1.
What expression do you think you should use for the moment of inertia of the tree branch?
Section 12.6 Torque Analysis
The force analysis you studied in Force Analysis for a Single System and Using Action-Reaction Pairs can now be extended to include torque.
Analyze and Represent: Identify all relevant systems and draw an Extended Free-body Diagram for each.
Calculating: Is the acceleration of each system \(0 \mathrm{~m/s^2}\) (static or dynamic equilibrium) or not \(0 \mathrm{~m/s^2}\) (dynamics)? What about the angular acceleration? Once you know, use the Law of Motion, the Rotational Law of Motion, and any action/reaction pairs between any interacting systems.
Sensemaking: All the sensemaking strategies you have will work, including Special-case Analysis, especially for special cases that reduce the context to one in which there is no rotational motion.
Exercises Real-world Context - The Tree Branch
Suppose you are taking a walk one day when you see a tree branch snap at its base and begin to rotate downward with the break near the trunk of the tree as a pivot point. You estimate the length of the branch to be about 3 meters.
2.
Estimate the initial angular acceleration of the branch.
3.
Can you estimate the mass of the tree branch from the given information? Why or why not?
