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Here's my general strategy for solving these types of problems -- start at the gear with the known rotation, and work out the rotation of the other gears from there. Arrows help. As per your discussion on bikes, the following should clear it up: The bike case is represented by the system on the right. Consider a simple design for a bike where the wheels ...

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I could tell you how to find it, but the answer is a mess... I wonder why you'd need it. You are essentially asking a question on how to compose three rotations $R_z (\alpha) R_x(\beta) R_z(\gamma)$ in a suitable extrinsic Euler angle convention, which you could convert to the angle of your choice. In effect, you are asking to convert the matrices provided ...

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Consider just a simple wheel that is spinning with constant angular speed $\omega$. Imagine there is a particle on the edge. Recall that velocity is speed with a direction. As the wheel spins, the velocity direction must change, but the speed remains constant (because the wheel is said to be spinning with constant angular speed). What kind of forces can ...

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Yes. If the angular momentum of a body about the origin is $\vec{L}=\vec{r} \times \vec{p}$, the angular momentum about an axis in the direction $\hat{n}$ is given by- $$L_{axis}=|\hat{n}.\vec{L}|$$ You can see that for yourself pretty easily. This is simply the projection of the angular momentum of the body about that axis. The perpendicular component of ...

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Consider what would happen if the normal force was not there. The person would simply move outwards, due to his inertia. Now because there is a wall there, the person will not be moving radially outwards. Instead, the person will apply a force on the wall, and by Newton's third law, the wall will apply an equal and opposite force on the person.

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