Torque & the See-SawFoundation

Rotational equilibrium of a lever — interactive Physics simulation for IIT-JEE.

Concept

Torque (moment) is force × perpendicular distance from the pivot: $\tau = rF\sin\theta$ . A body is in rotational equilibrium when clockwise and anticlockwise moments cancel — the principle of moments. A small child far from the pivot balances a heavy adult sitting close.

Key formula

\tau = rF\sin\theta, \qquad \text{Balance: } m_1 g d_1 = m_2 g d_2 \;\Rightarrow\; m_1 d_1 = m_2 d_2

Derivation

For a rigid body, $\sum \tau = I\alpha$ . Equilibrium requires $\alpha = 0$ , i.e. $\sum\tau = 0$ about any point.

Taking moments about the pivot kills the (unknown) pivot reaction — that is why you always choose the pivot. The reaction itself follows from force balance: $R = (m_1+m_2)g$ .

Scenarios to explore

Torque & the See-Saw — Principle of moments — balance m₁d₁ against m₂d₂.

Real-world applications

Beam balances and steelyard scales.
Wrenches & door handles — force far from the hinge.
Crane counterweights; human forearm as a class-3 lever.

JEE exam tips

Take moments about the point with the most unknown forces — they vanish.
For equilibrium you need BOTH ΣF = 0 and Στ = 0; exams love breaking one silently.
Uniform beam ⇒ its weight acts at the mid-point.

Common mistakes

Using the full distance instead of the PERPENDICULAR distance for angled forces.
Forgetting the beam's own weight when the pivot is off-centre.
Adding torques without assigning clockwise/anticlockwise signs.

Exam traps to avoid

Torque balance about one point + force balance is equivalent to torque balance about two points — pick the easier pair.
g cancels in m₁d₁ = m₂d₂ — a see-saw balanced on Earth is balanced on the Moon.