Lesson 12 of 12
Objective: SWBAT compare circular motion to straight line motion, explain how F=ma works in circular motion, and identify the role of friction in turning motion.
In this lesson students focus on how F=ma applies in situations where an object turns or moves in a circle.
Goals for the lesson
- Understand the parallels between circular and straight line motion.
- Understand how F=ma works in circular motion.
- Understand the role of friction in turning motion.
- A small unbreakable object (metal washer) tied to about 50 centimeters of string.
To begin, engage students by drawing the image below on the board and then provide the following prompt:
Imagine yourself in a car, driving at a steady speed along a country road. Most country roads aren't straight, so you would certainly go around curves quite frequently. Is your car accelerating when it goes around the curves? (If you took your accelerometer for a ride in a car think about what happened to the cork as you rounded a corner; what did this tell you about the direction the car accelerated?) What force is moving your car along the curves, rather than in a straight line?
Give students time to think and write and then call on students to share their ideas. The goal here is not to correct their thinking, or to teach. The objective of this exercise is to get students thinking about the problem, and surfacing their ideas so that you, and they, are aware of their conceptions related to this topic.
The path is complex, so a physicist might first try to understand it by defining a simpler system that focuses on only some aspect of the motion. One of these simplifying perspectives on motion is viewing any kind of complicated curving path as a series of small parts of circles. For example, the car traveling on the country road in this diagram can be thought of as traveling along parts of three circles.
If we can figure out what is happening when the car is traveling on each of the circles, we can understand how such a complicated motion could happen—what velocity, acceleration and force are involved.
In this session, students investigate how F = ma works when an object is moving in a circle or around a curve.
To explore this phenomena further, students imagine what will happen to an accelerometer as they spin in a circle. Students first predict the position of the cork, then grab an accelerometer and observe it while spinning. You may want to speak to your students about safety first, and space students out so they can safely move.
Students first record their predictions and then their observations in their journals.
Next, they imagine a scenario of a children's playground game called "Crack the Whip". In this game, students hold hands and spin around a central point. The student for this from this point experiences quite a bit of force. If they are not familiar with this game you may need to explain to them. We use this scenario to imagine the forces of this turning motion. They record their ideas in their journal.
Third, students use a simple manipulative, a string and a metal washer, to describe motion as the washer spins around the circle focusing on its speed, velocity and the forces at different positions as the washer spins around the central point. Again remind students of safety as they want to keep the washer and string on the table and not let them spin them in the air.
Students record their observations and notes in their journals.
Finally, they examine this Twirling Object Video (we used a spool of wire) and make a strobe picture of the video.
To see in which (approximate) direction the spool is moving between frames, they draw a line between its position in one frame and the next. They then use this information to answer the following questions in their journals.
This Centripetal Force video goes into greater detail. Use it both for your own learning and to share with students.
- How would you describe the velocity (speed and direction) of the spool as it goes around the circle?
- If the velocity changes, there is some acceleration, so some force must be involved; what force(s) do you think might be acting on the spool to get it to accelerate?
- What is the direction of the force?
Ask student to pull together their evidence from these three examples to think of all three examples of circular motion: the accelerometer, Snap the Whip, and the twirling spool.
- In what ways are they similar?
- What could be the force in each of these situations that causes the cork, the person or the spool of wire to move in circle?
In their journals, students draw a force diagram for each of these three situations and indicate how force and acceleration are related in each case.
Have them explain their thinking when finished.
This Turning Motion PPT is an exemplary example of student work created using Keynote.
Conclude this lesson by asking students to summarize their ideas.
How does F=ma work in these cases of circular motion? With their table group, sum up the relation between force and velocity in the following three cases:
- If the force is in the same direction as the object's velocity, what happens?
- If the force is directly opposed to the object's velocity, what happens?
- If the force is in some other direction than the object's velocity, what happens?
Think again about their ride on the country road, driving at a steady speed. In their journals, record their ideas for the following:
- In what direction is your car accelerating as it goes around the curves.
- In what direction is the force that makes it accelerate in this way?
- Where does the force come from that makes the car move in a curve? (Hint: think about friction.)
Give students time to think, write and share.