1.
What expression do you think you should use for the moment of inertia of the tree branch?
Section 5.17 Torque Analysis
The force analysis you studied in Section 3.9 and Section 3.16 can now be extended to include torque.
Understanding: Identify all relevant systems and draw an Extended Free-body Diagram for each.
Calculating: Is the acceleration of each system \(0 \text{ m/s}^2\) (static or dynamic equilibrium) or not \(0 \text{ m/s}^2\) (dynamics)? What about the angular acceleration? Once you know, use the Law of Motion, the Angular 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 (see Section 3.10), 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?
