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Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Ramping it Up

Age 16 to 18 Challenge Level:

Impulse function

The gradient is infinitely steep at the points where there is a step in value. These arrows are called delta functions. They are thought of as infinitely high and thin, and have a notional area equal to the value of the step jump. Thus when you integrate this derivative, you get back to the original step function.

A system's (for example a car suspension) response to an impulse (you might think of it as a sudden "bang") is very useful, and can be used on a process called "convolution" to find a system's response to any input.