Can I really think of 10 ideas based on a roll of toilet paper? probably not but I'll have a go.

1. Snatching a piece

Have you ever noticed how, by pulling fast, you can snatch off a piece from a full roll but not an empty one? It's all to do with the force required to accelerate the roll. Try dropping a fixed mass a fixed distance on the free end.

What is the relationship between the angular acceleration of the roll and the roll diameter?

Knowledge of rotational inertia required.

2. Rock and roll (1)

Similar to the above but simpler. Just hang a mass (a rock?) on the free end and measure the angular acceleration.

What is the relationship between the angular acceleration of the roll and the roll diameter?

3. Rock and roll (2)

Similar to the above but keep the size of the roll constant and vary the mass.

What is the relationship between the angular acceleration of the roll and the mass?

4. Rock and roll (3)

This time vary the diameter of the cylinder used to hold the roll.

What is the relationship between the angular acceleration of the roll and the diameter of the cylinder?

Changing the cylinder diameter offsets the centre which changes the rotational inertia.

5. Paper bridge (1)

Make a suspension bridge between two points and hang masses on the middle until it breaks.

What is the relationship between the force required to break the bridge and the length of paper?

Assuming the paper always breaks under the same force the longer the paper the more weight it should support.

HALF WAY THERE

6. Paper bridge (2)

Make a suspension bridge between two points and hang masses on the middle until it breaks.

What is the relationship between the vertical displacement of each sheet and its horizontal position?

Photo analysis in GeoGebra or LoggerPro could be useful.

7. Blowing in the wind (1)

Hang a long streamer in a light wind.

What is the relationship between the horizontal displacement and the distance from the top?

Probably difficult to do but can be modelled in Algodoo. Again, photo analysis in GeoGebra or LoggerPro could be useful.

8. Blowing in the wind (2)

Attach a streamer to a long pole and run with it

What is the relationship between the angle of the streamer and the velocity?

9. Andrex advert

There used to be an advert involving a dog, soft, strong and very long. Unroll the paper down a long slope.

What is the relationship between velocity and distance travelled?

Ideal for an iterative model in Excel.

10. Football hooligan

Hold the free end and throw the roll.

What is the relationship between the x and y displacement?

EASY I've obviously been doing this job for too long.

WARNING Apart from no. 1 these are all untried and untested. They are not guaranteed to get anyone a 7 but I think I could with most of them.