In lecture this week, we went over many types of olympiad problems. Most of these types of problems will occur on the USAPhO and above, but may occasionally appear on the $F=ma$. We encountered a few strategies that are generally helpful for solving complex dynamics problems:

1. Use kinematics strategies: From kinematics, we learned of how changing a frame of reference can simplify calculations. With dynamics, we can do the same.
   • When two bodies are interacting with one another, constraints may appear that define the accelerations of each object.
   • It's also occasionally helpful to shift into the rest frame of one of the objects. If a frame is accelerating, objects in that frame feel an extra component of force $ma$ due to the effective increase in gravity. (We'll explore this idea in more depth with fictitious forces later in the course.)
2. Radius of curvature: This topic is a bit more niche, but can come up occasionally. Using the definition of centripetal acceleration, an object with centripetal acceleration $a_\perp$ moving at speed $v$ is curved into a path of radius $$r=\frac{v^2}{a_\perp}.$$ This trick is helpful when trying to find the normal force between a particle and a track that is non-circular -- once an find the radius of curvature from analyzing an equivalent physical situation, and then apply that radius to the problem at hand. See the relevant problem for an application.
3. Integrals: Sometimes, in situations that seem to require an integral (or summing forces along tiny pieces of an object), we can bypass the integral with a clever application of Newton's laws. An example of this is problem 24 of the 2018 $F=ma$ B. This is again more of a niche subject; see the relevant problem for an application.