Unit 4 Reflection

The first thing I learned about in unit 4 was Rotational and Tangential velocity, in which we used many examples/scenarios. We learned that rotational velocity is the complete number of rotations or revolutions in a certain period of time. We then learned that tangential velocity is that a given point on a circle will rotate x number of times as it spins, where it increases if the point is farther from the center, and vice versa. We used an example of spinning gears, in which they have the same tangential velocity because any point on either gear will cover the same distance in a certain amount of time. They have different rotational velocities because the smaller gear has a make 2 rotations (assuming it's a 1-2 ratio) in the same amount of time as the big one makes one. Below is a helpful visual of how the gears actually work.

The next thing we learned about was rotational inertia, which we soon found out was a property of an object that resists change in spin or rotation. One of the first examples we used was an ice skater, and we looked into why the skater spins faster when they pull their arms and legs inwards. We found out that when the skater pulls in their limbs, they are moving their mass closer to their axis of rotation, therefore lowering their rotational inertia and increasing their rotational velocity. This is what allows them to spin faster, as you can see below. We also learned about angular momentum in this section, which is rotational velocity times rotational inertia. We also need to know that angular momentum before is equal to angular momentum after, which also applies to the image below.

The next thing we learned about was torque, and the formula for torque is torque=force x lever arm. I also learned that torque causes rotation. A lever arm is the distance from the axis of rotation, so if you have a big lever arm then you have a small force, and if you have a small lever arm you have a big force. A scenario we used was opening/closing a door, because we found that the hinges are placed where they are because it allows a greater lever arm, which will result in a easier force to open it. 

Following torque we learned about center of mass/gravity, which I found very helpful and interesting. The center of mass is the average position of all the mass, which is near the waist on most people. We used the example of why wrestlers bend their knees and spread their legs when wrestling. We found that lowering your body lowers your center of mass which makes you more stable, and also having a wider base makes you more stable, because your center of mass is easier to stay in your base. 

The last thing we learned about was Centripetal/Centrifugal Force. I found that centripetal force is a center or inward seeking force, and centrifugal force (even thought it's technically not a real force) is a center fleeing force. The most important problem was what was the force that pushes you against the car door when you're turning in a car. The answer to this problem is that there is no force actually it is Newton's laws, where the 1st says that you are moving and you want to keep moving, and the 3rd is that the you push the car door and the car door pushes you. Below is a helpful diagram.

Finding the Mass of a Meter Stick Without Using a Scale

     In the first step, my group and I simply drew three different scenarios in which the meter stick was balancing. We then labeled the force and lever arm that caused the torque on the first drawing, and the center of gravity, force, and the absence of a lever arm on the second diagram. On the last drawing, we drew a picture with the forces and lever arms that were causing the clockwise and counterclockwise torques. For step 2, we simply wrote out the equation FxLA=FxLA to start planning before we actually plugged numbers into it. This picture to the right accurately shows how we setup the meter stick with the 100g weight on the end.

      To start our plan, we figured out that the center of gravity with no weight was dead center of the meter stick, at 50 cm. We then figured that the center of gravity with the weight was at 75.5 cm. Knowing that the torques were equal on both sides, we started plugging in numbers to our earlier equation, and we got .98x24.5=fx25.5. The .98 is the force of the weight on the weighted end, and the 24.5 is the lever arm we found from the end of the weighted side to the center of mass. The 25.5 was the other lever arm we found, and we were solving for the weight, which we calculated was .94N. We then had to convert this to kg, which would be 95.9kgm/s^2.
      Using this method worked extremely well, because the actual weight of our meter stick was 95.8kgm/s^2, so we were only .1 off of the real weight! The meter stick balanced because the torques were equal, and since the weighted end had a greater force and a smaller lever arm, the unweighted end had a longer lever arm and a lesser force, making them balanced. On the right is a fully labeled drawing of the diagram we used in order to figure out some of the parts.

Torque Resource

      This youtube video from Khan Academy is in introduction to torque, as he explains what torque is, the formulas, etc.
      This video is very helpful in understanding torque because of the lecture style of teaching, along with the drawings and commentary provided. I also found that the examples he drew were very helpful in understanding torque, and even the bright colors helped me stay engaged in the material.

Angular Momentum Resource

      This youtube video is a good example of angular momentum presented in a fun way.
      This video is very helpful in understanding angular momentum, because at first these kids are farther away from the axis of rotation, and then they move closer to the axis of rotation, resulting in a faster spinning of the merry go round.