lift with all your strength. Second, you should grab onto the end of the lever, and not a point near
its axis of rotation. Third, you should lift in a direction that is perpendicular to the lever: if you
pull very hard away from the wall or push very hard toward the wall, the lever won’t rotate at all.
Let’s summarize. In order to maximize torque, you need to:
- Maximize the magnitude of the force, F, that you apply to the lever.
- Maximize the distance, r, from the axis of rotation of the point on the lever to which you
apply the force. - Apply the force in a direction perpendicular to the lever.
We can apply these three requirements to an equation for torque, :
In this equation, is the angle made between the vector for the applied force and the lever.
Torque Defined in Terms of Perpendicular Components
There’s another way of thinking about torque that may be a bit more intuitive than the definition
provided above. Torque is the product of the distance of the applied force from the axis of rotation
and the component of the applied force that is perpendicular to the lever arm. Or, alternatively,
torque is the product of the applied force and the component of the length of the lever arm that
runs perpendicular to the applied force.
We can express these relations mathematically as follows:
where and are defined below.
Torque Defined as a Vector Quantity
Torque, like angular velocity and angular acceleration, is a vector quantity. Most precisely, it is the
cross product of the displacement vector, r, from the axis of rotation to the point where the force is
applied, and the vector for the applied force, F.
To determine the direction of the torque vector, use the right-hand rule, curling your fingers
around from the r vector over to the F vector. In the example of lifting the lever, the torque would
be represented by a vector at O pointing out of the page.
EXAMPLE