Circular Motion Lab
By Andy, Aayush, Carol, Adithya K.
December 3, 2021
December 3, 2021
Research Question: How does the speed of an object in circular motion affect the acceleration?
Variables
Independent - Tangential Speed (m/s)
Dependent - Acceleration (m/s^2)
Controls - String, radius, mass, environment (no win)
How did we control the variables?
In order to control our variables, we kept the string, radius, and mass of the stopper constant. Different strings have different tensions. That's why we made sure the string was the same throughout the experiment to keep the net force constant. It is also important to keep the radius of the swing the same. The smaller the radius, the smaller the circumference, and less amount of time that is needed for the stopper to finish one rotation. The mass of the stopper also must be constant because the stopper impacts the downward gravitation force of the system. The force of gravity is the mass times the gravitation constant (g or 9.8). Finally, the environment must be kept the same to make sure there is no difference air resistance that could change the net force of the stopper.
Data Collection
When we were collecting the data, we had to make sure that our speed and acceleration were correct. We calculated the speed by measuring the amount of rotations per second, and then multiplying it by the circumference (2πr) to change rotations per second to meters per second. Since we kept the radius constant, we just had to ensure that the rotations per second was accurate. We did this by setting up a metronome, and swing the stopper so that it would finish one rotation every beat. While someone swung the stopper, a person was in charge of counting the rotations and another person was in charge of the time. This allowed us to find the rotations per second. We found the acceleration by using the formula a = ΣF/m. We found the net force by using a force sensor the measure the tension force of the string, and weighed the stopper to obtain the mass. By diving the ΣF by mass, we can find the acceleration of the object.
Procedure
1. Set radius of the string at a fixed distance of 0.5 m
2. Attach a motion sensor to the bottom of the string to determine the tension force
3. Start the metronome at different beats per minute (90, 100, 110, 120 bpm)
4. Swing the string to rotate once every time the metronome beats once such that the string is always taut
5. Start counting the number of rotations and start the stopwatch at the same time
6. After at least 25 rotations, stop the string
7. Record the time, number of rotations, beats per minute, radius, and tension force
Independent - Tangential Speed (m/s)
Dependent - Acceleration (m/s^2)
Controls - String, radius, mass, environment (no win)
How did we control the variables?
In order to control our variables, we kept the string, radius, and mass of the stopper constant. Different strings have different tensions. That's why we made sure the string was the same throughout the experiment to keep the net force constant. It is also important to keep the radius of the swing the same. The smaller the radius, the smaller the circumference, and less amount of time that is needed for the stopper to finish one rotation. The mass of the stopper also must be constant because the stopper impacts the downward gravitation force of the system. The force of gravity is the mass times the gravitation constant (g or 9.8). Finally, the environment must be kept the same to make sure there is no difference air resistance that could change the net force of the stopper.
Data Collection
When we were collecting the data, we had to make sure that our speed and acceleration were correct. We calculated the speed by measuring the amount of rotations per second, and then multiplying it by the circumference (2πr) to change rotations per second to meters per second. Since we kept the radius constant, we just had to ensure that the rotations per second was accurate. We did this by setting up a metronome, and swing the stopper so that it would finish one rotation every beat. While someone swung the stopper, a person was in charge of counting the rotations and another person was in charge of the time. This allowed us to find the rotations per second. We found the acceleration by using the formula a = ΣF/m. We found the net force by using a force sensor the measure the tension force of the string, and weighed the stopper to obtain the mass. By diving the ΣF by mass, we can find the acceleration of the object.
Procedure
1. Set radius of the string at a fixed distance of 0.5 m
2. Attach a motion sensor to the bottom of the string to determine the tension force
3. Start the metronome at different beats per minute (90, 100, 110, 120 bpm)
4. Swing the string to rotate once every time the metronome beats once such that the string is always taut
5. Start counting the number of rotations and start the stopwatch at the same time
6. After at least 25 rotations, stop the string
7. Record the time, number of rotations, beats per minute, radius, and tension force
Recorded Raw Data
The tempo was set by the metronome. We used a stop watch to record the total time, and one of our lab members counted the number rotations. The tension force was obtained by attacking a force sensor to the bottom of the string. We kept the radius constant at 0.5 m, and the mass of the stopper constant at 0.01 kg.
Uncertainty: Some uncertainty arose from the reaction time of the person on the stop watch, the shift in the radius of the string as it was spun around, and the accuracy of the tension force. The person who recorded the total time using the stop watch had a delayed reaction time resulting in differences in total time. As the string was spun around, the radius increased and decreased at certain points as the person spinning the string tried to keep it constant. Lastly, the force sensor may have not obtained the correct tension force as it was only recorded to one decimal point.
The tempo was set by the metronome. We used a stop watch to record the total time, and one of our lab members counted the number rotations. The tension force was obtained by attacking a force sensor to the bottom of the string. We kept the radius constant at 0.5 m, and the mass of the stopper constant at 0.01 kg.
Uncertainty: Some uncertainty arose from the reaction time of the person on the stop watch, the shift in the radius of the string as it was spun around, and the accuracy of the tension force. The person who recorded the total time using the stop watch had a delayed reaction time resulting in differences in total time. As the string was spun around, the radius increased and decreased at certain points as the person spinning the string tried to keep it constant. Lastly, the force sensor may have not obtained the correct tension force as it was only recorded to one decimal point.
Processed Raw Data
Rotations per second: rotations (2πr) / total time (s)
Tangential speed: 2πr * rotations per second
Acceleration: ΣF / m = Tension Force / mass of stopper (0.01 kg)
Rotations per second: rotations (2πr) / total time (s)
Tangential speed: 2πr * rotations per second
Acceleration: ΣF / m = Tension Force / mass of stopper (0.01 kg)
Presentation of Processed Data
This graph shows the relationship between speed and acceleration. A nonlinear, quadratic model was used for the data. The formula for a simple quadratic model is y = Ax^2. The A value in the equation is 3.227.
This graph shows the relationship between speed and acceleration. A nonlinear, quadratic model was used for the data. The formula for a simple quadratic model is y = Ax^2. The A value in the equation is 3.227.
Conclusion
The goal of our experiment was to find the relationship between speed and acceleration with objects in circular motion. We obtained the speed by dividing dividing the circumference by the rotations per second. This allowed us to find the tangential velocity. We obtained the acceleration by using the equation ΣF / m where the ΣF is simply the tension force and the mass is a constant 0.01 kg. While the mass is held constant during the experiment, ΣF is changing, which increases the acceleration. This acceleration, however, is a centripetal acceleration towards the center that the object is rotation around. The ΣF is acting towards the center of motion, while there is a tangential speed that is perpendicular to the radius. Newton's First Law of Inertia that stay that an object will keep traveling at a constant velocity unless it is acted upon by an unbalanced force. Therefore, without an unbalanced force the stopper would keep traveling in a circular motion. If the string was broken, however, the stopper would travel in the direction of the tangential speed, which is perpendicular to the radius. This is because without the tension force towards the center, the only force acting upon the stopper would be the force of gravity. That being said, centripetal acceleration is able to explain why we feel a pull towards the center of a circular motion. In the example of the merry-go-around, centripetal acceleration allows us to stay inside the merry-go-around even when it is spinning very fast. That's because although tangential force is moving perpendicular to the radius, the ΣF and the acceleration is towards the center, allowing us to stay not be thrown from the merry-go-around.
The goal of our experiment was to find the relationship between speed and acceleration with objects in circular motion. We obtained the speed by dividing dividing the circumference by the rotations per second. This allowed us to find the tangential velocity. We obtained the acceleration by using the equation ΣF / m where the ΣF is simply the tension force and the mass is a constant 0.01 kg. While the mass is held constant during the experiment, ΣF is changing, which increases the acceleration. This acceleration, however, is a centripetal acceleration towards the center that the object is rotation around. The ΣF is acting towards the center of motion, while there is a tangential speed that is perpendicular to the radius. Newton's First Law of Inertia that stay that an object will keep traveling at a constant velocity unless it is acted upon by an unbalanced force. Therefore, without an unbalanced force the stopper would keep traveling in a circular motion. If the string was broken, however, the stopper would travel in the direction of the tangential speed, which is perpendicular to the radius. This is because without the tension force towards the center, the only force acting upon the stopper would be the force of gravity. That being said, centripetal acceleration is able to explain why we feel a pull towards the center of a circular motion. In the example of the merry-go-around, centripetal acceleration allows us to stay inside the merry-go-around even when it is spinning very fast. That's because although tangential force is moving perpendicular to the radius, the ΣF and the acceleration is towards the center, allowing us to stay not be thrown from the merry-go-around.
Evaluating Processes
One of the limitations of our lab was the inaccuracies that stemmed from the swinging of the stopper. The radius was constantly changing because it was difficult to keep the radius constant while spinning the stopper. On top of that, there is also error that comes from the reaction time of human beings when clicking the stop watch. In the end we only obtained 4 trials which was not enough data. We had to settle with the simple quadratic fit as our model to predict the relationship between speed and acceleration. Also since 90 bpm was our first trial, errors may have resulted from that trial since we were inexperienced in data collection at first. Finally, the force sensor could have given us the incorrect tension force because we had difficulty calibrating it in the beginning.
Improvement
In order to improve our experiment, I would have done repeated trials in order to obtain a more accurate data for each trial. On top of that I would have used a wider range of speeds (bpm) in order to obtain more data points at higher speeds to confirm our prediction. If possible, it would have been better to use a robot to swing the object because the robot would do a more consistent job of applying to extra force and keeping the speed constant to match the metronome. Lastly, I would use a motion detector with a more decial points in order to obtain a more accurate tension force.
One of the limitations of our lab was the inaccuracies that stemmed from the swinging of the stopper. The radius was constantly changing because it was difficult to keep the radius constant while spinning the stopper. On top of that, there is also error that comes from the reaction time of human beings when clicking the stop watch. In the end we only obtained 4 trials which was not enough data. We had to settle with the simple quadratic fit as our model to predict the relationship between speed and acceleration. Also since 90 bpm was our first trial, errors may have resulted from that trial since we were inexperienced in data collection at first. Finally, the force sensor could have given us the incorrect tension force because we had difficulty calibrating it in the beginning.
Improvement
In order to improve our experiment, I would have done repeated trials in order to obtain a more accurate data for each trial. On top of that I would have used a wider range of speeds (bpm) in order to obtain more data points at higher speeds to confirm our prediction. If possible, it would have been better to use a robot to swing the object because the robot would do a more consistent job of applying to extra force and keeping the speed constant to match the metronome. Lastly, I would use a motion detector with a more decial points in order to obtain a more accurate tension force.