Chapter 12, Problem 37A

A toy train is initially at rest on a track fastened to a bicycle wheel, which is free to rotate. How does the wheel respond when the train moves clockwise? When the train backs up? Does the angular momentum of the wheel-train system change during these maneuvers? How would the resulting motions be affected if the train were much more massive than the track? If the track were much more massive?

To determine

The response of bicycle wheel if train moves clockwise. Also, the response when train backs up.

To identify: Whether the angular momentum of the wheel-train system change during these maneuvers.

To explain: The effect on resulting motions if train is much more massive than track. Also, the effect if track is much more massive.

Explanation of Solution

Introduction:

According to the conservation of angular momentum, the total momentum before and after the collision must remain conserved, even for a rotating object.

Angular Momentum = Moment of Inertia $\times$ Angular Velocity

  $\text{L=Iω}$

  $\text{Iω(initial)= -Iω(final)}$

When an object becomes massive, then there will be increase in moment of inertia. Because of increased moment of inertia, object moves with lesser velocity to conserve angular momentum and stable equilibrium.If an object is more massive so will be its moment of inertia. If the moment of inertia increases, then, angular velocity decreases. Since the object acquires huge mass, it is difficult for it to move with the same velocity. Thus, it slows down so that it can move without toppling.

Thus, the massive track and wheel move counter-clockwise at a lesser angular velocity when a less massive toy train moving clockwise. Also, the more massive track and the wheel will rotate at a lesser angular velocity than the lesser massive toy train in the direction that causes the wheel to be moving forward concerning the train.So, wheel-train system changes maneuvers, angular momentum will tend to conserve itself.

If an object is less massive so will be its moment of inertia. If the moment of inertia decreases, then angular velocity increases. For a less massive object, it is easier to gain momentum while moving or rotating.Thus, a massive toy train will move with lesser velocity, it would seem like the wheel is spinning. As the wheel and the track will have greater angular velocity.

Also, less massive toy train will move faster. As the wheel and the track have lesser angular velocity.