A uniform metre stick of mass M and length L | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The torque $	au$ about the hinged end is given by $	au = Mg \frac{L}{2}$.The moment of inertia $I$ of a uniform rod of mass $M$ and length $L$ a

Vedclass · Accepted Answer

$\frac{3g}{2L}$

Vedclass · Answer

(A) The torque $	au$ about the hinged end is given by $	au = Mg \frac{L}{2}$.The moment of inertia $I$ of a uniform rod of mass $M$ and length $L$ about an axis passing through one end is $I = \frac{ML^2}{3}$.Using the rotational analogue of Newton's second law,$	au = I \alpha$,where $\alpha$ is the angular acceleration:$Mg \frac{L}{2} = \left( \frac{ML^2}{3} ight) \alpha$.Solving for $\alpha$:$\alpha = \frac{MgL/2}{ML^2/3} = \frac{3g}{2L}$.Given the length of the metre stick is $L = 1 \ m$,we substitute $L = 1$:$\alpha = \frac{3g}{2(1)} = \frac{3}{2} g \ rad/s^2$.

$A$ uniform metre stick of mass $M$ and length $L = 1 \ m$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of the free end of the stick if the string is cut? (in $rad/s^2$)

Similar Questions

Consider a particle of mass $m$ having linear momentum $\vec{p}$ at position $\vec{r}$ relative to the origin $O$. Let $\vec{L}$ be the angular momentum of the particle with respect to the origin. Which of the following equations correctly relate $\vec{r}, \vec{p}$ and $\vec{L}$?

Write Newton's second law for a system of particles performing rotational motion.

$A$ flywheel is rotating at a rate of $150 \text{ rev/minute}$. If it slows at a constant retardation of $\pi \text{ rad/s}^2$, then the time required for the wheel to come to rest is (in $\text{ s}$)

What is the value of the torque acting on an object moving in a circular path with a constant angular speed? Why?

When a ceiling fan is switched off,its angular velocity reduces to $50\%$ while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)

Vedclass Test Series

Exam Paper Generator

Online Exam Module