Linear Tracking
need help on linear velocity math question?
a train wheel has a diameter of 30 inches to the rim, which rests on the track. The flange, which keeps from the slipping off the track, projects 1 inch beyond the rim. When the train is traveling 60 mph, what is the linear velocity of a point on the outer edge of the flange?
The question is not clear. Velocity relative to what? To the rail? To the train?
Assuming the question is to find the velocity of the outer point of the flange relative to the center of the wheel and that the wheel turns without slipping on the rail:
V = R(dA/dt) where V is the velocity of a point, measured relative to the center of rotation, R is the radius of the point.
Velocity of a point on the rim:
Vr = 15(dA/dt) = 60*5280*12/3600 = 1056 in/sec
dA/dt = 1056/15 sec^-1
Velocity of a point on the flange relative to the axis of rotation:
Vr = 16(1056/15) = 1126.4 in/sec = 64 mph
Assuming the question is to find the velocity relative to the rail:
Vr = 1126.4 -1056 = 70.4 in/sec = 4 mph (in a direction opposite to the direction the train is moving)
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