3) Centripetal acceleration is the rate of change of tangential velocity. The speed remains a constant magnitude but the direction changes as the object rotates. In order to prove this mathematically, we use the radius (r) from the center of the circle to the end of the circle, and define r in horizontal and vertical components. Since r will be out position of theta over time as the object rotates, we derive it until we get our acceleration which is omega square over r. Here is a picture with a better demonstration of our proof.
4) We will prove in this lab that our theory is correct. We use an apparatus of a circular motor platform. A mass is nearly on the edge of the circular platform with a string attached to the center of the circle. In the lab we changed the radius, angular velocity, and the mass to get different results and what relationships these components give to each other.
. The device that is by the center is a logger pro device to detect the force between the string and the mass and the angular velocity. Since the centripetal acceleration points towards the center of the circle, its intuitive that there is force also acting towards the center of the circle as well.5) In each test experiment, we wrote down the values we calculated according to logger pro's devices and the settings we adjusted.
. The components that are measured in the experiment are mass in grams, the radius in meters, a machine that varies different voltage readings to control the rotating motor of the circular platform, 10 revolutions as one reading, total time for 10 rotations, and the force the device read as it spanned which should be constant.6)
We graphed three different relationships these values share in the equation. The force vs angular velocity increases as your increase the magnitude of the angular velocity. I only used for rows to graph since the mass and the radius is the same for each test result. The slope is the relationship of the mass and the radius. Here is an example.
According to the data of the four rows recorded in the graph, the slope should be 0.108 kg*m and the slope the graph represents is 0.115. So our error percentage is around 7 percent. The same concept applies to the other graphs except the x-component is now the radius and mass.8) According to our theory we represented, the lab proves our theory is accurate when we want to find the relationship between the centripetal acceleration and angular velocity. Not only does the angular velocity shares a relationship but also the radius. The mass can also share a relationship, but mathematically, the mass values end up canceling out so it's not really a necessary value.
Show how the slope of the first graph should be 0.108
ReplyDeleteSaying that "The same concept applies to the other graphs except the x-component is now the radius and mass" is not the same thing as actually analyzing your data.