answer any questions we have throughout the lessons which you are about to see. As well as being members of Lancaster University Physics Department, we're all members of the Lancashire and Cumbria branch of the Institute of Physics, which funded this film in association with the Creative Learning Department of the Duke's Theatre in Lancaster. But before we get on to the science, you might want to think about just how accurate were we about Galileo's life? Did he really miss behaving church? Did he really drop weights off of the top of the tower? And did the Pope really visit him at home? You might want to research that yourself. Along your travels you might find out that England has its very own Galileo at about the same time, he's relatively unheard of. His name is Thomas Harriet and he made plenty of telescopic discoveries, possibly even earlier than Galileo did. We'll now revisit the drama and talk about the science involved in a little more detail. What Galileo actually did and how we might improve the measurements using modern equipment. For each topic we'll make some suggestions for experiments you might carry out in your school and we'll ask a few simple questions to make you think a bit more about the science involved. Sometimes we'll give you a hint to help you with the correct answer and suggest a website you could visit for more information. Now, can you join us in the last to do some experiments that Galileo would have loved to have seen with our modern-day technology? And here we are at the undergraduate physics laboratory here at Lancaster University where we're about to embark on some really interesting experiments about pendulum. Now, you should be able to recall from the film that Galileo measured the swinging rate of three different objects. The mouse, the incense burner and the chandelier. And he used his pulse to measure the time of the swing. We can do better. Come with me. Here we are. Using a metal bob on a string, try using a stopwatch to investigate the dependence of the time of the swing on lengths. You may be interested to know that dependence is a word related to pendulum, meaning a thing that hangs. But what do we mean by the time of the swing? Notice that the pendulum swings from the middle to the left to the middle to the right and back to the middle again. And it repeats this over and over again. We'll take the motion from the middle to the left to the middle to the right and back to the middle as one period of time, so the time of the swing. Can you plot a graph to show exactly how time depends on the length of the string? Mathematicians and physicists who lived after Galileo, such as Newton, showed that the time of the swing is shown by this equation where T equals 2 pi multiplied by the square root of L over G, where T is the time period, 2 pi is just a normal constant, L is the length of the string and G is the acceleration due to gravity. What graph would you plot to get a straight line? The time for one swing cycle moving from the centre to the far left, back to the centre to the far right and back to the centre again is given by the length of the pendulum and the effect of gravity. A mathematical treatment gives the equation T equals 2 pi square root of L over G, where T is the time for one swing, L is the pendulum length and G is the acceleration due to gravity. Note the square root sign. So, to answer Amy's question, a graph of length against time squared will give a straight line. Does changing the weight or making a bigger swing alter the time of the swing? Maybe you've seen two identical swings in the playground, one with a small child and one with a much larger child swinging higher. Who swings faster by setting your pendulum moving in a circular motion instead of a straight line like this? Does this alter your experiment to work out the time of the swing? If not, why doesn't it? The pendulum swings faster or slower on the moon and by about how much? To help look at how gravity was used in the equation given earlier. The mass of the pendulum does not affect the swing time as long as all the mass is concentrated in a single bob. We call such an arrangement a simple pendulum. Also, as long as the pendulum does not swing too far from the centre, the swing time is the same whatever the start position. This makes it ideal for a mechanical clock. Circular motion gives the same result as motion in a single plane. We have two identical pendulums moving at right angles to each other. Gravity on the moon is much less than that on the Earth's surface, so a pendulum will swing slower. Referring to the equation for the pendulum, we see that the time for one swing is proportional to one divided by the square root of the acceleration due to gravity. Putting in some numbers, the gravity on the moon is about one sixth of that on the Earth's surface. So the square root of six is about two and a half, which means that the time for one swing on the moon is about two and a half times longer than for an identical pendulum on the Earth. Can you think of another simple system that oscillates like the pendulum? Maybe a weight hanging from the end of a metal spring. The time of the oscillation depends on the length of the spring, just as the swing of the pendulum depended on its length. Does it depend on mass? Does it depend on anything else? Would the spring oscillate faster or slower on the moon? The spring is different. The time of oscillation doesn't depend on the length, but it does depend on the mass. This is the opposite of the pendulum, and it doesn't depend on gravity either, so it would be the same on the moon. But without a more detailed study of the motion, you'll just have to take my word for it. The movement of the pendulum and spring are examples of simple harmonic motion. SHM occurs when two conditions are present. Firstly, there is a force that acts towards the centre point of the motion. Secondly, that force is proportional to the distance from that centre point. This results in oscillatory motion that follows what we call a sine curve in time.