Car wheel speed

Classical Mechanics Level 2

A car is driving at 50 miles per hour down a straight road. What is the speed (in mph) of the front wheel at the point where it touches the ground?

50 -50 100 0

1 solution

Michael Mendrin
Jan 30, 2015

The ground isn't moving, so when that part of the tire touches it, it isn't moving either.

I used the story of how a fly stopped a train which uses your reasoning, and it led to many heated discussions.

It seems that a fly was going Northward following a railway track. This continued until it smacked into the windshield of a locomotive traveling Southward. The fly's motion was radically changed after the collision, from Northward to Southward.

Now to achieve this feat we must conclude that the fly was stopped at some point in time.

And where was it when it was stopped? Why, touching the windshield, of course!

Can we then reason that the windshield was stopped also, and being attached to the locomotive, the locomotive was also stopped? And, also the train?

Guiseppi Butel - 6 years, 4 months ago

I like your way of thinking about this! I'm glad I posed this problem and learned a new way of looking at this. I guess I should include that "the car is traveling without slipping"?

I was thinking of it as "car is moving forward at 50, but wheel is moving (backwards) at - 50, hence it should be 0".

Chung Kevin - 6 years, 4 months ago

Actually, my "answer" was probably just a bit disingenuous. It does need some qualification, namely that the velocity vector of that point on the tire just before it touched the ground did shrink down to $0$ . We can assume that the tire isn't slipping on the road at contact. As a counterexample, a bullet ricocheting from the ground still has a significant horizontal velocity component at the moment it "touched" the ground.

Michael Mendrin - 6 years, 4 months ago

great! that's exactly what I thought mam...

Sravanth C. - 6 years, 4 months ago

Car wheel speed

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