(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A wheel with spokes rolls without slipping on the ground. You take a picture with a stationary camera from the side of the wheel. Because the wheel is moving and the camera has a nonzero exposure time, the spokes are usually blurred. At what points in the picture do the spokes not appear blurred?

2. Relevant equations

Not really equations but a couple of hints I was given.

A common incorrect answer is that there is only one point.

Hint: The key idea is the following. All spokes are moving because a) the wheel is rotating and b) the wheel CM is translating (moving parallel to the floor). When you snap a picture, during a small interval dt (the exposure time) the spokes will have moved. However, there will be some points in the picture where the spokes will not appear blurred because that particular point in space will lie on the spoke throughout the motion. Note that this does not mean that the point will lie on the same point on the spoke, the spoke is still moving, but it moves in such a way that if you look at the position of the spoke at the beginning of the exposure and at the end of the exposure, one particular point will lie on the spoke in both cases. You have to find the locus of all such points.

3. The attempt at a solution

This is what I'm thinking. As the spoke moves through space, it sweeps out an area. The points I'm interested in are the points within that area that are on the spoke at t = 0 and t = dt. Sound good?

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# Homework Help: Picture of a rolling wheel

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