Particles 1 and 2, each of mass m, are attached to the ends of a rigid massless rod of length...?

Question

L1+ L2, with L1= 20 cm and L2= 80 cm. The rod is held
horizontally on the fulcrum and then released. What are the magnitudes of
the initial accelerations of (a) particle 1 and (b) particle 2?

Answer 1

Torque.

The weight of each particle is mg. The torque caused by particle 1 is mg * 20, counterclockwise, and the torque from particle 2 is mg * 80, clockwise. Therefore the net torque is mg * 60, clockwise.

So the force on the left particle is (mg * 60) / 20 = 3 mg, and the force on the right particle is (mg * 60) / 80 = 3/4 mg. Both of these are clockwise, so the left particle goes up and the right particle goes down. To get acceleration, just cancel m.