Walk the Spool

Physics, Math:	Torque, Right Hand Rule
Grade Range:	High School
Format:	Hands-on

This demonstration is intended to be more conceptual, and can be hard for some students to understand. Make sure you are familiar with the right hand rule before presenting this demonstration.

Materials

• Large Spool with String
• Optional: White Board with Markers

Safety Precautions

Please read the General Safety Precautions section of the Demonstration Safety page before performing this demonstration.

Demonstration

1. Set out the spool, and allow students to come and try to "walk" it across the floor. Allow them to try to figure out the best methods for walking the spool.
2. Ask students about the directions they had to pull the string to make the spool come towards them. Did it always behave how they expected?
3. Ask students about the directions they had to pull the string to make the spool go away from them. What causes the spool to behave this way?

Why This Works

The spool will roll one way or another based on a few factors: which direction you pull the string in, and which side of the spool the pulled string is wrapped around. This is because the spool rolls in accordance to the Torque, or rotational force it experiences. The torque applied can be measured using this equation:

Torque

τ = r F sin θ

τ: Torque

r: Radius from axis

F: Force applied

sin θ: Angle of applied force

In this equation, we can note that the radius and applied force are inversely proportional to each other. However, you might notice that the length of the string available does not seem to affect the amount of force you have to apply. This is because the radius, r, is in regards to the distance from the axis. The axis is in the center of the spool, and the applied force from the string is always the same distance from the center. Since the string is adhered to the side of the spool, it always applies the force at the same radius from the center.

When you pull on the string, the angle of the applied force is affected by two factors: which direction you pull the string in, and where the string is at on the spool when you pull.

• When you pull on the string, you are pulling in a single direction relative to the spool. This pull is perpendicular to the axis of rotation for the spool, which means the force will be applied along a side of the spool.
• The side of the spool that the string is across will result in a direction for the movement. This is independent of which direction you pull the string in; rather, it is dependent solely on which way the string is already wrapped around the spool.

When trying to determine which way the spool will roll, one can best predict the movement by using the Right Hand Rule:

Right Hand Rule

Thumb: Axis of rotation

Index: Direction of applied force

Curled: Rotation of spool

By using the right hand rule, you can determine which direction the spool will move in by determining the direction of the applied force. To do so, you can follow this guide:

String on the Spool: Index Position	Direction of String: Thumb Position	Result: Curled Fingers Position
Wrapped Clockwise Point Left	Pull Left Inward	Rolls Left, Unwinds Clockwise Curl
Wrapped Clockwise Point Left	Pull Right Outward	Rolls Right, Rewinds Counterclockwise Curl
Wrapped Clockwise Point Left	Pull Up Up	Stops at 30 deg Angle Towards Left Curl Inward
Wrapped Counterclockwise Point Right	Pull Left Inward	Rolls Left, Rewinds Counterclockwise Curl
Wrapped Counterclockwise Point Right	Pull Right Outward	Rolls Right Clockwise Curl
Wrapped Counterclockwise Point Right	Pull Up Up	Stops at 30 deg Angle Towards Right Curl Outward
Unwrapped Up	Pull Left Inward	Starts to Wind Counterclockwise Counterclockwise Curl
Unwrapped Up	Pull Right Outward	Starts to Wind Clockwise Clockwise Curl
Unwrapped Up	Pull Up Left Or Right	No Movement Curl Perpendicular to Axis

Additional Information

• This demonstration is easier to explain if you can use a whiteboard to draw it out.
• This demonstration pairs well with other demonstrations on torque, such as the Magic Spoon and Where's the Doorknob demonstrations.