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Homework Statement
Bicycle wheel is at rest, and can rotate frictionlessly about a fixed axle. A dart travels at velocity v (in plane of wheel) parallel to a line that goes through the centre of the wheel. It hits the rim of the wheel and sticks.
What kinetic energy, if any, is lost during impact?
Homework Equations
The Attempt at a Solution
I thought about something like 'the kinetic energy whose component is perpendicular to the rim of the wheel at impact is lost', but energy is scalar so that didn't seem right. Is there some better worded solution/reasoning? Perhaps the fixed axle buffers the wheel and so some kinetic energy is lost?
Or, am I supposed to answer these types of questions simply by directly calculating before/after?
Also (as an aside), is it correct to take the angular momentum of the dart simply to be about the axis of the wheel, and = ##\vec r\times \vec p## at the instant it hits the rim? (I haven't included the relevant question here.)