Calculating net torque

The same force, when applied at different locations relative to the rotational axis, produces different torques for eachThe same force can produce a different torque around a different center of rotation. The torque from any force depends on the line of action of the force relative to the location of the center of rotation. The drawing to the right shows the same +10 N force creating torques of +20, +10, and −20 N m when applied at three different places with different centers of rotation. Read the text aloud
Counterclockwise torque is a positive torque in the sign conventionTorques can be negative or positive depending on whether they tend to cause clockwise or counterclockwise rotation about any given center. By convention, a positive torque tends to increase the angle with the x-axis, which means counterclockwise rotation. A negative torque tends to decrease the angle with the x-axis, which means clockwise rotation. Read the text aloud
The torques caused by these three forces add up to zeroLike forces, torques add as vectors. The net torque is the sum of all torques acting around a particular center. Because torque depends on the choice of center, it is absolutely crucial that all torques be determined around the same center point in order to add them. In the example at right of a balancing board, the net torque from the three forces is zero. Read the text aloud Show Direction of the torque vector
Torque can be determined around any point in space; it does not have to be the actual center of rotation. You are free to choose the “center” to be anywhere. This is very useful for the following reason:

An object in equilibrium has zero net torque around any center!

If the net torque were not zero around some point in space, the object would rotate around that point. It follows that any object that is not moving must have zero net torque around all possible choices of “center.” For static equilibrium problems it is most convenient to choose the “center” to be the place where one or more unknown forces act. This is useful because the torque is zero for any force whose line of action passes through the center. Read the text aloud

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