LABORATORY 4: ROTATIONAL MOTION PLAYGROUND DYNAMICS: THE MERRY-GO-ROUND Written May-June 1993 by Melissa Wafer '95 In this laboratory period, you will use something that should be familiar to you to explain something that is new and mysterious. You will rely on your knowledge of translational dynamics to develop an understanding of rotational dynamics. We'll also assume you're already pretty proficient on the playground; you know how the equipment works. Now it's time to figure out why - not to eliminate the mystery, but to make you even more curious. GOAL: This lab should help you to become acquainted and more comfortable with the concepts, terms, and mathematics used in the study of rotational motion. There are many concepts in rotational motion that you will touch upon briefly in this lab, but this is only the beginning. Often, they will not be spelled out for you; the questions in the lab will try to lead you in the right direction so that you can figure out for yourself the principle that is being illustrated. You should be able to draw on the knowledge you have gleaned from the readings and the classwork to help you answer the questions and draw conclusions about your observations. Hopefully there will be time at the end of the laboratory period for you to play and explore. Take advantage of this freedom and experiment with the ideas that interest you. This is mentioned now so that you will be thinking about it as you go through the lab. When you finish with the outlined exercises, delve deeper into one of the areas in this lab or start fresh with another one, and devise a method for testing it. Make as many observations as you can (even if they seem obvious at first) and then try to explain them. Use data, equations, and laws of motion to back up your argument as much as possible. This is your chance to really show some creativity and insight. A. You have a stopwatch and a meter stick at your disposal. Give the merry-go-round a good enough push so that it makes it around three times easily without stopping, and calculate its average angular velocity (angular distance traveled/time elapsed) v = φ / t in radians/second for the first three revolutions. What is its average period of revolution? Its mean frequency of revolution? Then calculate average translational velocity of a point on the edge of the merry-go-round (distance traveled/time elapsed) v = s/ t in meters/second.
B. Does the merry-go-round seem to maintain the same speed throughout its three revolutions? Although it is more difficult to determine (because you don't have unlimited observers and stopwatches), we can gain a more accurate representation of the merry-go-round's motion by studying its instantaneous angular velocity, ω = dφ/dt. Explain how you might make a better approximation of the merry-go-round's instantaneous angular velocity with the limited resources you have in your lab group. (Hint: What makes dφ/dt different from φ / t?) C. Instantaneous translational velocity v = ds/dt is a vector quantity and so it should include both direction and magnitude. If every point on the merry-go-round moved with the same velocity at any given time, you would observe motion without any rotation; however this is not the case. Design and execute an experiment to determine the instantaneous translational velocity of some point you define on the merry-go-round not on the axis of rotation. You have at your disposal a meter stick, a stopwatch, some masses and string. Draw a vector diagram to indicate the direction (with arrows) and magnitude (the length of the arrows) of its instantaneous translational velocity at various points on the merry-goround. D. You should have noticed that the merry-go-round slows down with each successive revolution. Explain this observation while keeping in mind the following: Newton's First Law of Motion - The Law of Inertia: A body at rest will remain at rest unless some unbalanced external force acts on it; a body in motion will remain in motion (at constant velocity) unless some unbalanced external force acts on it. E. What does it mean for angular momentum to be "conserved?" Is angular momentum conserved in this case? F. Now you need to figure out how you might best approximate the deceleration (negative acceleration) a = dv/dt of the merry-go-round using the limited resources of your group. Refer back to part B for ideas. Be sure to explain your method. Note that the phrasing of the previous question encourages you to think only of the tangential component of a. Draw a diagram of the rotating and decelerating merry-go-round showing how a has both tangential and radial components, which sum to give a total acceleration!
G. Give the merry-go-round a push to send it spinning. Look at the two pictures below and explain why you push it one way rather than the other. Use a mathematical equation to back up your argument and explain the symbols involved. Hint: A diagram with vectors would probably help. H. Next take the metal bar that is available and fit it into the hole in the center pole of the merrygo-round so that the bar lies along a line parallel to a radius of the merry-go-round. This bar will help you to push in the most efficient manner, as determined in the previous section. Try exerting a force at various points along the bar (that is, at various distances from the axis of rotation) Try pushing as near to the center as possible and then gradually move outward along the bar. What do you notice? Record your observations and back them up mathematically. (Hint: Use the definition for torque.) I. It doesn't take a Hercules to make this merry-go-round spin. How about after you pile on a couple of weights - is it any harder to push? Now rearrange the weights. Is it easier to push the merry-go-round when they are lined up along the perimeter or when they are all heaped in the center? Why? What is the name for this? What equation explains what you observe? Try making a couple measurements and comparisons if you have the time. Try using a person as a "weight." What does this person feel as she moves on the rotating merry-go-round? J. What happens to a ball placed on a spinning merry-go-round? Why does this happen to a ball, and why doesn't it happen to the weights you placed on the rotating merry-go-round? Explain what force is holding the weights on the merry-go-round. Give an equation to determine its magnitude and tell its direction. Make sure that you talk about the force that is acting on the weights. Hang a mass from a few feet of string and stand on the merry-go-round. Notice the position of the mass with respect to the surface of the merry-go-round as it hangs freely. Now have someone start you rotating on the merry-go-round as you hold the weight on the string.
Notice how the position of the mass relative to the merry-go-round changes. Explain this change (use a free body diagram to help). K. The last section asked you about the force the merry-go-round was exerting on the weights; now how about the force the weights were exerting on the merry-go-round? We know there must be a reactive force according to Newton: Newton's Third Law of Motion : Every action has an equal (in magnitude) and opposite (in direction) reaction. L. Now go back and reread the paragraph just before section A. You're on your own! Good luck... Uncertainty : Remember to include an assessment of the uncertainty of your work. Be quantitative whenever possible (probably unlikely in this lab) and qualitative about the rest. Also mention possible sources for your uncertainty.
Lab 4 Checkout: Rotational Motion I While your TA is looking over the work you have done in the lab, please complete this sheet. Use only your own brain. Your answers to the first three questions will be graded as part of your lab, and your answers to all the questions will help us gauge the effectiveness of this lab. 1. What is the simple equation that links translational and rotational motion? Explain what it means in words or draw an explanatory diagram. 2. Tell two things you know about torque. You may use pictures, words, or mathematical equations. 3. What are the standard units for angular displacement, angular velocity, and angular acceleration? Comments or Suggestions: How did you feel about the lab? What was good about it? What would you change?