System Of Particles Rotational Motion

Given situation is shown in the figure.
Here,
x = 50 - 20 = 30 cm = 0.3 m
Apply law of moments about centre of the rod,


Hence according to options

Hence rod will not topple if second mass of
0.15 kg is hung at 70 cm mark.

Translational kinetic energy,

where = mass of the ring,
= speed of the centre of mass of the ring
Rotational kinetic energy,

Here,
So,

Let and be distances of centre of mass from the two bodies of masses and respectively.
As
or
or
Thus, the centre of mass is closer to the heavier body.

A person sitting firmly over a rotating stool has his arms stretched and as he folds his arms, centre of mass remain unchanged and therefore, angular momentum about the axis of rotation remain unchanged.

In central force motion (e.g., gravitational or electrostatic), the force is conservative. Hence, total mechanical energy (i.e., kinetic + potential energy) is conserved. But individually, kinetic and potential energies may change as the particle moves.

The rotational analogue of Newton's second law is: This holds when internal torques cancel out (equal and opposite pairs), and only external torque contributes to change in angular momentum.