Slow Your Roll
Most falling objects move too fast to easily explore changes in position and speed. In this Snack, you can investigate the motion of a slow-moving wheel on a track by using a timer, tape, and permanent marker.
- Wooden disk, 4-5 inches (10-13 cm) in diameter (available online or in arts-and-crafts stores)
- Ruler
- Pencil or box cutter
- Thick block of scrap wood (or other protective drilling surface; not shown)
- Center punch
- 3/8-inch (1 cm) or longer wooden dowel
- Pencil sharpener with adjustable holes
- Electric drill and drill bits: 3/8-inch (10 mm); 3/4-inch (19 mm) spade bit; 9/64-inch (3.5 mm)
- Safety glasses
- Hacksaw
- Four blocks of wood 1 x 2 x 4 inches (2.5 x 5 x 10 cm)
- Four #8-32 set screws
- Four #8-32 wing nuts
- Two 3-inch (7.5 cm) mending plates with #8 holes
Note: The actual size of the set screws is not crucial, but it is important that the screws, the holes in the mending plates, and the wing nuts are all the same size. - 5/64-inch (2 mm) Allen wrench
- Two 5-foot (1.5 m) lengths of 1/2-inch (1 cm) rigid metal conduit pipe
- Stack of books or something to elevate the track (not shown)
- Timer
- Partner
- Permanent marker
- Blue painter’s tape
- Scissors (not shown)
- Large graph paper or poster paper
- Optional: Center finder
This Snack is divided into two parts. In Part I you’ll build the wheel; in Part II you’ll assemble the track.
Part I: Build the wheel
- Find the center of the wooden disk by using a ruler to measure the greatest distance across the circle (the diameter) and marking it with a pencil or box cutter. Then turn the disk 90 degrees and make a second line. The circle’s center is at the intersection of the two lines (see left photo below). Alternatively, you can use a device called a center finder to locate the center (see right photo below).
- Place the disk on a scrap piece of thick wood. Use a center punch to start a hole in the center of the disk. Then use a 3/8-inch bit (10 mm) to drill a hole through center (see photos below).
- Use a saw to cut the dowel to a length of 3 1/8 inches (8 cm). Use a pencil sharpener to create a point on each end of the dowel (see photos below).
- Slide the dowel through the hole in the disk, making certain that the lengths on each side of the disk are equal. This is the wheel (see photo below).
Part II: Build the Track
- Using the ruler and pencil, make a line marking the vertical center on the face of one 1 x 2 x 4-inch (2.5 x 5 x 10 cm) wood block. Make another line approximately 1 inch (2.5 cm) down from the top edge of the block (see photos below). Use the center punch to make a mark where the lines intersect. Then, using the spade bit, drill a 3/4-inch (2 cm) hole all the way through the block. Repeat this procedure with the other three blocks (see photos below).
- Turn one block to work along the top edge, above the hole you just drilled. Use the ruler and pencil to find the center, drawing two intersecting lines as in the previous step. Using the 9/64-inch bit, drill a hole into the top edge of the block. Drill all the way into the previously drilled large hole (see photo below).
- Place a set screw into the hole and use an Allen wrench to screw it into the top of the block. Make sure that the screw does not enter the hole (the pipe will fit there). Repeat this procedure with the other three blocks (see photos below).
- Place one block on each end of a length of conduit pipe, ensuring that the pipe is placed near the top of the block. Tighten the set screws until the pipes are held firmly in place (see photo below). Be careful not to tighten the set screws too tightly or you could strip the threads. Repeat this process with the second length of conduit pipe and the two remaining blocks.
- Place the pipes parallel to each other to form a track for the wheel. Insert the set screws through the outermost holes of the mending plate, and screw the wing nuts on top (see photo below). Make sure they’re secure, but loose enough so the track can be adjusted.
Collecting Data
Place both ends of the track on a stack of books so that the starting line is higher than the finish line.
Place the wheel on the track and adjust the track’s width so that the zones where the dowel tips begin to narrow are directly on top of the pipe (see photo below). When the track is correctly spaced, tighten the wing nuts to fix it in place.
Release the wheel so it rolls down the track. Make sure it’s centered and will roll on its own with minimal wobble and without being pushed. The wheel should take between twenty and thirty seconds to travel the length of the track. Adjust the height of the track or re-center the wheel as needed.
To begin investigating, position the wheel at the top of the track and let it roll down. What do you notice? How fast do you think it is moving? You can use this relationship to get an estimate:
$$\text{speed} = \frac{\text{distance}}{\text{time}}$$
Does the speed of the wheel seem to change as it moves down the track? How can you tell? One way to find out is to use your timer to measure the time it takes to travel the first half of the track and compare it to the time it takes to travel the second half of the track. What do you notice? What do you think would happen if you were to divide the track into quarters? Into eighths?
You can also track the wheel’s position over time. Add a piece of blue painter’s tape to the side of the track, along its whole length. With a permanent marker, indicate the starting point of the wheel (zero seconds). It should line up with the point of the dowel. As the wheel travels down the track, have a partner using a timer shout out “Now!” every two seconds. When he or she does this, place a mark on the blue tape. (You can also use a metronome app to obtain a more consistent time.) Continue this process until the wheel reaches the end of the track (click to enlarge the photo below). What do you notice about the spacing of the marks as the wheel travels down the track?
Constructing Graphs
Cut a new piece of blue tape to match the length of the section of pipe that stretches from the zero-second mark to the first two-second mark. Place this new piece of tape on the left-hand side of the graph. This represents the position of the wheel at two seconds.
Repeat with another new piece of tape that stretches from the zero-second mark to the next two-second mark. Place it on the graph to the right of the first piece of tape. This represents the position of the wheel at four seconds. Repeat this process for each two-second interval, remembering to always begin at the zero-second mark. If the wheel reaches the end of the track before the end of a two-second interval, don’t use that data point.
Look at the completed graph and consider what it represents. Do you notice a pattern? Does any of the data seem to defy the pattern? What do you think you should label the x-axis? The y-axis? What should be the title of your graph? What does this graph tell you about the speed of the wheel as it moves down the ramp?
To further investigate how the speed of the wheel changes over time, create a second graph showing the distance traveled within each two-second time increment.
Return to the tape you originally marked on the track. Look at the first two-second interval and, with your scissors, cut it off at the first two-second mark. This represents the distance the wheel traveled in the time interval between zero and two seconds. Remove this tape and place it on a new graph. Now cut off the tape that represents the distance traveled in the next two-second interval (from two to four seconds) and place it to the right of the first piece on the graph. Continue this process to the end of the tape. If the wheel stopped before the end of a two-second interval, do not use that data point.
Look at the completed graph and consider what this graph represents. What do you notice? Is there a pattern? What does this suggest about the wheel’s speed and how the speed is changing as it moves down the ramp? Does any data seem to defy the pattern? How would you label the x-axis and the y-axis for this graph? How would you title the graph?
With this experiment, you’re replicating motion studies performed by the Italian physicist Galileo Galilei—studies that ultimately led to our understanding of the relationship between position, speed, and acceleration.
You probably noticed that, as the wheel traveled down the ramp, it sped up—that is, it accelerated. You also probably noticed that the wheel traveled faster in the second half of the journey than in the first. Pulled by gravity, the wheel’s speed increased at a constant rate, which caused the wheel to cover increasing distances during each equal time interval.
Assuming that air resistance and friction are small, and that the marks are placed in the right spots, your first graph should look like an upward-sweeping curve, representing the fact that the distance traveled by an accelerating object increases as the square of the time elapses (see photo below). Since each bar represents a two-second increment, the x-axis should be labeled time. The y-axis represents the position or distance the disk has traveled.
Your second graph shows the increasing speed of the wheel during each time interval. Each bar represents the distance traveled per two-second interval. Distance divided by time is speed, and this should be the label for the y-axis. The x-axis is still time since each bar represents a fixed interval. This graph should increase roughly like a straight line (see photo below). The slope of this line is the (constant) acceleration of the wheel.
While this method of using the tape helps build a more intuitive sense of the motion of the wheel, errors in timing and marking can reduce its accuracy. You probably noticed those inaccuracies in the graphs. One way to improve the accuracy of this method is to use video. By placing a large timer behind the track, video-recording the motion of the wheel, and analyzing the video with software, you can obtain a more accurate record of the motion.
When using this activity with students, we recommend building one track and wheel for each group of four students.
To slow the wheel even further, drill symmetrical holes in the outside edges of the wheel and add heavy bolts. If you do this, be warned that sometimes the wheel may be weighted in such a way that it rolls backward when placed at the top of the track. Just turn it slightly until you hit a position that will allow it to roll downhill without a push. Mark the top with a permanent marker so that students know the best starting position.
For middle school students, there is little emphasis placed on the difference between speed and velocity. While velocity does include a directional component that speed does not, the terms are interchangeable in this activity.
Students may need some background in interpreting position and velocity graphs before they begin. Simple activities in which they map walking or running over a period of time may help build these ideas.
Most of the supplies for this Snack are available at hardware stores, arts-and-crafts stores, and online, though some sizes of materials may be more difficult to find than others. The American Modeling Teacher Association has other versions of wheels on their website that use steel rods and CDs or golf tees.
