Torque, Equilibrium and Pulleys Simulator

What is torque?

Pushing a door close to its hinge is different from pushing at the handle. The same force can have a greater turning effect when applied farther from the axis. Torque measures the turning effect of a force about an axis. Move a mass along the simulated beam, predict the result and compare it with the worked solution.

Torque formula: τ = F · d

F is force in newtons (N). d is the perpendicular distance from the pivot to the force’s line of action, in metres. r is the distance to the point of application; θ is the angle between the position vector and force. Torque is expressed in N·m.

The lever arm is not necessarily the full beam length. If the force’s line of action passes through the pivot, d = 0 and its torque is zero. For a perpendicular 30 N force at 0.40 m, torque is 12 N·m. At 0.80 m it becomes 24 N·m. Torque and energy are different quantities even though they share physical dimensions; we use N·m for torque and J for work.

Beam balance: must the masses be equal?

No. Compare the products of weight and perpendicular distance. Choose counterclockwise as positive and clockwise as negative, and use that convention consistently.

For a weightless horizontal beam, a 2 kg mass at 0.60 m balances a 3 kg mass at 0.40 m on the opposite side: 2 × g × 0.60 = 3 × g × 0.40. The common g cancels. A heavier mass can balance at a shorter distance.

Move the pivot in the simulator. A uniform beam’s own weight acts at its midpoint; when the pivot moves away from that point, the beam’s weight also produces torque. Include it in your calculation.

Both equilibrium conditions matter

For static equilibrium in a plane, both the net force and net torque must be zero:

Zero net torque alone does not prevent translational acceleration. Zero net force alone does not prevent a turning effect. A support force acting through the chosen pivot has zero torque about that pivot, but it still matters in the force balance.

How to calculate two support reactions

Let supports A and B be separated by L. A beam has weight G_b acting at x_b, and a load has weight G_l acting at x_l. Measure distances from A. For downward loads to the right of A:

Take moments about A to find N_B, then use vertical force balance for N_A. Reconsider torque signs if the arrangement changes.

Worked example: Supports are 2 m apart. A uniform beam weighs 40 N, acting 1 m from A. An 80 N load sits 1.5 m from A.

1. N_B × 2 = 40 × 1 + 80 × 1.5 = 160.
2. N_B = 80 N.
3. N_A = 40 + 80 − 80 = 40 N.
4. The reactions add to 120 N, equal to the total weight.

A support underneath an unfastened beam can push upward but cannot pull downward. A negative calculated reaction means the assumed two-contact equilibrium is impossible. At the tipping threshold, the reaction at the losing contact is zero.

Pulleys: less force means more rope

The simulator uses ideal pulleys: massless ropes and pulleys, with no friction. For equilibrium or constant-speed lifting, if n rope segments support the moving load assembly:

G is the moving assembly’s weight, F the pulling force, h the rise and s the length of rope pulled. Count the rope segments supporting the moving assembly, rather than every rope or pulley in the picture. Tension is the same throughout one ideal rope.

Example: Lift a 200 N load by 0.50 m with four supporting segments. F = 50 N, s = 2 m and work = 100 J, equal to G × h. An ideal pulley offers a force advantage, not a work advantage.

A practical exam-solving routine

1. Select the system and draw its forces. Weight is G = m·g, not mass alone.
2. Choose a pivot. Passing through an unknown force can simplify the calculation.
3. Mark perpendicular distances. Convert centimetres to metres.
4. Decide each force’s turning direction.
5. Write both force and torque equilibrium equations.
6. Check whether the result makes physical sense, including possible loss of contact.

The simulation uses g = 9.81 m/s². If an exam question specifies g = 10 m/s², use the given value. This lesson supports conceptual physics practice, including Turkish YKS/AYT preparation.

Check your understanding

Before moving a mass, predict the direction of rotation. Then test your prediction and compare your calculation with the simulator’s solution panel.