Physics · System Of Particles And Rotational Motion · NEET
Yes, a moment IS torque. NCERT defines moment of a force as tau = r x F. The 'principle of moments' is just the special balance case: when a lever is in rotational equilibrium, the sum of moments about the pivot is zero, so anticlockwise moment = clockwise moment. So torque is the quantity, principle of moments is the balance rule that uses it.
Always the perpendicular distance of the force from the fulcrum (pivot), never the total rod length. In NEET problems the rod is marked in cm; you subtract the pivot position from each force's position. Example: force at 20 cm mark, pivot at 40 cm mark, so its arm is 40 - 20 = 20 cm. Getting this subtraction wrong is the most common mistake.
Because the pivot reaction R acts exactly at the fulcrum, so its distance from the fulcrum is zero. Moment = force x distance = R x 0 = 0. That is why taking moments about the pivot is smart: it removes the unknown reaction and leaves only the forces you care about. NCERT notes R still matters for translational equilibrium (R = F1 + F2).
Imagine the force acting alone and ask which way it would spin the rod about the pivot. Forces on opposite sides of the pivot spin it opposite ways. NCERT convention: anticlockwise is positive (+), clockwise is negative (-). For balance, positive moments = negative moments in magnitude. Just be consistent for the whole problem.
In a lever, the load F1 is the weight you want to lift and its distance from the fulcrum d1 is the load arm. The effort F2 is the force you apply and its distance d2 is the effort arm. Mechanical advantage = load/effort = d2/d1. If the effort arm is longer than the load arm, a small effort lifts a large load - that is why a crowbar or see-saw works.
Yes, if the rod is uniform its whole weight acts at its centre (the 50 percent mark, or 100 cm mark of a 200 cm rod). If the pivot is NOT at the centre, this weight sits at a distance from the pivot and adds a real moment you must include. Only when the pivot is exactly at the centre does the rod's weight give zero moment.
A uniform metre-scale style rod of length 200 cm and mass 500 g is balanced on a wedge (pivot) placed at the 40 cm mark. A 2 kg mass hangs from the 20 cm mark and an unknown mass m hangs from the 160 cm mark. For the rod to stay balanced, the value of m is (take g = 10 m/s^2):
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For a body balanced about a pivot, the total anticlockwise moment equals the total clockwise moment: d1 x F1 = d2 x F2. This is the rotational-equilibrium condition (sum of torques about the pivot = 0).
The fulcrum is the fixed pivot point about which the lever turns. In NEET problems it is the wedge, knife-edge or support. Moments are always taken about the fulcrum because its reaction force gives zero moment there.
Mechanical advantage = load/effort = effort arm/load arm = d2/d1. If it is greater than 1, a small effort lifts a large load. A crowbar, see-saw and the beam of a balance are all levers.
At its geometric centre - the mid-point (for a 200 cm rod that is the 100 cm mark). You treat the whole weight as one downward force acting there when writing moments.
Because the unknown reaction force at the pivot has zero arm there, so it drops out of the equation. This leaves you with only the known/unknown loads, making the algebra shortest. For NEET speed, always pick the pivot as the moment point.
