![]() You're going 1 2 3 4 5, so that gives us 10, or 2 pi 2 pi 2 pi 2 pi 2 pi radians every time, you're doing it five times a second. These cancel out and you get 5 times 2 pi which gets us to 5 times 2 pi gets us 10 pi radians per second And it works out the dimensional analysis and hopefully it also makes sense to you intuitively If you're doing five revolution a second, each of those revolutions is 2 pi radians so you're doing 10 pi radians per second. Every second it's making 5 revolutions So how could we relate that to how many radians it is doing per second? Remember radians is just one way to measure angles You could do with how degrees per second If we do it with radians, we know that each revolution is 2 pi radians If you go all the way around a circle, you have gone 2 pi radians which is really just you say you've gone 2 pi radii, whatever the radius of the circle is and that's where actually the definition of the radian comes from So if you go 5 revolutions per second and they're 2 pi per revolution then you can do a little bit of dimensional analysis. Let's say we have some object that's moving in a circular path Let's say this is the center of the object path, the center of the circle So the object is moving in a circular path that looks something like that counterclockwise circular path-you could do that with clockwise as well I want to think about how fast it is spinning or orbiting around this center how that relates to its velocity? So let's say that this thing right over here is making five revolutions every second So in 1 second, 1 2 3 4 5. So if it takes X amount of work to open the door if you push on the side opposite the hinge it moves mich further than close to the hinge so since the amount of work will always be X the force will have to be greater near the hinge.įor example if a door requires 10 Nm (Newton meters the SI unit of work) to open and the edge opposite the hinge moves 2 meters when you open it it only takes a 5N force to open it but if the portion of the door near the hinge you push on moves only 0.1m then you need to use a force of 100N to open it. Work is defined as a force acting over a distance, if there is no movement there is no work. ![]() To swing the door from the closed position to fully open is the same regardless of where it is pushed, this comes from the conservation of energy. This comes from the amount of work that is required to move the door. The closer you are to the pivot point the harder you have to push. ![]() The case of the door the pivot point it at one edge and the "weight" can be considered to be at the center of the door. If you move the pivot point to one side of the other the ration of weight(force) to balance it changes. You are probably familiar with a teeter-totter where you have a lever with a pivot point in the middle of the lever so that to lift 50Kg on on end takes 50kg of force on the other. ![]() The easiest to explain is using the lever. ![]() The other has to do with levers and work. One has to do with the concepts of rotational motion which involve moment or moment of inertia. ![]()
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