(C) Given: Moment of inertia $I = 2 \; kg \cdot m^2$,Initial angular velocity $\omega_i = 60 \; rpm = \frac{60 \times 2\pi}{60} \; rad/s = 2\pi \; rad

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$ \frac{\pi}{15} \; N \cdot m $

(C) Given: Moment of inertia $I = 2 \; kg \cdot m^2$,Initial angular velocity $\omega_i = 60 \; rpm = \frac{60 \times 2\pi}{60} \; rad/s = 2\pi \; rad/s$,Final angular velocity $\omega_f = 0 \; rad/s$,Time $t = 1 \; minute = 60 \; s$.The angular acceleration $\alpha$ is given by $\alpha = \frac{\omega_f - \omega_i}{t} = \frac{0 - 2\pi}{60} = -\frac{\pi}{30} \; rad/s^2$.The magnitude of the torque $\tau$ is given by $\tau = |I \alpha| = 2 \times \left| -\frac{\pi}{30} \right| = \frac{2\pi}{30} = \frac{\pi}{15} \; N \cdot m$.

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

Medium

$A$ wheel having a moment of inertia $2 \; kg \cdot m^2$ about its vertical axis rotates at the rate of $60 \; rpm$ about this axis. The torque required to stop the wheel's rotation in one minute is:

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A
$ \frac{2\pi}{15} \; N \cdot m $
B
$ \frac{\pi}{12} \; N \cdot m $
C
$ \frac{\pi}{15} \; N \cdot m $
D
$ \frac{\pi}{18} \; N \cdot m $

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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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$A$ light rope is wound around a hollow cylinder of mass $5\,kg$ and radius $70\,cm$. The rope is pulled with a force of $52.5\,N$. The angular acceleration of the cylinder will be.....$rad\,s^{-2}$.

MediumJEE MAIN 2023

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Find the ratio of linear acceleration $(a)$ to angular acceleration $(\alpha)$ of the center of mass $(COM)$ for the given diagram. Given: $m = 2 \, kg$,$r = 10 \, cm = 0.1 \, m$,and force $F = 20 \, N$ applied at the center.

MediumAIIMS 2019

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$A$ uniform disc rotates at $10$ revolutions per second. $A$ torque is applied to it, producing an angular acceleration of $5 \text{ rad s}^{-2}$. After $2 \text{ s}$, its angular velocity is ...... $\text{rad s}^{-1}$ and the number of revolutions completed by the disc in $2 \text{ s}$ is ...... .

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$A$ torque of $30 \, N \cdot m$ is applied for $10 \, s$ on a wheel of mass $5 \, kg$ and moment of inertia $2 \, kg \cdot m^2$. The angular displacement of the wheel in $10 \, s$ will be ....... radians.

Medium

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$A$ uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A.$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $ml^2/3$,the initial angular acceleration of the rod will be:

MediumAIPMT 2007

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$A$ wheel having a moment of inertia $2 \; kg \cdot m^2$ about its vertical axis rotates at the rate of $60 \; rpm$ about this axis. The torque required to stop the wheel's rotation in one minute is:

Similar Questions

$A$ light rope is wound around a hollow cylinder of mass $5\,kg$ and radius $70\,cm$. The rope is pulled with a force of $52.5\,N$. The angular acceleration of the cylinder will be.....$rad\,s^{-2}$.

Find the ratio of linear acceleration $(a)$ to angular acceleration $(\alpha)$ of the center of mass $(COM)$ for the given diagram. Given: $m = 2 \, kg$,$r = 10 \, cm = 0.1 \, m$,and force $F = 20 \, N$ applied at the center.

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$A$ uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A.$ The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $ml^2/3$,the initial angular acceleration of the rod will be:

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