Module 5—Circular Motion

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 Visualizing Circular Motion

 

centripetal: directed toward the centre of a circle

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?

 

 

horizontal plane: a plane perpendicular to a radius of Earth, usually used to suggest that there is no vertical component to motion or forces

 

 

 

 

 

 

 

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.

 

Self-Check

 

SC 1. In your own words, explain why the ball moves the way it does once the string has been cut in the simulation.

 

Check your work.
Self-Check Answers

 

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 and Second Laws Applied to Circular Motion

 

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.

 

Module 5: Lesson 1 Assignment

 

Remember to submit the answer to TR 1 to your teacher as part of your Module 5: Lesson 1 Assignment.

 

Try This

 

TR 1. Use the Circular Motion: Horizontal simulation and Newton's laws to help answer the following questions.

  1. When the string is attached to the ball and the ball moves in a horizontal circle, does the string exert a force on the ball? If so, in which direction is the force always directed?

  2. While the string is attached to the ball and the ball moves in a horizontal circle, does the force change either or both the direction and speed of the ball? Explain.

  3. When the string is released, is there any force acting on the ball?

  4. According to Newton's first law, what type of motion should result when the string is released? Is this confirmed by your observations?

  5. When a ball is twirling at a uniform speed on the end of a string, the inward force is zero. Is this statement true or false? Explain your reasoning.

  6. An object can be accelerating while maintaining a uniform (constant) speed. Is this statement true or false? Explain your reasoning.
Read

 

To help put in context what you learned in the tutorial, read "Defining Circular Motion" on pages 242 to 243 of your textbook.

 

Self-Check

 

SC 2. Choose the correct answer. The direction of the velocity vector at any instant in circular motion is always

  1. radially in toward the centre
  2. a tangent to the circle
  3. radially out away from the centre
  4. curved around the direction of the circle      
Check your work.
Self-Check Answers

 

SC 2. B

 

 

Read

 

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.

 

Self-Check

 

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?

 

Check your work.
Self-Check Answers

 

SC 3.


Variables


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.

 

Procedure
  • Set up a data table with four columns. Label the first two to record the speed and the corresponding force.
  • Start with a speed of 1.0 m/s. Run the simulation, and record the force required.
  • Repeat: Add 3 m/s to the value of the previous speed every time.
  • Graph the results with speed on the horizontal axis.
  • If the graph does not show direct proportionality (a straight diagonal line), use the other columns of the data table to fill in v2 or . Then graph that value against the force until you find a graph that gives the straight diagonal graph line indicating direct proportionality.
Conclusion

 

Express the relationship as a mathematical proportionality.

 

SC 4. The meaning of the word centripetal from its Latin roots means “centre seeking.”