Question

Your doctor’s scale has arms on which weights slide to counter your weight, Fig. 9–35. These weights are much lighter than you are. How does this work?

Short answer

The scale balances when the torque produced by your weight (small lever arm, large mass) is similar to the torque produced by the sliding weights (large lever arm, small mass). This is a condition of rotational equilibrium.

Step-by-step solution

Understanding rotational equilibrium

Rotational equilibrium is a state in which the object's angular acceleration equals zero. It must be true for any axis of rotation.

Working of doctor’s scale 

The sliding weights on the movable scale are located farther away from the pivot than the force exerted by your weight. These can produce a torque to balance the torque induced by your weight even though they weigh less. When the torques are similar in magnitude and opposite in direction, the arms will be in rotational equilibrium.