ShowMe - Circular Motion: Horizontal

Circular Motion: Horizontal simulates the motion of a mass on a rigid rod that is moving along a horizontally-oriented circular path. It also explores the relationship between the inward force acting on an object travelling in uniform circular motion and the object's mass, path radius, and speed.

This document shows you how to use this applet in a step-by-step manner. You should have the applet open; toggle back and forth between the ShowMe file and the applet as you work through these instructions.

Using the Free Body Diagram to Illustrate Inward Force, Centripetal Acceleration, and Tangential Velocity
Adjusting the Basic Parameters: Mass, Radius, Velocity
Demonstrating the Relationship between Inward Force, Centripetal Acceleration, and the Basic Parameters
Contrasting Circular and Tangential Motion

1. Using the Free Body Diagram to Illustrate Inward Force, Centripetal Acceleration, and Tangential Velocity

Give the mass a small velocity (5 m/s) by adjusting the velocity control at the bottom of the applet, and then click "Play".

Once the mass begins to move, click "FBD" to display the free body diagram and tangential velocity vector.
Note that both vectors remain fixed in magnitude. The blue vector represents the tension in the rod, which pulls the ball at right angles to its direction of motion (magenta vector). This illustrates the essential role that the inward force plays: the inward force accelerates the mass by changing its direction of motion rather than the magnitude of its velocity.

Try changing the velocity and note how the magnitudes of the two vectors change in response to this.

2. Adjusting the Basic Parameters: Mass, Radius, Velocity

The basic parameters for this applet are easily adjusted by moving the appropriate slider.

3. Demonstrating the Relationship between Inward Force, Centripetal Acceleration, and the Basic Parameters

The Circular Motion: Horizontal applet can be used to illustrate the basic connection between force, velocity, and radius. Recall that the expression for the inward or centripetal force is where m is the mass, v the velocity, and r the radius.

As an example, set the mass to 2 kg, the radius to 5 m, and the velocity to 5 m/s. You should observe that the output panel along the top of the applet displays both the inward force and tension in the rod. Both are equal to 10 N.

Since you know the magnitude of the inward force and the mass being accelerated, you can also calculate the centripetal acceleration. In the previous example it is easy to see that since F= ma, a = 10 N/ 2 kg = 5 m/s². This is also consistent with the expression .

4. Contrasting Circular and Tangential Motion

The applet Circular Motion: Horizontal is particularly effective at contrasting circular and tangential motion.
To illustrate this, pick a convenient velocity - for example, 5 m/s - and click "Play". Once the motion begins, use "Cut" to break the connection between the rod and ball. Observe the abrupt transition from circular motion to linear motion. Since there is no longer a net force acting on the ball, it will (according to Newton's First Law) continue to move at a constant velocity. This means that neither the magnitude nor the direction of the velocity will change. Note that the both the Tension and Inward force values drop to zero in the output display panel.