## Tuesday, January 26, 2010

### Circular Motion and Gravitation

Although grasping the concept of circular motion and gravitation can be difficult, I learned many new things about physics. When an object is in a constant or uniform speed traveling in a circle, the object is in uniform circular motion. Also, the distance and object travels around a circle is the perimeter. One complete revolution around the perimeter of a circle is the circumference. The equation 2*pie*r represents the circumference of a circle. In addition, the speed of the object in uniform circular motion is given by v=2*pie*/T m/s. Period T is the variable for the time it takes for the object to make one full revolution around the perimeter, and it is given in seconds. Also, the frequency is the number of rotations per unit of time an object makes around the perimeter, and is given in Hertz, abbreviated as Hz. Therefore, T=1/f s and f=1/T Hz. Also, objects moving at a constant speed don't have a constant velocity. This is because an object in uniform circular motion is constantly changing direction. However, the magnitude of the velocity of the object will remain constant. Tangential is best used to describe the direction of the velocity vector of an object while in uniform circular motion. Furthermore, when an object changes direction, it accelerates. This acceleration is called centripetal acceleration. Centripetal acceleration means that the acceleration will always be directed towards the center of the circle.  Another fact is that the acceleration will always be perpendicular to the velocity. In addition, centripetal force is the force that must be applied to keep an object moving in a circle. The centripetal force is not a force by itself, but the centripetal force is provided by the force that keeps the object in a circle. the equation to solve for the centripetal force is Fc=mv^2/r N. When an object moves in a vertical circle at the end of a string, the tension varies with the position of the body. At the highest point the centripetal force equals Ft+mg=mv^2/r N. When it is at the lowest point Fc is found by Ft-mg=mv^2/r N. We also learned that Newton discovered that the gravitational force varies inversely with the square of the distance between two objects, which is called the inverse square law.  The Law of Universal Gravitation states that "Every object in the universe attracts every other object in the universe with a force that varies directly with the product of their masses and inversely with the square of the distance between the centers of the two masses." Therefore the equation for the force of gravitation is Fg=Gm1m2/r^2 N. To find the acceleration due to gravity of an object of mass we can use Newton's Law of Universal Gravitation. The equation can be manipulated into another equation: g=GM/r^2. We have learned a lot this unit, but overall it has been very interesting.

What I have found difficult about what we have learned is the period and frequency. I constantly get confused and mixed up between the both. Also, I find it difficult to find the centripetal force requirement, especially when many forces are acting on the object.However, I feel that I can get confident in these areas of weakness if I keep practicing.

My problem solving skills are pretty good I would say. Sometimes I can make careless mistakes and not realize it. Other times the answer is right in front of me, but I just can't see it. The key to my success is practice because that is how I learn. It gives me more and more experience and prepares me to solve even harder problems in that area. If I continue to do this, I believe I can get better at problem solving.

1. Good reflection, however, at the very beginning you state that: "When an object is in a constant or uniform speed, the object is in uniform circular motion." How is that possible? An object in constant speed can also travel in a straight line! Please correct this.
You also said that you confuse revolution with frequency. I believe that you meant period and frequency.
Finally, I do not agree that problems can be simply solved by equations found on the blue sheet. What happens when you have several forces acting in both axes? What happens when forces are at an angle?
Your reflection needs a little more digging...

2. Puja,

Excellent reflection. I sympathize with your difficulties in confusing period and frequency; I once had that problem myself. Just remember that frequency is the reciprocal of the period and you should be able to tell them apart.
Also, you may want to try drawing out a diagram that shows all the forces acting on an object; it'll help you remember the directions of each of the forces and stop you from making careless mistakes.
Best of luck with your Physics project! If there's any way I can help, just let me know.