On a circular carnival ride, such as the Polar Express, an inward force acts on the passengers to keep them moving along a circular path. In other words, the seat pushes on the passengers, forcing them to remain on a circular path. An inward force is often called a centripetal or centre-seeking force based on its direction.
For simplicity, a simulation will be used in this lesson to investigate and visualize the forces acting on a passenger using a vector diagram of a ball attached to a string moving in a horizontal circle.
Imagine that a ball is being twirled on a string in a horizontal plane (as illustrated here). What would happen if the string attached to the ball were cut while it was in motion? Would the ball fly away, stop, or continue on the circular path?
uniform circular motion: the motion of an object with a constant speed along a circular path
The applet used in this simulation helps you explore the inward force acting on an object travelling with uniform circular motion. Open the Circular Motion: Horizontal simulation. You can learn more about the simulation and how to use it by reading Show Me found at the top of the simulation screen.
The direction of the initial velocity is toward the right, but because the direction is continually changing, the speed is what we will be working with.
SC 1. In your own words, explain why the ball moves the way it does once the string has been cut in the simulation.
SC 1. When the ball was released, it travelled in the direction in which it was moving the moment the string was cut. This occurs because the string is no longer pulling on the ball and Newton’s first law comes into play.
Newton’s first law of motion says a body continues in its state of rest or of motion in a straight line with a constant speed unless an external, unbalanced force acts on it.
Newton’s second law of motion says the rate of change of velocity of an object is proportional to and in the same direction as the unbalanced force acting upon it. Expressed as an equation, it is
Both Newton’s first and second laws can be applied to circular motion. Newton’s first law helps to understand the motion of the ball when the string is cut. The second law helps to understand the motion of the ball when it travels along a circular path.
Remember to submit the answer to TR 1 to your teacher as part of your Module 5: Lesson 1 Assignment.
TR 1. Use the Circular Motion: Horizontal simulation and Newton's laws to help answer the following questions.
To help put in context what you learned in the tutorial, read "Defining Circular Motion" on pages 242 to 243 of your textbook.
SC 2. Choose the correct answer. The direction of the velocity vector at any instant in circular motion is always
SC 2. B
Read “Centripetal Acceleration and Force” on pages 243 to 247 of your textbook to see some of the differences between circular motion and the linear motion you have studied in previous units.
SC 3. Design an experiment using the simulation that would investigate the relationship between the speed and the force in uniform circular motion. Describe the manipulated, responding, and controlled variables.
SC 4. What does the word centripetal mean from its Latin roots?
SC 3.
Choose speed as the manipulated variable and force as the responding variable. The controlled variables are the length of the string, the mass of the ball, and the plane of the rotation.
Express the relationship as a mathematical proportionality.
SC 4. The meaning of the word centripetal from its Latin roots means “centre seeking.”