(A) Given: Initial angular velocity $\omega_1 = 240 \ rpm = \frac{240 \times 2\pi}{60} \ rad/s = 8\pi \ rad/s$. Angular deceleration $\alpha = \pi \ r

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$8 \ s, 16 \ \text{revolutions}$

(A) Given: Initial angular velocity $\omega_1 = 240 \ rpm = \frac{240 \times 2\pi}{60} \ rad/s = 8\pi \ rad/s$. Angular deceleration $\alpha = \pi \ rad/s^2$. Final angular velocity $\omega_2 = 0 \ rad/s$. Using the equation $\omega_2 = \omega_1 - \alpha t$: $0 = 8\pi - \pi t \implies t = 8 \ s$. Using the equation $\omega_2^2 = \omega_1^2 - 2\alpha \theta$: $0 = (8\pi)^2 - 2(\pi)\theta \implies 64\pi^2 = 2\pi\theta \implies \theta = 32\pi \ rad$. Number of revolutions $N = \frac{\theta}{2\pi} = \frac{32\pi}{2\pi} = 16 \ \text{revolutions}$.

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

Medium

$A$ 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?

A
$8 \ s, 16 \ \text{revolutions}$
B
$12 \ s, 24 \ \text{revolutions}$
C
$10 \ s, 8 \ \text{revolutions}$
D
$6 \ s, 12 \ \text{revolutions}$

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

$A$ disc of radius $0.4 \,m$ and mass $1 \,kg$ rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration of the disc is $10 \,rad/s^2$. The tangential force applied to the rim of the disc is (in $\,N$)

MediumMHT CET 2021

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Consider a body shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = MV$ (where $V$ is the linear velocity of a ball) is imparted to the body at one of its ends,what would be its angular velocity?

MediumMHT CET 2022

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$A$ wheel of mass $20 \,kg$ and radius $30 \,cm$ is rotating at an angular speed of $80 \,rev/min$ when the motor is turned off. Neglecting the friction at the axis, calculate the force that must be applied tangentially to the wheel to bring it to rest in $5 \,rev$. (in $\pi \,N$)

MediumTS EAMCET 2021

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If the external torque acting on a system is $ \tau = 0 $, then:

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$A$ wheel is rotating about an axis through its centre at $720 \, rpm$. It is acted on by a constant torque opposing its motion for $8 \, s$ to bring it to rest finally. The value of torque (in $N \cdot m$) is (Given $I = \frac{24}{\pi} \, kg \cdot m^2$)

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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?

Similar Questions

$A$ disc of radius $0.4 \,m$ and mass $1 \,kg$ rotates about an axis passing through its center and perpendicular to its plane. The angular acceleration of the disc is $10 \,rad/s^2$. The tangential force applied to the rim of the disc is (in $\,N$)

Consider a body shown in the figure,consisting of two identical balls,each of mass $M$,connected by a light rigid rod of length $L$. If an impulse $J = MV$ (where $V$ is the linear velocity of a ball) is imparted to the body at one of its ends,what would be its angular velocity?

$A$ wheel of mass $20 \,kg$ and radius $30 \,cm$ is rotating at an angular speed of $80 \,rev/min$ when the motor is turned off. Neglecting the friction at the axis, calculate the force that must be applied tangentially to the wheel to bring it to rest in $5 \,rev$. (in $\pi \,N$)

If the external torque acting on a system is $ \tau = 0 $, then:

$A$ wheel is rotating about an axis through its centre at $720 \, rpm$. It is acted on by a constant torque opposing its motion for $8 \, s$ to bring it to rest finally. The value of torque (in $N \cdot m$) is (Given $I = \frac{24}{\pi} \, kg \cdot m^2$)

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