Race the jam jars down a slope to see which one is faster.

## In a Nutshell

Show people that rotational motion is a bit weird - you have to account for the distribution of mass not just the overall properties.

## Setup

Not much to do. Place the ramp on the floor (if using a board then use a couple of jars/ spare box or find something else to hold the back end up). If using an opened t-shirt box to catch the jars, place at the bottom of the ramp, or if using foam, place about 10cm past the end of the ramp (taping it down helps if its small).

## The Experiment

Gain attention by telling people they'll be racing jars down a hill. Explain what's in the jars.

First, bring out the drop test objects and ask kids which one is heavier (they can feel this for themselves) and ask which one will hit the ground first if they're dropped from the same height at the same time. Both should hit at the same time (demonstrate a couple of times, from different heights if necessary). Get them to tell you what force pulls things down. The heavier something is, the stronger the gravity. BUT, the heavier something is, the harder it is to get it to move. These effects cancel each other out so all objects fall under gravity at the same rate.

***CHaOS Plus/ super interested:*** Explain that we are ignoring air resistance (or get them to tell you that). Go into Newton’s second law to explain how mass doesn’t affect acceleration under gravity. However, physicists currently don’t know why the inertial mass term in Newton’s second law happens to be the gravitational mass. Einstein used this fact in his ‘Equivalence Principle’ where he equates the gravitational force experienced by an observer to the same force that would be experienced if the observer were accelerating. This then lead to his Theory of General Relativity: The currently used theory that describes the effect of gravity.

The rest of the experiment is easier to understand if the falling masses are described by their energies. As the mass falls, gravitational potential energy is converted into kinetic energy, but again (use equations to show) the speed at which they fall is the same.

Now ask them to think about what will happen on the ramp - if gravity doesn't care how 'heavy' things are, should the weight of the jars make any difference? Will they all reach the bottom at the same time. Feel free to prompt some more (why do you think X, what might cause Y) if the group is old enough to engage.

Let the kids pick up the jar of jam and the empty jar to get a feel for the weights, and then race! (if the kids are eager and you can get them to release when you say, then they can hold the jars and let go when you tell them to. Alternatively, a pole or stick can be used as a release mechanism). The jar of jam should beat the empty jar.

It looks like the heavier jar wins but this makes no sense since we've already seen gravity doesn't care about weight. What is the difference between falling and rolling? When falling (or sliding on the slope), the jar stays one way round (in one orientation) whilst moving. When rolling, as well as moving down the slope, the jar is also spinning. This is what changes things. Gravity needs to put in extra effort to get the jars spinning as well as going down.

Get the kids talking about it a bit and then ask them if they've been on a roundabout/ merry-go-round/ turntable thing at a park. Does it just start spinning on its own without any pushing? What about pushing the thing if someone else is on it - is it easier to make it spin fast if the other person is in the middle or at the edge? (You can also try to connect this to Spinny Chair experiment if it is also out.) Exactly the same thing is happening here with the jars. The empty jar has almost all of its mass concentrated in a very thin layer of glass a long way from the axis of rotation whereas the one full of jam has a lot of mass quite close to the middle. It's therefore much 'easier' to make the full jar spin than the empty jar (could be worth mentioning, to reinforce the idea that weight is irrelevant, that if there were no friction the jars would all slide (not roll!) down the hill in the same amount of time).

Next try the jar of jam vs the jar of water. The jar of water wins, why? What’s the difference between the water and the jam? Answer: Jam is sticky, but water isn’t. When the jar of the water rolls down, the water doesn’t have to spin, only the jar, whereas in the jar of jam both the jar and jam are spinning. This means the jar of water can go faster.

The interesting case of the half-full jar and the jam jar can now be the ultimate race. The jam jar has the extra weight, but the half-full water jar doesn’t have to spin as much, so you can get the kids to bet on which will win. This one is actually quite close, so you’ll have to see which wins on the day!

In conclusion for linear motion the distribution of mass is irrelevant, only the total, whereas for rotational motion it's not just the mass that matters, its position is important as well.

***CHaOS Plus/ super interested:*** What force is it that causes something to spin in the first place? (Friction acts at the point of contact of the jars). All of the problems can be explained by considering the energy of the jars. When the objects were dropped before, gravitational potential energy was converted into kinetic energy, but with spinning added, we need to incorporate a new energy term for the rotation of jam about the centre of the jar - rotational kinetic energy. The amount of rotational energy that you need to put in depends on where the mass is, so the empty jar has the worst distribution of mass and rolls slowest. For the full jar of water the water isn’t rotating so the rotational energy is only for the glass, meaning it can roll quicker.

We can write the rotational kinetic energy down in an equation similar to the linear kinetic energy:

LKE = (½)mv^2

RKE = (½)Iw^2

W is how quickly the jar is spinning. I is called the moment of inertia, and increases as mass gets further away from the centre, so more energy will be required. Actual definition is sum of mass * (distance from rotation axis)^2. E.g. figure skating: if a skater brings her arms in she's reduced her MOI but to keep the same rotational energy the same she has spins faster"). Can demo this in the playground - several people stand at the edge of a roundabout spinning fairly slowly and walk in to the middle. The roundabout should speed up and if they walk back out it should get slower again.

The wikipedia page on 'moment of inertia' has more information and a nice gif animation of (front to back) a solid cylinder, cylindrical shell, ball and spherical shell racing down a slope. http://en.wikipedia.org/wiki/Moment_of_inertia#Scalar_moment_of_inertia_...