Parallel axis theorem
Rigid body kinematics · Physics
Simple pendulum
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Study notes
Problem: Find the moment of inertia of a uniform rod of mass M and length L about an axis passing through one end and perpendicular to the rod. Solution: 1. We know the moment of inertia of a rod about its center of mass (Icm) is (1/12)ML^2. 2. The distance (d) from the center of mass to the end is L/2. 3. Using the Parallel Axis Theorem: I = Icm + Md^2. 4. Substitute the values: I = (1/12)ML^2 + M(L/2)^2. 5. Simplify the term M(L/2)^2: M(L^2/4) = (1/4)ML^2. 6. Add the terms: I = (1/12)ML^2 + (1/4)ML^2. 7. Find a common denominator (12): (1/12)ML^2 + (3/12)ML^2. 8. Final Answer: I = (4/12)ML^2 = (1/3)ML^2.