A uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity ω about a vertical axis passing through one end. The tension in the rod at a distance x from the axis is A. 1/2mω²x B. 1/2mω²x²/l C. 1/2mω²l (1 - x/l) D. 1/2mω²/l [l² - x²]
Added by Teresa C.
Step 1
The moment of inertia of a uniform rod rotating about an axis passing through its center of mass is given by (1/12)ml^2. However, in this case, the axis is passing through one end, so we need to use the parallel axis theorem to shift the axis to the end. The Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 70 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is (a) $\frac{1}{2} m \omega^{2} x$ (b) $\frac{1}{2} m \omega^{2} \frac{x^{2}}{l}$ (c) $\frac{1}{2} m \omega^{2}\left(1-\frac{x}{l}\right)$ (d) $\frac{1}{2} \frac{m \omega^{2}}{l}\left[l^{2}-x^{2}\right]$
A thin rod of length $\ell$ and mass $M$ rotates about a vertical axis through its center with angular velocity $\omega .$ The rod makes an angle $\phi$ with the rotation axis. Determine the magnitude and direction of $\overrightarrow{\mathbf{L}}$.
A thin rod of mass $m$ and length $2 l$ is made to rotate about an axis passing through its centre and perpendicular to it. If its angular velocity changes from 0 to $\omega$ in time $t$, the torque acting on it is (a) $\frac{m l^{2} \omega}{12 t}$ (b) $\frac{m l^{2} \omega}{3 t}$ (c) $\frac{m l^{2} \omega}{t}$ (d) $\frac{4 m l^{2} \omega}{3 t}$
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD