Why are big wheels better in a mousetrap car?
The short answer is that the circumference of the wheel scales as the radius and the distance traveled is determined by the circumference. The idea goes something like this: 1) Locomotion is driven by pulling on a string that is wound around the axle. 2) When 2*pi*(radius_axle) length of string is pulled, the axle undergoes 1 rotation. 3) The number of rotations undergone by the axle the number of rotations undergone by the wheel since the wheel is mounted to the axle. 4) When the wheel undergoes 1 rotation, the distance it turns through is 2*pi*(radius_wheel) 5) conclusion: pulling on 2*pi*(radius_axle) length of string results in 2*pi*(radius_wheel) distance traversed (assuming the wheels do not slip.) Caveat: Too large a wheel is not good either. The spring pulling the string supplies a limited amount of force. This force produces (force * radius_axle) amount of torque to spin the axle. Again, because the wheel is mounted to the axle, (force available to move car) * radius_wheel (force_supplied by spring) * radius_axle. (force available to accelerate car) (force spring) * (radius_axle / radius_wheel) So the same radius ratio that provides the distance advantage via circumference also provides a force disadvantage via torque. This creates a natural limit on how big to make the wheels. Make the wheels too small and you lose the distance advantage. Make the wheels too big, and the force disadvantage will prevent your car from accelerating at all. The objective is to use as large a wheel that you can to still have enough force provided by the spring to create the torque necessary to accelerate the car.
because the circumperence of the wheel is 5 times longer the axle
compare 2 wheel sizes One wheel with 50 mm radius and another with 100 mm radius Circumference of 1st wheel is 314.15 mm (2*pi*r) that is it moves 314.15 mm in 1 rotation Circumference of 2nd wheel is 628.31 mm It moves twice the distance when compared to 1st wheel I hope this could clear your doubt