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Yes, torque can have a negative value in physics.

Torque is vector energy. Torque is the vector analogue of Work involving force (F) and displacement (D) vectors and the angle (FD).

For example Work W = -F.D= -|FD|cos(FD) and Toque T = FxD =|FD|sin(FD).

Torque can be negative dependent on the sine(FD).

Work and torque is an example of the quaternion nature of physics; for example

Quaternion energy E = FD = -F.D + FxD, the real energy is called work F.D and the vector energy is called torque, FxD.

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