Levers and Moments

The Anatomy of a Lever and the Nature of Moments

A lever is one of the foundational mechanisms you will encounter on the Mechanical Comprehension subtest. By definition, a lever is a simple machine consisting of a rigid bar that rotates about a pivot point called a fulcrum. When you work with levers, you interact with two forces across this pivot: the effort force and the load force. The input force applied to a lever to perform work is called the effort force. Meanwhile, the load is the object being moved. The load or resistance force is the opposing force that the lever works against, which is often simply the object's weight.

To understand how a lever turns, you must understand torque, which is also called a moment of force. Torque is defined as the tendency of an applied force to rotate an object around a pivot or axis. Rather than just asking how hard you push, torque accounts for where and how you push relative to that pivot. Torque equals the applied force multiplied by the perpendicular distance from the fulcrum to the force's line of action. In US customary units, torque is commonly expressed in pound-feet (lb·ft) or pound-inches (lb·in). In metric units, torque is expressed in newton-meters (N·m).

The distance between the pivot and the applied force plays a decisive role in rotational motion. The effort arm is the perpendicular distance from the fulcrum to the effort force's line of action, while the load arm, or resistance arm, is the perpendicular distance from the fulcrum to the load force's line of action. Increasing the effort arm increases the torque produced by a given force when its direction stays the same. For a given force applied at a given point, torque is greatest when the force is perpendicular to the line from the fulcrum to that point. Applying a force at an angle less than 90 degrees to the line from the fulcrum to the point of application produces less torque than a perpendicular force of the same size.

You experience this relationship directly when turning hardware. With the same perpendicular force applied at the handle, a longer wrench produces more torque on a bolt than a shorter one. The longer handle provides a longer effort arm, multiplying your rotational effectiveness without requiring any extra muscular input.