The application of F = ma to complex systems is enough, on its own, to account for this. The fact that structures in the Universe exert forces on one another as they move, and that these structures are extended objects rather than point sources, can lead to torques, angular accelerations, and rotational motions. The ball will continue on, constantly, with its motion unchanged it’s an object in motion with no external forces in that direction. This explains why when you hit a golf ball on the Moon, gravity only affects its motion in the “up and down” direction, not in the side to side direction. The same applies for the y-and- z-directions as well: What happens in those directions only affects those directions. What happens in the x-direction - in terms of force, position, velocity, and acceleration - only affects the other components in the x-direction. One of the remarkable things about these sets of equations is that they’re all independent of one another. ( Credit: MichaelMaggs Edit by Richard Bartz/Wikimedia Commons) Here, a ball under the influence of gravity accelerates only in the vertical direction its horizontal motion remains constant, so long as air resistance and energy loss from impacting the ground are neglected. The fact that F = ma is a three-dimensional equation doesn’t always lead to complications arising between dimensions. Given that we live in a three-dimensional Universe, every one of these equations with a “bold” quantity in it is actually three equations: one for each of the three dimensions (e.g., x, y, and z directions) present in our Universe. That’s because they’re not just quantities they’re quantities with directions associated with them. In addition, you’ll notice that some of the letters are bolded: x, v, a, and F. The relationship between position, velocity, acceleration, force, mass, and time is profound - it’s one that scientists puzzled over for decades, generations, and even centuries before the very basic equations of motions were successfully written down in the 17th century. Similarly, velocity itself is a change in position ( x) over time, so we can write v = Δ x/Δt for an average velocity, and v = d x/dt for an instantaneous velocity. We normally express this as a = Δ v/Δt, where the “ Δ” symbol stands for a change between a final and an initial value, or as a = d v/dt, where the “ d” denotes an instantaneous change. An acceleration is a change in velocity ( v) over a time ( t) interval, and this can either be an average acceleration, such as taking your car from 0 to 60 mph (approximately the same as going from 0 to 100 kph), or an instantaneous acceleration, which asks about your acceleration at one particular moment in time. The way to take F = m a to the next level is simple and straightforward, but also profound: It’s to realize what acceleration means. ( Credit: rmathews100/Pixabay) More Advanced If two of the three of force, mass, and acceleration are known, you can find the missing quantity through properly applying Newton’s F = ma. In this stop-motion composite, a man starts at rest and accelerates by exerting a force between his feet and the ground. While it might seem like there’s very little to it, the truth is that there’s a fantastic world of physics that opens up when you investigate the depths of F = m a. In addition, it’s just three parameters - force, mass, and acceleration - related through an equals sign. Part of the reason why it’s so undervalued is because it’s so ubiquitous: After all, if you’re going to learn anything about physics, you’re going to learn about Newton, and this very equation is the key statement of Newton’s second law. Yet it’s the one that physics students learn more than any other at the introductory level, and it remains important as we advance: through our undergraduate educations, through graduate school, in both physics and engineering, and even when we move on to engineering, calculus, and some very intense and advanced concepts.į = m a, despite its apparent simplicity, keeps on delivering new insights to those who study it, and has done so for centuries. Despite the fact that it’s been in widespread use for some ~350 years now, since Newton first put it forth in the late 17th century, it rarely makes the list of most important equations. If there’s one equation that people learn about physics - and no, not Einstein’s E = mc 2 - it’s Newton’s F = m a.
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