Centripetal Acceleration
Centripetal Acceleration is described as the centre-directed acceleration of a body moving continuously along a circular path. it is the quotient of the square of the objects velocity and the radius of the circle. The equation is :
Ac = v2/r
This equation can help to describe why larger wheeled unicycles travel faster. Say you were to ride two different unicycles at the same acceleration of 4 m/s2. One has a 20" diameter and the other has a 36" diameter. Which will go faster?
20" = 50.8 cm 36" = 91.44 cm
Ac = v2/r Ac = v2/r
4 = v2/.254 4 = v2/.4572
1.016 = v2 1.829 = v2
1.01 m/s = v 1.35 m/s = v
The larger wheel goes faster because it has a larger circumference, so with every pedal revolution more distance is covered. We can also use centripetal acceleration to compare cranklength speeds. Say you were riding two different unicycles with the same wheelsize, but one has 4" cranks and the other has 5" cranks at the same acceleration of 2 m/s2. Which goes faster?
4" = 10.2 cm 5" = 12.7 cm
Ac = v2/r Ac = v2/r
2 = v2/10.2 2 = v2/12.7
20.4 = v2 25.4 = v2
4.52 m/s = v 5.04 m/s = v
The shorter cranks go faster, because you don't have to push the pedal as far on the short cranks to get the same rotation as you would on the long cranks. Which is harder to stop? To find out go to the Physics Questions page.
