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

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(A) The torque $\tau$ about the hinged end is given by $\tau = Mg \frac{L}{2}$.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,$\tau = I \alpha$,where $\alpha$ is the angular acceleration:$Mg \frac{L}{2} = \left( \frac{ML^2}{3} \right) \alpha$.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 $L = 1$:$\alpha = \frac{3g}{2(1)} = \frac{3}{2} g \ rad/s^2$.

Class 11 Physics System of Particles and Rotational Motion Relation between Torque and Angular acceleration and it's Application

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$A$ 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 $rad/s^2$)

A
$\frac{3g}{2L}$
B
$g$
C
$3g$
D
$4g$

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

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MediumAP EAMCET 2023

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$A$ constant torque of $31.4 \, Nm$ is exerted on a pivoted wheel. If the angular acceleration of the wheel is $4\pi \, rad/s^2$,then the moment of inertia will be ....... $kg \cdot m^2$.

EasyAIIMS 2001

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$A$ rope of negligible mass is wound round a hollow cylinder of mass $3\; kg$ and radius $40\; cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30\; N$? What is the linear acceleration of the rope? Assume that there is no slipping.

Medium

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$A$ 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

$A$ disc of mass $25 \ kg$ and radius $0.2 \ m$ is rotating at $240 \ r.p.m.$ $A$ retarding torque brings it to rest in $20 \ s$. If the torque is due to a force applied tangentially on the rim of the disc,then the magnitude of the force in newton is

The moment of inertia of a wheel about its vertical axis is $2 \ kg \ m^2$. It is rotating about this axis at a speed of $60 \ rpm$. What torque must be applied to bring the wheel to rest in $1 \ minute$?

$A$ 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 $\text{ s}$)

$A$ constant torque of $31.4 \, Nm$ is exerted on a pivoted wheel. If the angular acceleration of the wheel is $4\pi \, rad/s^2$,then the moment of inertia will be ....... $kg \cdot m^2$.

$A$ rope of negligible mass is wound round a hollow cylinder of mass $3\; kg$ and radius $40\; cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30\; N$? What is the linear acceleration of the rope? Assume that there is no slipping.

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