5.1

Uniform Circular Motion and Centripetal Force

Student Notes

The simulation shows a ball moving in a circular path. The radius of the path can be changed, as can the initial angular velocity of the ball. Initially only uniform circular motion is visible, although you can set the simulation to non-uniform circular motion, allowing you to see the difference between uniform and non-uniform circular motion.
First view the default motion.

1. | From the difference between the black position vectors at nearby times, construct the direction of the velocity vector. Compare your construction to the velocity vector shown when you enable velocity vector display using the control on the simulation.
2. | Turn on or leave on the velocity vector display. From the difference between the velocity vectors at nearby times, construct the direction of the acceleration vector. Compare your construction to the acceleration vector shown during this time interval when you enable acceleration vector display using the control on the simulation.
3. | Turn off the acceleration vector. Predict how the velocity vector will change if you increase the initial speed of the ball. Use the initial angular velocity control to increase the ball's speed. Check your prediction using the simulation.
4. | Using the change in the velocity vector you observed in the previous step, predict how the acceleration vector has changed due to the increase in the ball's speed. Check your prediction using the simulation.
5. | How would the velocity vector change if the radius of the motion increased? Assume that the ball still completes one trip around the circle in the same period of time. Check your prediction using the simulation.
6. | How would the acceleration vector change if the radius of the motion increased? Assume that the ball still completes one trip around the circle in the same period of time. Check your prediction using the simulation.
7. | If the speed of the ball moving in a circular path is constant, the motion is called uniform circular motion. This simulation can also show nonuniform circular motion by increasing the speed of the ball steadily. Describe how both the velocity and acceleration vectors will appear when the ball speeds up as it moves. Set the simulation to nonuniform circular motion, and run the simulation to check your prediction.

Self-test

How would the velocity and acceleration vectors appear if you change the direction of travel of the ball? Make a prediction and check your answer using the simulation, setting the initial angular velocity to a negative value.

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