In this unit we learned about UNIFORM CIRCULAR MOTION, or UCM. I learned about UCM in many different ways. We started out with easy stuff like the circumference and period, and then moved to a little more complicated things. We learned about the frequency, the tangential to the circle, the centripetal acceleration, the centripetal force requirement, and centripetal force. Ok, so, starting with the basics. UCM is the motion of an object with a constant (uniform) speed. For UCM to be possible, the object must be moving in: 1- A perfect circle where the radius does NOT change, and 2- with constant speed. Now for the parts of UCM. The circumference of the circle is the distance around the circle and the period is the time of one rotation in seconds. So if the circumference is 2πr and the period is T, you can conclude that v=2 πr/T. But, that is just the velocity. I also learned about the frequency which is f=1/T. The frequency is the number of revolutions per unit of time, and the unit is Hz. Now back to the velocity, even though in UCM the speed is constant, the direction changes. So the magnitude of the velocity remains the same but not the direction. And, the direction of a circle can be very confusing, so the way to find the direction is by finding the tangential to the circle. Now for another part of UCM, there is the centripetal acceleration. Centripetal means towards the center, so if the velocity is tangential to the circle, then the acceleration must be perpendicular in order for it to be towards the center. The centripetal acceleration is ac=v2/r. And last of all, we can find the centripetal force. There are many different centripetal force requirements; it can be tension, gravity, friction, and others depending on what the situation is. This requirement keeps the object moving in a circle. But, whatever different force the requirement is, you still use Fc=mv2/r. As you can see, in the equation, everything is related. The velocity equation is used to find the acceleration, and then the centripetal force equation is the acceleration equation with mass added to it. So everything I learned in this unit is all related to the end result of the centripetal acceleration.
What I have found difficult about this unit is mostly the conceptual problems. I can do everything that is with numbers, but on the conceptual problems I can get kind of lost. I just feel like I have trouble understanding the science behind all of these parts of UCM, but when but into the context of a problem, I understand them perfectly. It’s hard to explain but I tried to give an idea.
My problem skills have definitely been enhanced during this unit. I put a lot of effort into trying to understand more about circles. I have never really been good with circles but since we did labs and because of the demonstrations on the PowerPoint’s, I understand it much better. I never knew that you could relate the sizes of circles to time which then gives you velocity. I felt that distance in a circle, the time around a circle, and velocity would NEVER relate. But now with the equation v=2 πr/T, I now get it. I kept trying and trying the problems, and after all of that effort, I now understand all of the relations in UCM. I’m very good at solving for equations that require substitution such as substituting all of the equations into the net force equations on the vertical circle problems. If Ft=Fg, and Ft=Fc, but there was also a missing variable, I was able to find cancellations and eventually cancel out the missing components until I found the correct answer. And, like I said earlier, my weakness was in the conceptual parts. I was just kind of lost in those places. But now after the test, I understand what I did wrong and I’m working on fixing it. I now get why the speed is constant and the velocity isn’t. IT ALL MAKES SENSE NOW!!!
This Unit was really interesting and different than anything I’ve ever learned about circles. I hope to learn more about it and I hope I can use it to help me in other units!