(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

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DifficultJEE MAIN 2019

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$A$ uniform rod of mass $M$ and length $L$ is hinged at one end as shown in the figure. Initially,the rod is kept horizontal by a massless string. When the string is cut,the angular acceleration of the rod 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?

Similar Questions

$A$ 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 $\text{ s}$)

$A$ 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 ...... .

$A$ rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis (see figure). When released from the initial horizontal position,its instantaneous angular acceleration will be

$A$ rod of mass $M$ and length $L$ is placed in a horizontal plane with one end hinged about a vertical axis. $A$ horizontal force of $F = \frac{Mg}{2}$ is applied at a distance $\frac{5L}{6}$ from the hinged end. The angular acceleration of the rod will be:

$A$ uniform rod of mass $M$ and length $L$ is hinged at one end as shown in the figure. Initially,the rod is kept horizontal by a massless string. When the string is cut,the angular acceleration of the rod is:

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