Resource: Torque

In rotational motion, all parts of a solid object move in circular paths around an axis of rotation, or pivot point. For example, a wheel rotates around an axle and the rigid bar of a lever rotates around a fulcrum.

Just as the application of a force changes linear motion, the application of a rotational force known as torque changes rotational motion. The greater the torque, the greater the change in rotational motion. Torque is determined by both the amount of force and the point at which the force is applied; it is defined as the vector product of the lever arm (the distance between the pivot point and where the force is applied) and the force applied perpendicular to the lever arm. [Note that torque is a vector quantity and has both magnitude and direction; its direction is perpendicular to both the direction of the lever arm and the force.] You can increase torque by either increasing the force or increasing the length of the lever arm.

The demonstration in the interactive activity shows the rotational motion of a beam that pivots about its center. When a mass is hung on one side of the beam, the weight produces a torque, which causes the beam to tilt. When a mass is hung on the other side of the pivot, it creates a torque in the opposite direction. The net torque of the system is equal to the sum of all the torques; if the net torque is zero, the beam is balanced in equilibrium.

Different combinations of masses and distances can achieve equilibrium in different ways. For example, two equal masses hung at a given distance on one side can be balanced by a single equal mass hung twice as far away on the other side. Interestingly, equilibrium can be maintained even when a mass is moved vertically above or below the beam. As seen in the interactive activity, the beam is balanced with equal masses hung at equal distances on either side of the pivot; when one of the masses is moved to a lower position at the same horizontal distance from the pivot, the beam remains balanced because neither the force nor the lever arm changes and therefore neither does the torque.

Some tools make use of the concept of torque to give you a mechanical advantage. For example, unscrewing a bolt with your fingers can be very difficult, but with the help of a wrench, the task is made easier. The handle of the wrench increases the torque by increasing the lever arm. Therefore, if you want to achieve greater torque without applying more force, you can do so by using a wrench with a longer handle.

To learn about a real-life example of torque, check out Segway Technology: What's Newton Got to Do with It?.

To learn more about vectors, check out Virtual Car: Velocity and Acceleration.

To learn more about levers, check out Lever an Obelisk and Levers: Raising the Moai on Easter Island.

• What relationships did you notice involving the masses and their relative distances from the pivot?
• Why does it take many more masses near the pivot to support one mass at a distance from the pivot? What does this have to do with "leverage"?
• How does the demonstration help you explain the action of a wrench?