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Bouncing Balls and Falling Toast

Public summary: 

A selection of mechanics experiments which investigate the properties of bodies with added spin. From bouncing balls of walls to dropping toast from tables we find out the hidden influence of angular momentum and why it makes our carpet buttery.

Looking at odd properties of bodies with spin.
Useful information
Kit List: 

Superbouncy balls
Vertical wall
Hardback book

There's also two rattlebacks which could be talked about when mentioning odd angular momentum

Packing Away: 

Packs into Misc Box.

Frequency of use: 

A superball is a solid rubber ball, we'll assume it's elastic and close to lossless. It also grips any surface so contacts are no-slip. We assume conservation of momentum, angular momentum around any point and no-slip and assume points of impact store and release energy in zero time. Impact via elastic particle model.

Stuff about elastic and inelastic collisions.

How to do the experiment (part I):

1 - Take the bouncy ball and roll it gently across a horizontal surface towards a wall. Watch to see how far it bounces back.

2 - Repeat, but this time roll the ball towards a wall lubricated with a little vaseline.

They're different! What's going on?

The point of this experiment is not only to look at how far the ball bounces back, but to think about how the spin direction changes. After saying this you may want to repeat the experiment to investigate. If you think of the ball rolling clockwise when it moves towards the wall, then on the way back it must be rolling anticlockwise. This change in spin direction requires energy, but where is the energy coming from? For advanced groups you can relate this to its angular momentum and this change in momentum requires a force.

When rolling the ball against a dry wall, you may have noticed that it bounces at the wall. It is this bounce that helps the ball to change its spin direction, and it's the wall that's providing the kick.

Taking a closer look, you will see that as the ball approaches the wall, it tries to continue up the wall, rolling in the direction it was going (ie: clockwise). However, gravity means that it can't do that for very long, and so it has to fall back down again. This makes the ball start to bounce and roll the other way (to see a graphical simulation of this effect, go to Hugh Hunt's website).

So what happens when there is oil on the wall? In contrast to when the wall was nice and dry, the ball can no longer grip and roll upwards. This prevents the ball from bouncing and can no longer use the wall to change its spin direction.

The result is that the ball starts rolling back to us spinning the wrong way (ie: still in the clockwise direction). The only way it can start to spin anticlockwise is by relying on friction between the ball and the floor. However by the time it's done so, the ball has lost all of its energy and comes to a complete stop.

This is why the ball doesn't roll back as far when there is oil on the wall. The oil reduces the friction, stops the ball getting a kick up the wall, and leaves the ball still rolling forwards even though it's moving backwards.

So can we see this effect anywhere else? You might expect to see balls bouncing in this way when they roll towards the cushion in a game of snooker. In fact, you won't see this at all because the cushions are specially designed so that the ball won't jump when it bounces back. The cushions are angled so that the point of contact between the ball and the cushion is not exactly half way up the ball (as when it hits a vertical wall), but higher up on the ball's surface. This gives a downwards force.

How to do the experiment (part II):
Bounce the ball under a table so that it comes up and hits the table, and, due to its spin, returns to you by bouncing back out (c.f. Lampard's 2010 World Cup no-goal which hit the crossbar and bounced back and out of the goal due to this effect). Note that it enters without spin, picks up spin in the direction it enters and this then reverses on the underside of the table and remains in this direction.
The ball also returns very close to its entry path, compare this to what a light particle would do. Is this an issue with the particle theory of light? Only if we assume that bouncy balls act like particles, in fact they don't and it's not an issue. We assume light particles are massless and have no physical size which defo isn't true of the ball.

How to do the experiment (part III):
Make sure the book is together with an elastic band and says butter on one side.

Place the book on the table and gradually push it towards the edge, get it to be perfectly balanced then nudge it 1mm further. There are three phases to it falling, no-slip, slip and free-fall.
Think of its angular velocity around the table edge, in no-slip it's increasing. The frictional force from the table is preventing the book slipping, the angle normally reaches 20-30 degrees (pi/9-pi/6 radians) before we enter the next phase.
In the slip phase gravity overcomes friction and the book starts to slide, notice how it remains in contact with the table during this phase. Here the book gains most of it's angular velocity as the forces are becoming less balanced, when the angular velocity is great enough it causes the book to loose contact with the table and we enter the free fall stage.
We now need to consider what happens next, we know via simple mechanics the toast will accelerate at 9.81ms^2 due to gravitational forces. It's also likely to fall upside down if it rotates between 90 and 270 degrees. While we don't know things like the frictional coefficient and air resistance or even the height of the table we find most combinations result in the toast falling butter side down.
[Hugh claims mu in 0.1-0.5 and initial push over 1mm-2mm are all similar]
One could experiment with this with some high and low friction table covers or from more height to calculate the angular velocity to work out what table heights work. Not sure what effect the weight of the 'toast' would have either (air resistance factors in). Also how far over the edge the toast is will alter the phases slightly.

Lots of ideas for this experiment came from Hugh Hunt's website. He has several high quality gifs of these experiments being done.

We have two Rattlebacks which currently live in here due to them not really fitting anywhere. If you're talking about angular momentum these are a very interesting thing to think about. Spin them in one direction and they act normally, in the opposite direction they stop and sometimes even reverse, the rattle is the way of conseving angular momentum but someone who knows more should improve this.

Risk Assessment
Date risk assesment last checked: 
Sun, 22/07/2018
Risk assesment checked by: 
Date risk assesment double checked: 
Sun, 22/07/2018
Risk assesment double-checked by: 
Risk Assessment: 

Bouncing superbouncy balls under coffee tables and rolling them against walls and dropping books.

1. Minimal risk of injury from balls if thrown by children
2. Loose balls could pose a trip hazard
3. Toast could be dropped onto feet/face.

Control Measures:
1. Keep hold of the balls not being used. Recover balls if being used inappropriately.
2. Don't set up the experiment in a thoroughfare where the balls could be a trip hazard. If a ball rolls into thoroughfare, retrieve it immediately.
3. Keep drop zone clear when preparing, don't let people look from underneath only the side.

In case of accident:
In case of injury, call a first aider.