An equilateral triangle ABC is made of a unif | vedclass

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

Question

(B) $1$. The system consists of the triangle and the two beads. The only external forces acting on the system are gravity and the normal force from th

Vedclass · Accepted Answer

Total angular momentum and total energy

Vedclass · Answer

(B) $1$. The system consists of the triangle and the two beads. The only external forces acting on the system are gravity and the normal force from the pivot at $A$. Since the pivot force acts at the axis of rotation,its torque is zero. Gravity also exerts no torque about the vertical axis $AO$. Therefore,the net external torque on the system about the axis of rotation is zero,which implies that the total angular momentum $L$ is conserved.$2$. Since there is no friction and the only forces doing work are gravity (a conservative force),the total mechanical energy of the system is conserved.$3$. As the beads slide down,their distance from the axis of rotation increases,which increases the moment of inertia $I$ of the system. Since $L = I\omega$ is constant and $I$ increases,the angular velocity $\omega$ must decrease. Thus,neither $\omega$ nor $I$ are conserved.

Similar Questions

The angular speed of a body changes from $\omega_1$ to $\omega_2$ without applying a torque but due to changes in moment of inertia. The ratio of radii of gyration in two cases is

$Assertion$ : For a system of particles under a central force field,the total angular momentum is conserved.
$Reason$ : The torque acting on such a system is zero.

$A$ thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity:

Vedclass Test Series

Exam Paper Generator

Online Exam Module