Rotational Motion

Instructor: Jodi Christiansen (11/14/08)

Click here for the simulation: Then Click on “Run Now.”

1. Try turning the disk with your mouse. If you push back and forth you’ll see crazy acceleration and velocity vectors appear on the ladybug that are “real” but hard to understand. If you throw the disk and then watch it rotate without your intervention you can probably figure out the velocity and acceleration vectors. Where do the vectors point when the disk rotates counterclockwise? Where do they point when the disk rotates clockwise? Explain why the vectors point where they point. You may need to review chapter 3.4.

2. Click “Reset All” near the bottom to clear everything out. Click on the tab that says “Rotation” near the top of the simulation. There’s a slider on the bottom near the plots that sets the “sim speed.” Go ahead and set the “sim speed” to fast because this one runs pretty slowly.

a. Use the textbox to set the angle to 100, 250, and 360. What happens?

b. Set the angular velocity to 150. Click “go”. What happens?

c. What are the units of angle and angular velocity?

d. Let the simulation run until the plot has reached at least 10 seconds on the time axis. Explain the waves in the “Position” plot of x_ladybug and y_ladybug.

3. Clear the plots. Next, under “Show graphs”, switch from “q, w, x & y” to “q, w, a.” Use the text boxes to set q = 100, w = 150, a = -30. Start the simulation and let it run until the plot has reached 20 seconds on the time axis. These plots should look similar to the moving man simulation that we did earlier.

a. Explain how the “Anglular velocity” plot relates to the clockwise/counterclockwise motion of the ladybug. You may want to use the “Playback” feature.

b. At what time does the motion stop and turn around? What features in the plots indicate that the motion has a turning point?

c. What are the rotational kinematic equations for constant angular acceleration? You may need to look at chapter 9.1-2. Why do they apply to this situation?

d. What are q₀ and w₀ for the simulation plots?

e. Please compute q at the times listed in the table and compare it to the values in the plot.

time (s)	Calculated q (deg)	q from plot (deg)	Do they agree?
2.5
5
10

4. Clear the plots. Place the beetle on the disk near the outer edge the ladybug pretty close to the center of the disk. Start the disk moving.

a. Notice that both the ladybug and beetle are now plotted on the graphs. How do the angles, angular velocities and angular accelerations of the bugs compare to each other?

b. How do the velocity and acceleration vectors on the ladybug compare to the vectors on the beetle?

c. Can you find a motion or setting where the acceleration vector on the bugs doesn’t point directly toward the center of the circle? Tell me how you accomplished this.

d. Can you explain these 3 results with the information from chapter 9?

Turn it in:

Print your report (Don’t forget your name).

Due Monday at the start of class.