system
Given the following post, respond as if you're commenting on Reddit:
human
Is it possible to calculate the speed of the engine components themselves ie pistons in kph/mph?

It's just something that has fascinated me. Sure I know that at 5000rpm the crankshaft is spinning 5000 times per minute and the piston goes up and down for every rotation but what is the actual SPEED of the piston? 

Say, my Harley which has a stroke of 101mm. What would the piston speed be at 5000rpm?
gpt
The piston moves in oscillatory motion with a maximum travel length of L (~stroke length) with frequency f (=RPM) then it's position at time t is given by:

x(t) = L/2 sin(2 pi f t)

Then it's velocity is

v(t) = dx/dt = pi L f cos(2 pi f t)

Thus the maximum speed is: |v|*_max_* = pi L f. If the stroke length is 10 cm and the engine runs at f = 5000 RPM = 83 s^(-1), then the max speed is ~26 m/s = 94 km/h = 58 mph.