Q.Explain the types of equilibrium with suitable examples.

Step 1. Translational equilibrium.

A body's linear momentum stays constant exactly when the net external force on it vanishes:

In practice this is checked by resolving every force into horizontal and vertical components and demanding that the resultant vanish separately along each direction. A body satisfying only this condition need not be motionless — it may still be spinning.

Step 2. Rotational equilibrium.

A body's angular momentum stays constant exactly when the net external torque about any chosen point vanishes:

with a consistent sign convention (say, anticlockwise positive) applied throughout. A body satisfying only this condition need not be at rest — it may still be translating.

Step 3. Mechanical (static) equilibrium.

Mechanical equilibrium requires both conditions together, $\vec F_{net}=0$ and $\vec\tau_{net}=0$. Within this, static equilibrium is the special case where the linear momentum and angular momentum are not merely constant but exactly zero — the body is genuinely motionless, neither translating nor rotating. A book resting on a table, or a ladder leaning safely against a wall, are in static equilibrium.

Step 4. Dynamic equilibrium.

Dynamic equilibrium is the case where linear and angular momentum are constant but need not be zero — for example, a body coasting at a steady velocity in a straight line, or a flywheel spinning at a constant angular speed with no net torque acting on it. Both $\vec F_{net}=0$ and $\vec\tau_{net}=0$ still hold; the body simply isn't at rest.

Step 5. Stable equilibrium.

Cutting across the above, a separate question is how a body in equilibrium responds to being slightly disturbed. In stable equilibrium, the body returns to its original equilibrium position once released after a small disturbance. On disturbance, its center of mass rises slightly and its potential energy — which was at a local minimum in the equilibrium position — increases; the restoring effect of this increased PE (via gravity, for instance) is exactly what pulls it back. Example: a marble resting at the bottom of a bowl — nudge it up the curved side and it rolls back down to the bottom once released.

Step 6. Unstable equilibrium.

In unstable equilibrium, the body cannot return to its original position once disturbed; it instead moves further away. On disturbance, its center of mass falls and its potential energy — which was not a minimum — decreases still further, so there is no restoring tendency at all, only a tendency to keep moving away. Example: a pencil balanced vertically on its sharpened tip — the slightest nudge sends it toppling further, never back to vertical.

Step 7. Neutral equilibrium.

In neutral equilibrium, the body simply settles into its new position when disturbed, neither returning to the old position nor moving further away. Its center of mass and potential energy remain unchanged by the disturbance, since every nearby position is equally an equilibrium position. Example: a ball resting on a flat, horizontal table — roll it a little to one side and it just stays there, at the same height, with the same PE.

Classification by force/torque balance conditions, and separately by the potential-energy response to a small disturbance

• Treating 'stable equilibrium' and 'static equilibrium' as the same idea — one classifies the response to a disturbance, the other classifies whether the momenta are exactly zero or merely constant; a spinning top can be in dynamic (not static) equilibrium while still being stable to small wobbles.
• Assuming a stable equilibrium's potential energy DECREASES on disturbance (confusing it with the unstable case) — the restoring tendency exists precisely BECAUSE the PE increases when displaced, pulling the body back down the PE curve.
• Forgetting that true mechanical equilibrium needs BOTH $\vec F_{net}=0$ AND $\vec\tau_{net}=0$ simultaneously — a body can have zero net force (translational equilibrium) yet still be spinning up under a net couple that gives it nonzero net torque.