A circular platform rotates in a horizontal p | vedclass

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

Question

(C) The angular momentum $L$ of the system (platform + tortoise) about the axis of rotation is conserved because there is no external torque acting on

Vedclass · Accepted Answer

Vedclass · Answer

(C) The angular momentum $L$ of the system (platform + tortoise) about the axis of rotation is conserved because there is no external torque acting on the system.$L = I(t) \omega(t) = 	ext{constant}$Here, $I(t)$ is the moment of inertia of the system at time $t$.Let $R$ be the radius of the platform, $M$ its mass, and $m$ the mass of the tortoise.The moment of inertia of the platform is $I_p = \frac{1}{2}MR^2$.The tortoise moves along a chord. Let the distance of the chord from the center be $d$. At time $t$, the distance of the tortoise from the center is $r(t) = \sqrt{d^2 + (vt)^2}$, where $v$ is the constant speed of the tortoise relative to the platform.The total moment of inertia is $I(t) = I_p + mr(t)^2 = I_p + m(d^2 + v^2t^2)$.Since $L = I(t) \omega(t)$, we have $\omega(t) = \frac{L}{I_p + m(d^2 + v^2t^2)}$.As the tortoise moves from the edge towards the center (or vice versa), the distance $r(t)$ first decreases until it reaches the point closest to the center (at $t=0$ if the chord passes through the center, or at some $t$ if it doesn't) and then increases.When $r(t)$ is minimum, $I(t)$ is minimum, and therefore $\omega(t)$ is maximum.Conversely, when $r(t)$ is maximum (at the edges), $I(t)$ is maximum, and $\omega(t)$ is minimum.Since the tortoise starts at the edge, $r(t)$ decreases as it moves towards the center, causing $I(t)$ to decrease and $\omega(t)$ to increase. After passing the point closest to the center, $r(t)$ increases, causing $I(t)$ to increase and $\omega(t)$ to decrease.Thus, the angular velocity $\omega(t)$ increases and then decreases.

Similar Questions

$A$ mouse of mass $m$ jumps on the outside edge of a rotating ceiling fan of moment of inertia $I$ and radius $R$. The fractional loss of angular velocity of the fan as a result is

$A$ child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is $K$. The child now stretches his arms so that the moment of inertia of the system becomes double. The kinetic energy of the system now is

$A$ hot solid sphere is rotating about a diameter at an angular velocity $\omega_0$. If it cools so that its radius reduces to $\frac{1}{\eta}$ of its original value,its angular velocity becomes .............

The angular momentum of a system of particles is not conserved:

Vedclass Test Series

Exam Paper Generator

Online Exam Module