Torque is an important quantity for describing the dynamics of a rotating rigid body. We see the application of torque in many ways in the world, such as when pressing the accelerator in a car, which causes the engine to apply additional torque on the drivetrain. Here, we define torque and provide a framework to create an equation to calculate torque for a rigid body with fixed-axis rotation.
Torque can be considered as the rotational counterpart to force. Since forces change the translational motion of objects, the rotational counterpart must be related to changing the rotational motion of an object about an axis. We call this rotational counterpart torque.
In everyday life, we rotate objects about an axis all the time, so intuitively we already know much about torque. Consider, for example, how we rotate a door to open it.
The first point implies that the farther the force is applied from the axis of rotation, the greater the angular acceleration; the second implies that the effectiveness depends on the angle at which the force is applied; the third implies that the magnitude of the force must also be part of the equation. Note that for rotation in a plane, torque has two possible directions; torque is positive when the rotation is counterclockwise and negative when the rotation is clockwise.
This text is adapted from Openstax, University Physics Volume 1, Section 10.6: Torque.
Consider a pottery wheel. If a force is applied on the wheel’s edge, away from the center, the pottery wheel rotates easily. It shows that to rotate an object easily, force should be applied at a distance from the rotational axis.
The displacement vector from the rotational axis to the application point of the force is called the lever arm.
Torque is the cross product of this lever arm and the applied force. Therefore, it is perpendicular to both the force and the lever arm.
If a force vector is at an angle θ to the position vector, the magnitude of the torque is calculated using the component of the force perpendicular to the lever arm, which is then equal to rFsinθ.
If the right-hand fingers curl in the direction of the object’s rotation, the thumb shows the direction of the torque.
Conventionally, if the object's rotation is counterclockwise, then the torque is positive. Similarly, if the object's rotation is clockwise, the torque is then considered negative.
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