(A) Initial angular velocity $\omega_0 = 10 \text{ rev/s} = 10 \times 2\pi \text{ rad/s} = 20\pi \text{ rad/s} \approx 62.8 \text{ rad/s}$.Angular acc

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(A) Initial angular velocity $\omega_0 = 10 \text{ rev/s} = 10 \times 2\pi \text{ rad/s} = 20\pi \text{ rad/s} \approx 62.8 \text{ rad/s}$.Angular acceleration $\alpha = 5 \text{ rad/s}^2$.Time $t = 2 \text{ s}$.Final angular velocity $\omega = \omega_0 + \alpha t = 20\pi + (5)(2) = 62.8 + 10 = 72.8 \text{ rad/s}$.Angular displacement $\theta = \omega_0 t + \frac{1}{2} \alpha t^2 = (20\pi)(2) + \frac{1}{2}(5)(2)^2 = 40\pi + 10 = 125.6 + 10 = 135.6 \text{ rad}$.Number of revolutions $n = \frac{\theta}{2\pi} = \frac{135.6}{2 \times 3.14} = \frac{135.6}{6.28} \approx 21.59 \text{ revolutions}$.

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

Medium

$A$ 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
$72.8, 21.59$
B
$52.6, 18.5$
C
$12.6, 4.8$
D
$82.6, 34.6$

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System of Particles and Rotational Motion

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Relation between Torque and Angular acceleration and it's Application

$A$ flywheel attains a speed of $540 \, r.p.m.$ in $6 \, s$. Its angular acceleration is:

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$A$ body rotating at $20 \ rad/s$ is acted upon by a constant torque providing it a deceleration of $2 \ rad/s^2$. At what time will the body have kinetic energy same as the initial value if the torque continues to act?

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$A$ 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

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$A$ rectangular plate of mass $20 \ kg$ is suspended from points $A$ and $B$ as shown in the figure. If the pin at $B$ is suddenly removed,find the angular acceleration of the plate in $rad/s^2$.

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$A$ uniform metre stick of mass $M$ and length $L = 1 \ m$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of the free end of the stick if the string is cut? (in $rad/s^2$)

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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 ...... .

Similar Questions

$A$ flywheel attains a speed of $540 \, r.p.m.$ in $6 \, s$. Its angular acceleration is:

$A$ body rotating at $20 \ rad/s$ is acted upon by a constant torque providing it a deceleration of $2 \ rad/s^2$. At what time will the body have kinetic energy same as the initial value if the torque continues to act?

$A$ 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

$A$ rectangular plate of mass $20 \ kg$ is suspended from points $A$ and $B$ as shown in the figure. If the pin at $B$ is suddenly removed,find the angular acceleration of the plate in $rad/s^2$.

$A$ uniform metre stick of mass $M$ and length $L = 1 \ m$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of the free end of the stick if the string is cut? (in $rad/s^2$)

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