Rotational Equilibrium
- State the two conditions for static equilibrium
- Solve balanced-beam and seesaw problems
- Choose a pivot point to simplify a torque equation
Two conditions for static equilibrium
An object is in static equilibrium when it is neither translating nor rotating — and that requires two conditions: the net force must be zero (ΣF = 0) so it does not accelerate, and the net torque must be zero (Στ = 0) so it does not start spinning. Balancing the forces alone is not enough; an object with balanced forces could still rotate if the torques do not cancel.
Balancing a beam
For a seesaw or beam, equilibrium means the clockwise torques equal the counterclockwise torques about the pivot. Since torque is (force)(distance), a small weight far from the pivot can balance a large weight close in. When you compute torques about the pivot itself, the pivot’s own support force has zero lever arm and drops out — one unknown gone for free.
A 30 kg child sits 2 m to the left of a seesaw’s pivot. Where must a 20 kg child sit on the right to balance it? (g cancels)
- 1.Balance torques about the pivot: (left weight)(left distance) = (right weight)(right distance).
- 2.The g in each weight cancels, so 30 × 2 = 20 × d.
- 3.That gives 60 = 20 × d.
- 4.Solve: d = 60 ÷ 20 = 3 m to the right of the pivot.
Take torques about the point where an unknown force acts, and that force vanishes from the equation (zero lever arm). Choosing the pivot cleverly can turn a two-unknown problem into a one-step solve.
A 40 kg child sits 1.5 m from the pivot of a seesaw. A 30 kg child sits on the other side. How far from the pivot must the 30 kg child sit to balance it?
For an object to be in complete static equilibrium, which condition must hold?
Free-response equilibrium problems almost always need both conditions. Write ΣF = 0 and Στ = 0 as two separate equations — many setups are unsolvable from the force equation alone.
Answer the 2 checkpoints as you read.
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