Lesson 1 - 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.

Prerequisites

Students should have a working knowledge of Newton's First and Second Laws of Motion. Basic graphing skills and an understanding of vector quantities are also required.

Learning Outcomes

Students will develop an understanding that Newton's Laws of Motion can be used to explain uniform circular motion and that uniform circular motion requires an inward force of constant magnitude. Students will perform an experiment to determine the relationship among the inward force acting on an object in uniform circular motion, its mass, path radius and velocity.

Instructions

Students should understand the applet functions that are described in Help and ShowMe. The applet should be open. The step-by-step instructions in this lesson are to be carried out in the applet. You may need to toggle back and forth between instructions and applet if your screen space is limited.

Contents

1. Visualizing Circular Motion
2. Newton's First and Second Laws Applied to Circular Motion
3. How Inward Force is Related to Velocity
4. How Inward Force is Related to Radius
5. How Inward Force is Related to Mass

1. Visualizing Circular Motion

Imagine that a ball is being twirled on a string in a horizontal plane. Figure 1 shows the ball and string a moment before the string is released. Draw the path that the ball will follow immediately after the string is released (You are looking straight down). Figure 1

On the applet, set the initial velocity to approximately +2.0 m/s. Click "Play" () and release the ball by clicking "Cut" (). You may wish to reset () the applet and view the release several times. Explain in your own words why the ball moves the way it does when the ball is released.

2. Newton's First and Second Laws Applied to Circular Motion

Newton's First Law of Motion

An object will either remain at rest or in a state of uniform motion unless acted upon by a net force. Newton's First Law is not expressed by an equation.

Newton's Second Law of Motion When an object is acted upon by a non-zero net force, it will begin to accelerate in the direction of the net force. Expressed as an equation: Quantity Symbol SI Unit acceleration m/s2 net force N mass m kg Both acceleration and net force are vector quantities. This means they both have size (magnitude) and direction that define them.

Using Newton's First and Second Laws to help answer the following questions.

1. When the string is attached to the ball and it 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 it moves in a horizontal circle, does the force change the direction and/or 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: true or false? Explain your reasoning.
   
   
   
   
   
   
   
6. An object can be accelerating while maintaining a uniform (constant) speed: true or false?
   Explain your reasoning.
   

When an object travels in a circular path, there must be an inward force causing the direction of the motion to change. This is a direct application of Newton's First and Second Laws of Motion. It should also be clear that there is a relationship between the size of the force and the speed of the object, the mass of the object, and the radius of the arc through which the object moves. The applet will be used to investigate these relationships.

To identify the relationships between variables, you may wish to use the following graphical analysis reference:

Relationship: y α x

Relationship: y α 1/x

Relationship: y α x²

3. How Inward Force is Related to Velocity

Click "Data Options" () and set the mass to be 1.00  kg and the radius to 1.00 m. Next, run the applet and adjust the velocity to the values indicated in the table. Record the Inward Force (tension) and sketch the graph in the space provided.

Velocity vs. Inward Force

(Alternately, you can put this data into a spreadsheet and graph it using the spreadsheet.)

Compare your graph to the graphical analysis reference table and state the relationship between the inward force and the velocity.

F_c α ______

Suppose you were to triple the speed with which you twirled a ball on a string. How would that affect the size of the inward force (tension) in the sting?

4. How Inward Force is Related to Radius

Click "Data Options" () and set the mass to 1.00 kg. Set the velocity to be 10.0 m/s. Next, run the applet and adjust the radius to the values indicated in the table. Record the Inward Force (tension) and sketch the graph in the space provided.

Radius vs. Inward Force

(Alternately, you can put this data into a spreadsheet and graph it using the spreadsheet.)

Compare your graph to the graphical analysis reference table and state the relationship between the inward force and the radius.

F_c α ______

Suppose you were to reduce the size of the arc through which you twirled a ball on a string by one-half. How would that affect the size of the inward force (tension) in the string?

5. How Inward Force is Related to Mass

Click "Data Options" () and set the radius to 2.0 m. Set the velocity to 5.0 m/s. Next, run the applet and adjust the mass to the values indicated in the table. Record the Inward Force (tension) and sketch the graph in the space provided.

Mass vs. Inward Force

(Alternately, you can put this data into a spreadsheet and graph it using the spreadsheet.)

Compare your graph to the graphical analysis reference table and state the relationship between the inward force and velocity.

F_c α ______

Suppose you were to increase the mass of the ball by 5 times. How would that affect the size of the inward force (tension) in the string?

Use your answers to exercise 4, 6, and 8 to give a mathematical expression for the inward force as a function of mass, velocity, and radius.

F_c α ______

a. Show that this expression is dimensionally correct (it produces the correct units).





b. Provide three examples in which you show that your formula predicts the values produced by the applet. For example, pick a mass, velocity, and radius and calculate the expected inward force. Use the applet to verify your answer.

Physics 20-30 v1.0
©2004 Alberta Learning (www.learnalberta.ca)

Last Updated: June 16, 2004