# Torque: Kinetic Energy

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WHAT IS TORQUE? Torque is a measure of how much a force acting on an object causes that object to rotate. The object rotates about an axis, which we will call the pivot point, and will label 'O '. We will call the force 'F '. The distance from the pivot point to the point where the force acts is called the moment arm, and is denoted by 'r '. Note that this distance, 'r ', is also a vector, and points from the axis of rotation to the point where the force acts. (Refer to Figure 1 for a pictoral representation of these definitions.) |
Figure 1 Definitions |
Torque is defined as
= r x F = r F sin().
In other words, torque is the cross product between the distance vector (the distance from the pivot point to the point where force
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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: 1. Maximize the magnitude of the force, F, that you apply to the lever. 2. Maximize the distance, r, from the axis of rotation of the point on the lever to which you apply the force. 3. 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