9.4

Newton's Second Law of Rotation

Student Notes

This simulation shows a half- Atwood's machine. This is similar to the Atwood's machine covered in a previous simulation, the difference being that in the Atwood's machine there are two blocks connected by a string that passes over a pulley, while in a half-Atwood's machine there is one block hanging from a string wrapped around the pulley. In the Atwood's machine the focus was on the forces and the straight-line motion; here the focus will be on the torque and the rotational motion.
Here are some things to investigate:

1. | Before you press the "Start" button, the system is held in equilibrium by a downward force applied to the pulley on the left. Note the values displayed by the simulation. Now press the "Start" button to release the system from rest. Which values change? Why do they change?
2. | Using the free-body diagram of the block, you can apply Newton's second law to generate an equation relating the block's weight, the tension, and the acceleration. A similar process can be carried out for the pulley, although because the pulley rotates it is the torque and Newton's second law for rotation that are important. Combine the equations to determine the acceleration of the block and the angular acceleration of the pulley - do your values agree with those arrived at by the simulation.
3. | With everything else fixed, adjust the radius of the pulley. Which values are affected? Determine how these values depend on the radius - is there a linear relationship, or is it more complicated? Remember to re-run the simulation each time to see the effect of a change in radius.
4. | Set the mass of the block and the mass of the pulley to 5 kg. Which pulley shape and radius will maximize the block's acceleration? Which settings will minimize the acceleration? Predict the settings and verify your predictions using the simulation.

Self-test

1. | Why does changing from one pulley to another of a different shape, with exactly the same mass and radius, affect the acceleration?
2. | With the mass of the block set to a particular value, there are three different ways to change the angular acceleration of the pulley. What are these? You can check your answer using the simulation. Make each of your proposed changes one at a time, and re-run the simulation to see how the change affects the angular acceleration of the pulley.

Copyright © 2006 John Wiley & Sons, Inc. All rights reserved.