University Physics I · Rigid-body rotation and angular momentum
Uniform rod inertia from an integral
Problem
Use an inertial laboratory frame and the stated right-handed axis; treat bearings, strings, and contacts as ideal only where stated, and use SI units. A thin uniform rod of mass $M$ and length $L$ lies along the $x$-axis from $-L/2$ to $L/2$. Derive its moment of inertia about the $z$-axis through its center.
Hint
Write the uniform linear density as $M/L$.
Check your work
Work the problem yourself first. Then open it in Training to check your answer and read the full worked solution.
The answer check and full solution for this problem come with ProofAnvil Practice membership ($19 USD monthly). See membership. Or start with the free University Physics I sample problem: Try the free sample problem.
More University Physics I practice problems
- Average speed is not average velocity magnitudeVector kinematics and relative motion
- Two launch angles reach the same targetVector kinematics and relative motion
- Kinetic friction under a horizontal pullNewton laws and force models
- Two angled support cablesNewton laws and force models
- Work of a quadratic position-dependent forceWork, energy, and conservative systems
- Turning points in an inverse-square-plus-quadratic potentialWork, energy, and conservative systems
- Impulse from a triangular force pulseMomentum, impulse, and collisions
- Explosion at the apex of a projectile pathMomentum, impulse, and collisions
- Field of a thin spherical shellGravitation and orbital motion