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- Homework Statement
- A wheel of radius ##R## is spinning at angular velocity ##\omega##. What distance does a pedestrian walking behind the vehicle have to walk, to not be hit by a piece of mud falling off the wheel.

- Relevant Equations
- None really, it's all about the thought.

So, my idea would be that this happens at an angle ##\theta = \frac{\pi}{2}##, or quarter of a whole rotation. At this point, the wheel starts moving right again, after going to the left. Due to it's inertia, the piece of mud would want to keep it's current direction of motion and therefore fall off. The problem I'm facing now is that the acceleration always points to the center of the wheel, thus the mud would be accelerated towards the cars movement direction, rather than being thrown backward where it could hit the person.

Is my idea of the angle wrong or did I calculate the acceleration vector incorrectly? Help is very apprechiated.

Is my idea of the angle wrong or did I calculate the acceleration vector incorrectly? Help is very apprechiated.