# Choo Choo Train

### Model Description

Relative motion and no-slip wheel relationships are brought to life by means of a moving locomotive train. This demonstration should take 10 minutes.

### Engineering Principle

The following relationships are utilized to investigate the velocity and acceleration of the engine piston and push arm given a train velocity and instantaneous position of the wheel.

No-clip wheel:

$v_{PC} = 0$          $v_{ctr} = \omega_{wh}r_{wh}$

$a_{PC} = \omega_{wh}^2r_{wh}$          $a_{ctr} = \alpha_{wh}r_{wh}$

Relative motion:

$v_b = v_a + v_{b/a}$

$a_b = a_a + a_{b/a}$

### What You Need

Item Quantity Description/Clarification
Demo Board 1 Rotating wheel, arm, and sliding piston that represent an engine cycle.

The demo board can be made of ½ inch plywood.  Base dimensions are approximately 4 feet long by 3 feet high.  Further dimensions can be seen in Image 2.  This is  a difficult and time consuming build.

### How It’s Done

Before Class: Build the demonstration board.

In Class: Read the problem and ensure setup is complete. The board is utilized to assist in classifying the motion for the wheel, push arm, and piston.  Because the board isn’t translating like the train, it brings up the fun moment of having students reenact a live “Choo Choo train” across the classroom (good laugh for all).

### Cite this work as:

Tom Messervey (2019), "Choo Choo Train," https://www.handsonmechanics.org/dynamics/600.