This tells us that the acceleration due to the gravitational field of Earth must also be the same for all masses. Newton’s work was inspired by Galileo who dropped objects of different masses from the leaning tower of Pisa to show that the time they took to reach the ground is independent of their mass. When people talk about the gravity of a planet, in general what they mean is the free fall acceleration due to its gravitational field g (which is dependent on the mass that is responsible for the gravitational field) and not G (which is a constant). His theory describes the force F between two objects of masses m1 and m2 separated by a distance r. It is important to note that Newton’s theory is that of the Universal gravitational constant G (also called 'Big G'). Jump to:Īs the apocryphal story goes, Sir Isaac Newton sat beneath an apple tree, when an apple fell onto his head and inspired his work on the theory of gravitation. Nevertheless, gravity is something we can measure here on Earth. On small scales however, gravity appears to act much weaker than its counterparts. It just appears in places you wouldn't expect.Of the four known forces of nature, gravity is the strongest on large scales - it has an ability to lock planets, stars and galaxies in their orbits. I feel like that is an insufficient answer - but it's the truth. Since we have a sine function for the answer, the period would have to have a pi in it. I don't know what else to say other than that gives us a solution. Then why? I guess the best answer is that solution to simple harmonic motion is a sine or cosine function. The equation of motion for a oscillating mass on a spring (simple harmonic motion) has the same form as the small angle pendulum and it isn't moving in a circle. Is it because the pendulum moves in a path that follows a circle? No. Why is Pi in the period expression for a pendulum? That's a great question. This is a Pi Day post, so I should say something more about Pi. Now we define the meter as the distance light travels in a vacuum in a certain amount of time. Then how do you define a meter? For a time, the idea was to a particular bar of a certain length and at a certain temperature. As you move around the Earth, the value of g changes (as I stated above). Anyone can make one with some very simple tools. Well, why not use the seconds pendulum? It almost seems like a perfect way to define a standard. It just doesn't seem like this would be easy to measure. I'm not sure how good of an idea this was, but one definition of the meter was that 10 million meters would be the distance from the North pole to the Equator passing through Paris. Of course, there are other ways to define this length. The seconds pendulum was one of the ways to define the length of one meter. Suppose we want to call this 1 meter? In that case, I have to have g = π 2. That is the length of your seconds pendulum. I'm not going to derive it, it isn't too difficult to show that for a pendulum with a small angle the period of oscillation is: Here is a quick example of a seconds pendulum I put together. Either way, it should take about 1 second to go from one side to the other. If you like, you can make a video or just use a stopwatch. Now make the distance from the center of the mass to the pivot point 1 meter and let it oscillate with a small angle (maybe about 10°). Metal works well since it's weight will likely be significantly larger than the air drag force so that you can ignore it. Get a small mass like a nut or metal ball. A simple pendulum of length L has all of the mass concentrated in a tiny bob at the end of the length. It isn't a simple pendulum, so it doesn't have to be a meter long. If you measure the length of the swinging arm, it will be close to 1 meter long. Ok, that is a grandfather clock and not actually a seconds pendulum.
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