Evidence of Work

Our Process

For our project, our first task was to come up with what we thought made a tree swing fun. From there, we were supposed to design a basic swing, one that could do translational motion and also rotational motion, and so we chose a tire swing. My group also chose a place to hang it up, which would be on metal poles outside our school's maker's space.

From there, we had to decide on a given length of the theoretical rope that our tire swing would be on, and then from there, we could do the rest of our calculations. First, we did the translational, or harmonic, motion. This was the data as the tree swing swung slightly back and forth after a 'push'. Next, we added a torque to the swing to make it swing in a large circle to add the rotational motion components. We were able to use other equations to determine our swings theoretical rotational motion, and after made a presentation with our findings for our theoretical swing (below, with calculations).

Content

Period

An object's period is the amount of time that it takes the object to do a full oscillation (harmonic motion) or a full rotation (rotational motion). This is essential when doing the calculations for pendulums because it sets the stage for the rest of the quantities that follow. The equation for period (pendulum) is: 2(pi)*(the square root of (length of rope / acceleration due to gravity)).

Velocity

Velocity is the speed an object is going at a certain time. For this translational motion piece, velocity was important because the highest point of velocity was when the pendulum was hanging straight down, and the velocity was zero when the pendulum was at its peak on both sides. The equation for velocity is: change in displacement / change in time. For the rotational motion aspect, the type of velocity changes to angular velocity.

Tension

Tension is important because it notes how much force the rope of the pendulum was holding at one time. Tension is the greatest at the bottom of the pendulum and is the least (but not zero) when it is at its peak on the sides. The equation for tension also changes depending on the location that it is measured from, but it can be related to the force that the rope has on it.

Arc Length/Swing Angle

The arc length and swing angle are correlated because a larger angle means a longer arc length and a shorter arc length equals a smaller angle. The bigger the arc length and angle, it is most likely that the period will be longer too, but that ultimately is dependent on the length of the rope.

Displacement

Displacement is the distance that an object has moved, whether that is horizontally, vertically, or both. There is no specific equation for displacement, but it can be either measured or calculated in multiple ways. For this, the displacement was the change in height that the pendulum made from when it was hanging at the bottom to when it was at its peak on the sides.

Angular Velocity

Angular velocity is the rotational speed that an object travels at a certain time. It is most often used in rotational motion, and so we were able to apply it to our swing when it swung in a large circle. The equation for angular velocity is: change in angle / change in time, but it can also be calculated using other methods too.

Angular Acceleration

Angular acceleration is the acceleration of an object that is in rotational motion. It is often used in similar situations as angular velocity and the equation for it is: change in angular velocity / change in time.

Torque

Torque is similar to force, but in rotational terms. The equation for torque is: force * radius, but it can be calculated in other methods too. In our project, when we applied a torque to our swing while it was in translational motion, this is what caused it to enter rotational motion to get it spinning.

Moment of Inertia

The moment of inertia of an object is that object's resistance to rotational motion, and it is slightly similar to the weight of an object for translational motion. The moment of inertia is calculated in multiple different ways and this depends on the object's shape and the axis that it is rotated about, but once this is found, it can be applied to find out the results for angular velocity, angular momentum, torque, and more.

Reflection

For this project, two things that I think went well were problem solving and critical thinking, and two things that I think we could have worked on were communication and collaboration. For problem solving and critical thinking, they kind of go together because they fall under the same category. My group was able to figure out all of the required concepts and fill in the blanks of the variables using the information we were given or had to make up. We didn't seem to run into much trouble with the calculations part and were often done early.

For things we could have worked on, in collaboration, I feel like all four of us worked mainly on our own and only shared ideas and work when we were stuck and needed the help, but other than that, the work we each did was our own even though it turned out to be mostly the same. For communication, this was a problem later when we were trying to put together a presentation because we all had done different work and so the slideshow was a little unorganized at first. However, we were able to figure it out and present a slideshow with all of the required material on it that showcased our idea for a tree swing with accurate calculations. Overall, I think this project turned out fairly well in the end, even if it was harder towards the beginning.