(B) Given: Moment of inertia $I = 2 \ kg \cdot m^2$,Initial angular velocity $\omega_0 = 60 \ rpm = \frac{60 \times 2\pi}{60} \ rad/s = 2\pi \ rad/s$,

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(B) Given: Moment of inertia $I = 2 \ kg \cdot m^2$,Initial angular velocity $\omega_0 = 60 \ rpm = \frac{60 \times 2\pi}{60} \ rad/s = 2\pi \ rad/s$,Final angular velocity $\omega = 0$,Time $t = 1 \ minute = 60 \ s$.Using the equation of rotational motion: $\omega = \omega_0 - \alpha t$.$0 = 2\pi - \alpha(60) \implies \alpha = \frac{2\pi}{60} = \frac{\pi}{30} \ rad/s^2$.The torque required is given by $\tau = I\alpha$.$\tau = 2 \times \frac{\pi}{30} = \frac{\pi}{15} \ N \cdot m$.

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

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The moment of inertia of a wheel about its transverse axis is $2 \ kg \cdot m^2$ and it is rotating at $60 \ rpm$ about that axis. The torque required to stop the wheel in one minute is:

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

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Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

At time $t = 0$,a $2\, kg$ particle has position vector $\vec{r} = (4\hat{i} - 2\hat{j})\, m$ relative to the origin. Its velocity is given by $\vec{v} = 2t^2\hat{i}\, m/s$. The torque acting on the particle about the origin at $t = 2\, s$ is ........ $\hat{k}\, N\cdot m$.

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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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$A$ circular disc of radius $2 \ m$ is rotating at $240 \ rpm$. If a torque is applied to the disc, it slows down at a rate of $\pi \ rad/s^2$. How long will it take to stop? How many revolutions will the disc complete before coming to rest?

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The power $(P)$ is supplied to a rotating body having moment of inertia $I$ and angular acceleration $\alpha$. Its instantaneous angular velocity $\omega$ is

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$A$ thin solid disk of $1 \ kg$ is rotating along its diameter axis at the speed of $1800 \ rpm$. By applying an external torque of $25 \pi \ Nm$ for $40 \ s$,the speed increases to $2100 \ rpm$. The diameter of the disk is . . . . . . $m$.

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The moment of inertia of a wheel about its transverse axis is $2 \ kg \cdot m^2$ and it is rotating at $60 \ rpm$ about that axis. The torque required to stop the wheel in one minute is:

Similar Questions

At time $t = 0$,a $2\, kg$ particle has position vector $\vec{r} = (4\hat{i} - 2\hat{j})\, m$ relative to the origin. Its velocity is given by $\vec{v} = 2t^2\hat{i}\, m/s$. The torque acting on the particle about the origin at $t = 2\, s$ is ........ $\hat{k}\, N\cdot m$.

$A$ 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 ...... .

$A$ circular disc of radius $2 \ m$ is rotating at $240 \ rpm$. If a torque is applied to the disc, it slows down at a rate of $\pi \ rad/s^2$. How long will it take to stop? How many revolutions will the disc complete before coming to rest?

The power $(P)$ is supplied to a rotating body having moment of inertia $I$ and angular acceleration $\alpha$. Its instantaneous angular velocity $\omega$ is

$A$ thin solid disk of $1 \ kg$ is rotating along its diameter axis at the speed of $1800 \ rpm$. By applying an external torque of $25 \pi \ Nm$ for $40 \ s$,the speed increases to $2100 \ rpm$. The diameter of the disk is . . . . . . $m$.

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