A thin uniform rod,pivoted at O,is rotating i | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The angular momentum $L$ of the insect about the pivot $O$ is given by $L = I\omega$,where $I$ is the moment of inertia of the insect. Since the i

Vedclass · Accepted Answer

$A$ plot showing a linear increase of torque with time for $t  T$.

Vedclass · Answer

(A) The angular momentum $L$ of the insect about the pivot $O$ is given by $L = I\omega$,where $I$ is the moment of inertia of the insect. Since the insect is at a distance $r = vt$ from $O$,its moment of inertia is $I = m(vt)^2 = mv^2t^2$.Thus,$L = (mv^2t^2)\omega = mv^2\omega t^2$.The torque $	au$ required to maintain constant angular speed is the rate of change of angular momentum:$	au = \frac{dL}{dt} = \frac{d}{dt}(mv^2\omega t^2) = 2mv^2\omega t$.Since $	au = 2mv^2\omega t$,the torque is directly proportional to time $t$ for $0 \le t \le T$. This represents a straight line passing through the origin $(0,0)$.For $t > T$,the insect stops moving,so its angular momentum becomes constant,and the torque becomes zero.Therefore,the plot should show a linear increase from $t=0$ to $t=T$ and then drop to zero.

Similar Questions

If the earth suddenly contracts to $(1/3)^{rd}$ of its present size without any change in its mass, the ratio of the kinetic energy of the earth after and before contraction will be (Earth is assumed to be a rotating sphere about itself).

$A$ bullet of mass $m$ is fired horizontally into a large sphere of mass $M$ and radius $R$ resting on a smooth horizontal table. The bullet hits the sphere at a height $h$ from the table and sticks to its surface. If the sphere starts rolling without slipping immediately on impact,then

$A$ square lamina $OABC$ of side length $10 \ cm$ is pivoted at $O$. Forces act on the lamina as shown in the figure. If the lamina remains stationary,then the magnitude of $F$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module