Newtons' Second Law for rotational motion.
Moment of inertia.
Pre-requisite skills: Basic algebra, basic understanding of rotational dynamics.
Approximate completion time: 30 minutes.
Provide sufficient detail to verify that the assignment was completed in a meaningful manner.
MERLOT site: Rotational Dynamics, by Angel Franco Garcia. (direct link).
Applet by Angel Franco Garcia
This applet simulates the operation of the familiar Atwood machine, but with a twist: The strings that connect the two masses do not wrap around the pulley at the same radius.
1. Will the two masses accelerate by the same amount (magnitude) in this situation? To be sure, make the inner radius much smaller than the outer radius and observe the respective motion of the two masses. Describe mathematically how you can ascertain whether the accelerations are different.
2. In general, are the tensions in the two strings the same? Explain.
3. With the inner radius set to 20 cm, start the applet by pressing the Start (Empiaza) button. When the blue mass reaches about 50 cm, stop the applet and write down the elapsed time. From the information presented to you on the screen, calculate the moment-of-inertia of the pulley? You can verify your answer by pressing the Result (Resultado) button.
4. In terms of the radii of the pulley and the tensions in the string, what are the conditions required in order for the two masses to experience no acceleration? What must be the relative mass of the two masses in this situation? Verify your answer by setting the parameters in the applet accordingly and pressing the Start button.
Helpful Resources
- Rolling with Friction by Angel Franco Garcia.
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