Unit 4 Reflection

This unit in physics I learned about…

Rotational and Tangential Velocity:
We began our unit by differentiating between tangential and rotational velocities.

Tangential Velocity: How much distance you cover
Rotational Velocity: Number of rotations per unit of time

We learned, for example, that when on a merry-go-round, the outside travels a greater distance vs. the inside. Therefore, since the outside has a greater distance to travel in the same time that the inside

travels, its tangential speed will be larger. Both outside and inside will have the same rotational speeds because they're rotating the same number of times, just at different speeds. We learned the same concept with a different example shown in the picture to the right. With the two gears, one has 24 prongs and the other, 12. This is a 2:1 ratio, and that means that the smaller gear, in two rotation, goes around twice as much as the larger gear which only went around once. This means that: The large gear has a smaller rotational speed vs the smalls gears large rotational speed. The tangential speeds for both gears are the same because any point along the edge of rather gear will cover the same distance in the same time interval.

Train wheels are made in a way that self corrects themselves. The larger part of the wheel is on the inside and the skinny part in on the outside. This is because when the train starts to go off track, the larger part of the wheel will be on the track at the same time that the small part is. The larger part of the wheel has a greater distance to cover in the same time as the small wheel, therefore it will move faster, and thus move itself back on track.

Rotational Inertia and Conservation of Angular Momentum:
The main thing to remember about rotational inertia is that there is a larger rotational inertia if the mass is farther away from the axis. This explains why ice skaters pull in their arms to spin faster.

Rotational Inertia: Property of an object to resist changes in the spin

Spinning velocity is all about the distribution mass. When an ice skaters arms are away from her axis of rotation, she will slow down, and she will have a large rotational inertia. But when an ice skater pulls her arms in toward her axis of rotation, she will move fast and have a smaller rotational inertia.

Angular momentum before = angular momentum after

This means that if you have your arms away from your axis of rotation, you will have a small rotational velocity and a large rotational inertia. Therefore, when you pull your arms towards you, your rotational inertia and rotational velocity will have to be opposite of the before (spinning with arms away) in order to have both momentums equal. So the equation will look something like this:

Rotational Velocity x Rotational Inertia = Rotational Velocity x Rotational Inertia

In the video form the movie Ice Princess, the ice skater demonstrates her rotational velocity increasing when she pulls her arms in vs when her arms are away from her. (Start at :35)

Torque and Center of Mass:

Torque = force x lever arm (distance form axis of rotation)

When you are trying to unscrew a screw with a wrench, what do you do to make it easier? There are two things that can help this, one is to add more force, and the other is to increase the lever arm, or do both. By doing these things, you will increase your torque and thus, make it easier to unscrew the screw.

The center of mass is the average position of an objects mass. So in the picture to the left, the three boxes have different centers of mass, and this either makes it easier of harder to push them over. For A and B the center of gravity is within the base of support, therefore the boxes will not fall over. But box 

C's center of mass is not within the base of support, therefore the box will fall over. In the example below that, the boxes all have the same center of gravity in the center of the box. The only difference is the angle of the box. In order for the box to stay up, the center of gravity must be within the base of support, and the only examples of this is in box A and B. Box C has a center of gravity that is out of the base of support and therefore will fall over. This is why in sport such as football, the players stand with their feet wide 

apart. This is done in order to create a wider base of support so that their center of gravity will be harder to move out of. They also bend their knees, and this is done so that their center of gravity is also closer to the ground so it is harder to knock them over. With a baseball bat balanced at its center of gravity. The side with the heavier end will weight more even though it is shorter. This is because the force on that side makes up for the short lever arm. Both sides have to have an equal torque, so therefore the baseball bat balances because one side has force and the other, a lever arm, thus creating no net torque. 

In the example below, a long stick is balanced. To find how many meters the ball is away form the fulcrum to make the system balanced, we use these steps and equations:


counter clockwise torque = clockwise torque

lever arm x force = lever arm x force  --> before and after

1x = 2(4)
x = 8m

These steps are the same to find the weight of the meter stick, just plugging in different numbers. 

Centripetal/Centrifigual Force:

Centripetal force: Center seeking force that keeps you going into a curve.

Centrifugal force: center fleeing force (fictional)

An example that we learned that helps to understand centripetal forces is: You are riding on a bus and suddenly wake up form your nap because the bus just turned. The force that causes you to slam into the person sitting next to you is the centripetal force. This is because the bus is moving towards the center, and you are still moving straight, so you hit the person next to you. Nothing causes me to hit the person, only the fact that I was moving one way and the bus was moving the other. 

An example to understand centrifugal force is: when the water flies out of a washing machine, there is no centripetal force, therefore the water moves in a straight line path and moves out of the washing machine.

The reason why a racetrack is elevated in because the cars need more centripetal force than friction or they would fly off the track into the stands. So in the picture, the fgravity is going straight down and the fsupport is going perpendicular to the car. When these vector are added together, the direction formed is in the direction of the center, thus the centripetal force. This force and the velocity going straight help the car to go in a curved path.

Difficulties this unit…

I found it hard to wrap my head around centripetal and centrifugal forces. But I was able to get past this by asking my piers and also going online and looking up videos about it and watching my piers blogs postings on it to gain there feedback and ideas about it. I was able to persist through the mass of a meter stick lab with my group by thinking about all the equations that we had learned thus far and putting it all together. This helped me to gain confidence, and this new found confidence has helped me to understand the unit better than other units before. My goals for the next unit are to improve my open note quiz grades by taking much better notes. The open note quizzes are very important because they help me to see where I am and what I need to know. But this will be easier if I already understand because of the helpful noted I take before.

Connections…

This unit, I was able to make a connection in the real world one day on the weekend when I was playing soccer with a friend. The friend I was playing with is very tall and I was able to knock him over because of physics. Because he did not have his feet spread apart to widen his base of support, and bend his knees to bring his center of gravity closer to the ground, I was able to knock him over. I found this the most interesting and personal even though I continued to find physics all over in the world around me.

Mass of a Meter Stick Problem

Part 1:
During this lab, the first thing that we did was test at which point the meter stick would not balance on the edge of the table. When the meter stick did not balance, its center of gravity was off the edge, and therefore it had a counter clockwise torque. Then, we tested at which point the meter stick would balance, and we discovered that when the center of gravity was in line with the pivot point, the stick stayed balanced, and therefore had no torque. The first example had a torque because it had both a force (gravity) and a lever arm (distance pivot point is away from the center of gravity where it starts to fall). The second example did not have torque because even though there was the force of gravity acting on it, it however didn't have a lever arm and therefore had no torque.

Part 2:
Next we added a 100 gram mass to the edge of the meter stick and watched how the balance point changed. To find the torque of the meter stick, we used the equation:

Torque = Force x Lever Arm 

We discovered that the meter stick balanced at 29.5 cm away from the pivot point. With this information we plugged in numbers to the equation. For force, we used gravity, 9.8, and for lever arm, we used the distance away fro the pivot point which was 29.5. The next thing we did was plan how we were going to find the mass of the meter stick. My group and I decided that the equation that we needed was the Angular Momentum equation.

For this equation, we needed to know the lever arm both before and after. To find this we used our knowledge that the center of gravity was acting on the 50 cm point. And since the lever arm for before (when it is balanced) was 29.5 cm, we subtracted 29.5 from 50 and got 20.5 to find the lever arm for after (distance from pivot point to center of gravity. We knew this because no matter how much mass we put on the stick, its mass by itself will remain the same. Now, since we already knew the force for before (9.8=gravity) we were now just solving for the force after.

Part 3:
Now, all that was left to do was plug in numbers and solve for the mass of the stick. Using the equation:
Counterclockwise torque = Clockwise toque 
                             .  .  .
Lever Arm  x Force = Lever Arm x Force
         before                           after

29.5 x .98 = 20.5x

28.91 = 20.5x
20.5       20.5

x = 1.41 N

Now we know the weight of the stick, we have to convert Newtons to kilograms. To do this we had to use the equation:
w = mg

Plugging in the numbers, we got,

1.41 = 9.8m
 9.8      9.8

There for the mass of the meter stick = .143 kg

Torque vs Twerk?

This video in a creative/strange way, explains torque and lever arms. A lever arm gives a better torque, meaning that when you are unable to unscrew a screw, increasing the length of the lever arm will here increase the torque, therefore help move the screw much easier. 

Angular Momentum

 In this video on Angular Momentum, Hewitt explains how there is linear momentum and angular momentum. When an object is moving in a circular movement, the object has momentum (mass x speed). Looking closer, the object has angular momentum since it is rotating an axis. This is represented by linear momentum x radial distance. Angular momentum = m x v x r. We also know that a net force is needed to change linear momentum, and the same goes for angular momentum: a net torque is needed to change its angular momentum.