Unit four photo

Why is it that my dog places her paws right below her shoulders when she sits instead of right next to each other like you would expect? The reason for this is if she puts her paws together she lowers her range of base of support therefore making it more difficult to keep her center of gravity above it. So, she keeps her paws spaced out so that she will be able to comfortably sit without worrying about balancing and falling.

Unit Four Blog Reflection

     The first thing that I learned about in this unit was tangential and rotational velocity. Tangential velocity can most easily be described when relating it to a merry go round. When children are playing on a merry go round, the one closest to the center of the unit will be the one with the lowest tangential velocity. This is because it does not need to cover as much distance to make one rotation in the same amount of time as the person on the outside of the merry go round. The person on the outside needs to cover more distance to make one rotation, and therefore needs to travel faster. This is easily relatable to rotational velocity as well. Rotational velocity refers to how many rotations an object makes. Though the kid closest to the center of the merry go round and the kid furthest from the center have different tangential velocities, they have the same rotational velocity. This is because though traveling at different speeds they are both making a full rotation in the same amount of time.
      In this unit the second thing that I learned about was rotational inertia and angular momentum. Rotational inertia measures how quickly an object can spin. An object with high rotational inertia, such as a wooden hoop, spins much slower than an object with a low rotational inertia, such as a steel ball. The reason that a steel ball with low rotational inertia spins more quickly is because their is more mass in the center of the object than a wooden hoop, who has no mass near the center. The more mass that is near the center of an object, the lower rotational inertia. Angular momentum relates to rotational inertia in that it is when an object changes to pull mass either closer or farther towards its center. A great example of this is in ice skating. When ice skaters want to spin in the air or on the ice, they pull their arms into their chest to that they are right next to their axis of rotation, this helps them to complete three full turns in a triple axis. When they land and want to slow down, they put their arms out so they can glide at a regular speed.
    The third thing I learned about was conservation of momentum. This law says that a rotating objects momentum is found with the rotation inertia times the rotational velocity of that object. It also tells us, like we learned in the last unit, that the momentum before is equal to the momentum after.
     The next thing I learned about in this unit was torque, center of gravity, and center of mass. Torque measures the ability for an object to move. The equation for torque is torque equals lever arm times force. The longer the lever arm, the bigger torque. A perfect example of this is a door stop. The closer to the axis of rotation the door stop is, the less force and smaller lever arm and there fore the less easily it holds the door open. When you put the door stop at the end of the door, however, farthest away from its axis of rotation, the lever arm is as long as possible and therefore there is a great force. The center of mass of an object is where it is balanced. For example, if you hold a broom near the bottom of the handle, you can balance it. This because that is where the masses on either side are equal. The center of gravity can most easily be explained through wrestlers. This is the point in an object that holds it up. This means that the center of gravity is normally near the center of an object and it is over the base of support which is the reason why people do not fall over. For example, the center of gravity for humans is normally around their hips. This is why a wrestler bends his knees and lowers his hips so much. The more your center of gravity can be supported by your base of support the more difficult it will be to knock you over. This is also why people that walk on tightropes carry a long stick. The stick lowers their center of gravity therefore making it more difficult for them to fall off the rope.
     The last thing we learned about in Unit four is centripetal and centrifugal motion. Centripetal motion is the force that keeps you in a circle when your turning on a bike, in an airplane, and even on a race track. By drawing vectors, you see that centripetal motion is the force that keeps a stead circle. Centrifugal motion is a fictional force. It is the force that pushes the water out of a washing machine as it empties or pushes you up against the passenger door when you turn a sharp corner. This is not real, it is simply inertia working and the door keeping you inside of the car. An example of this can be found in this picture of the airplane, with the vectors drawn in.

     What I have found difficult in this unit is remember the differences between tangential and rotational velocity and center of mass versus center of gravity. I overcame these difficulties by pairing each concept with a concrete example in my mind so that I always had an easy way to remember it. My problem solving skills and effort this unit have been pretty good. I have tried to complete all my homework to the best of my ability and really pay attention when taking notes and learning new material. I am pretty confident in this unit because I have thought deeply when solving problems and have really gone in depth about each concept that we have learned.
     My goals for next unit are to try to grasp the concepts just by learning them and not by examples so that I am able to apply them easily to everything and I am going to do this by focusing on the concept rather than how I am learning about it.
     The biggest and most clear connection I can make to what we are studying is ice skating. This is because I used to figure skate therefore I have found it fascinating that rotational inertia, angular momentum, center of mass, and center of gravity can all relate to things I have done on ice before. Another connection I can make that I haven't talked about in this post yet is train wheels. Train wheels are designed so that the circle on the outside is smaller than the circle on the inside, as you can see in this picture.

     This is because the smaller side has a higher tangential velocity than the bigger side, and therefore can more quickly correct when turning corners. 

Meter Stick Challenge

My initial plan to solve this challenge was very vague. I was not sure how to tackle the problem at all but I did know that it had something to do with torque. Since I knew the equation for torque was lever arm multiplied by force that is the first thing that I wrote down. Since I knew that there was two torques in this situation I wrote lever arm times force = lever arm times force. I knew that the weight was one hundred grams and since that is mass instead of force I calculated that the force of the weight was .98 newtons. From there I was stuck. However, my group members helped me figure out that the center of gravity of the stick was at the 50 centimeter mark because that is the point at which it balanced like a sea saw on the edge of the table. With the weight on the end, the center of mass was at the 25 centimeter mark. Therefore, we figured that the lever arm lengths were 25 and 75 centimeters. However, we realized that the center of gravity is where the counter clockwise lever arm began. From there, we filled in the equation and the only variable we had left was the force for the clock wise torque. We solved for that and converted it from newtons to grams and got that the meter stick was 100 grams. When we weighed it we found that it was 101 grams. The reason that the meter stick could balance on the center of mass and the center of gravity because in both cases there was an equal force on each side.

Torque

Torque is the ability for something to turn on a certain axis. Torque is equal to lever arm times force. There is a center of gravity of every object and also an axis of rotation. The two are not the same but the torque of each object depends on both. The reason that this diver can flip so many times is because their center of gravity is in their waste and by pulling in both their arms and legs they make their axis of rotation where their center of gravity is as well. Their arms are legs are the level arms and because they are small the force is big therefore making the torque big.

Rotational Inertia and Angular Momentum

In this video you can see that the women is thrown up into the air at a small speed but gains tons of momentum when she is in the air by pulling her arms close together. This is has to do with angular momentum and rotational inertia. High rotational inertia means that most of the weight of an object is away from it's axis therefore making it hard for the object to turn. Low rotational inertia means most of the weight in near the center of the object making it easier to turn. This is when when she brings her arms in it adds weight to her axis therefore helping her turn more quickly, or lowering her rotational inertia. Angular momentum is when there are not many sharp angles on an object making it easier for it to turn or move quickly. This is also why when she draws her arms in she attempts to lay them as flat as possible on her chest, in order to have a lot of momentum by having not a lot of angles.