2014: Problem 1

Topic: Dynamics
Concepts: Angular momentum, Circular motion


Solution:

In the driver’s perspective, the position vector r\vec{r} points left from the center of the circle to the car. The velocity vector v\vec{v} always points forward. The angular momentum vector is given by

L=r×pr×v\vec{L}=\vec{r} \times \vec{p} \propto \vec{r} \times \vec{v}

By the right-hand rule, r×v\vec{r} \times \vec{v} points into the page (downwards for the driver) so that is also the direction of L\vec{L}. Since the car is undergoing uniform circular motion, there is only centripetal acceleration directed toward the center of the circle. Thus, a\vec{a} points to the right relative to the driver. The answer is E.

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