Redemption: Uniform Circular Motion and Universal Gravitation

Lately, our physics class has been learning about the motion of objects in a circle, and the force of gravity. In the unit over uniform circular motion (hence the title), we learned about centripetal force, how to calculate the tangential velocity, the centripetal acceleration, period, and frequency. In uniform circular motion, an object moves around the perimeter of a circle with a constant speed. The time it takes to travel one rotation around the circle is known as the period, and frequency is the number of revolutions that an object can travel during a certain time period. Centripetal force is the force that keeps the object moving in a circle. Centripetal force is always pointed toward the center of the circle, and is equal to an object's mass multiplied by its velocity squared divided by the radius of the circle that the object is traveling around.
Universal gravitation is the law that proposes that all objects in the universe are attracted to all other objects in the universe. The force of this attraction can be determined by the multiplying the product of the masses with the value of G (6.67 E -11) and then dividing this by the square of the distance between the two objects.
The area of the unit that I had the most trouble with was identifying the centripetal force. The reason I had trouble with this is because I tend to over think things, and often confused other forces with the centripetal force. In order to overcome this difficulty, I just needed to remember that centripetal force is the only force pointing toward the center of the object's circular route. In order to remind myself which force is the centripetal force, I drew sketches of the situation described in each problem. For instance, if a rock is being swung around on the end of a string, the centripetal force is provided by the string, so the tension force supplies the centripetal force. And, for a change, I didn't have any outstanding problems with universal gravitation.

This unit of physics has many practical uses. One such use could be gaining respect and eventually power from your peers through your superior knowledge of physics. For instance, if you are rounding a corner with your friends in the car, and your dashboard hula dancer slides away from where it was lovingly placed, slipping toward the precarious edge of the dashboard, you will know what's going on. One of your friends, awed by this phenomenon, asks why the hula hooping doll seems so attracted to the edge of the car. You, with your extensive physics knowledge,  are able to answer, "The doll lacks a source of centripetal force, and continues moving in the same direction it was moving in before the car turned." Your friend responds by saying, "Oh, yeah. I totally knew that," but secretly admiring you because they did not, in fact, know that. Later, when said friend conquers the world, they will grant you a high ranking government position, even though you aren't really qualified and have been dodging the international authorities for years. Effectively, you will be granted a life of riches, power, and diplomatic immunity, all because you knew the inner workings of centripetal force.
Or you could figure out the coefficient of static friction of tires against asphalt while you're on a mind numbingly boring road trip. Universal gravitation can be used to find out how attracted you really are to your significant other. (If your mass is 100 kg, and your boyfriend's mass is 150 kg, and y'all are sitting two meters apart, then you are .000000250125 N attracted to him. That's not very much. Maybe y'all should break up.)

Either way, it's pretty useful.