(D) Given the angular velocity $\omega = \frac{k}{\theta}$.Since $\omega = \frac{d\theta}{dt}$,we have $\frac{d\theta}{dt} = \frac{k}{\theta}$.Rearran

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(D) Given the angular velocity $\omega = \frac{k}{\theta}$.Since $\omega = \frac{d\theta}{dt}$,we have $\frac{d\theta}{dt} = \frac{k}{\theta}$.Rearranging the terms to integrate,we get $\theta d\theta = k dt$.Integrating both sides with the initial condition $\theta = 0$ at $t = 0$:$\int_{0}^{\theta} \theta d\theta = \int_{0}^{t} k dt$.This yields $\frac{\theta^2}{2} = kt$.Solving for $\theta$,we get $\theta^2 = 2kt$,which implies $\theta = \sqrt{2kt}$.

Class 11 Physics System of Particles and Rotational Motion Rotation Motion Basic, Motion of Connected Mass

Medium

$A$ solid body rotates about a fixed axis such that its angular velocity depends on $\theta$ as $\omega = k \theta^{-1}$,where $k$ is a positive constant. At $t = 0$,$\theta = 0$. Then,the time dependence of $\theta$ is given as ..........

A
$\theta = k t$
B
$\theta = 2 k t$
C
$\theta = \sqrt{k t}$
D
$\theta = \sqrt{2 k t}$

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Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Rotation Motion Basic, Motion of Connected Mass

$A$ wheel of radius $1.5 \ m$ rotates with a constant angular acceleration of $10 \ rad/s^2$. Its initial angular speed is $(\frac{60}{\pi}) \ rpm$. What will be its angular speed and angular displacement at $t = 2.0 \ s$?

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Explain the definitions of angular position,angular displacement,and angular speed for the motion of a rigid body.

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What is pure translational motion?

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$A$ uniform cylinder of mass $m$ can rotate freely about its own axis,which is horizontal. $A$ particle of mass $m_0$ hangs from the end of a light string wound around the cylinder,which does not slip over it. When the system is allowed to move,the acceleration of the descending mass will be

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Explain that angular velocity is a vector and its direction is given by the right-hand screw rule.

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$A$ solid body rotates about a fixed axis such that its angular velocity depends on $\theta$ as $\omega = k \theta^{-1}$,where $k$ is a positive constant. At $t = 0$,$\theta = 0$. Then,the time dependence of $\theta$ is given as ..........

Similar Questions

$A$ wheel of radius $1.5 \ m$ rotates with a constant angular acceleration of $10 \ rad/s^2$. Its initial angular speed is $(\frac{60}{\pi}) \ rpm$. What will be its angular speed and angular displacement at $t = 2.0 \ s$?

Explain the definitions of angular position,angular displacement,and angular speed for the motion of a rigid body.

What is pure translational motion?

$A$ uniform cylinder of mass $m$ can rotate freely about its own axis,which is horizontal. $A$ particle of mass $m_0$ hangs from the end of a light string wound around the cylinder,which does not slip over it. When the system is allowed to move,the acceleration of the descending mass will be

Explain that angular velocity is a vector and its direction is given by the right-hand screw rule.

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