View source for Walk the Spool

{| class="wikitable" style="color:black; background-color:#ddd; margin-left: auto; float:right"
| [[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 ==

# 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.
# 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?
# 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:
{| class="wikitable" style="color:black; background-color:#ddd; text-align: left; margin-right: auto"
|+ 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'':

{| class="wikitable" style="color:black; background-color:#ddd; text-align: left; margin-right: auto"
|+ 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:

{| class="wikitable" style="color:black; background-color:#ddd; text-align: left; margin-right: auto"
| '''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.