(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

Difficult

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

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

$A$ rope is wound round a hollow cylinder of mass $5\,kg$ and radius $0.5\,m.$ What is the angular acceleration (in $rad/s^2$) of the cylinder if the rope is pulled with a force of $20\,N$?

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Write the Newton's second law for rotational motion about a fixed axis.

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$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane. One of its ends is hinged on a vertical axis. $A$ horizontal force $F = Mg/2$ is applied at a distance of $5L/6$ from the hinged end. What will be the angular acceleration of the rod?

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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)

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$A$ torque of $10^5 \ N \cdot m$ is applied to a disc of mass $10 \ kg$ and radius of gyration $50 \ m$. What is the value of the angular acceleration in $rad/s^2$?

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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

$A$ rope is wound round a hollow cylinder of mass $5\,kg$ and radius $0.5\,m.$ What is the angular acceleration (in $rad/s^2$) of the cylinder if the rope is pulled with a force of $20\,N$?

Write the Newton's second law for rotational motion about a fixed axis.

$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane. One of its ends is hinged on a vertical axis. $A$ horizontal force $F = Mg/2$ is applied at a distance of $5L/6$ from the hinged end. What will be the angular acceleration of the rod?

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)

$A$ torque of $10^5 \ N \cdot m$ is applied to a disc of mass $10 \ kg$ and radius of gyration $50 \ m$. What is the value of the angular acceleration in $rad/s^2$?

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