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No, a single force cannot produce a zero torque. Torque, represented by the symbol
τ, is the measure of the force's tendency to cause an object to rotate about an axis or pivot point. Mathematically, torque is defined as the cross product of the force vector and the position vector from the axis of rotation to the point of application of the force:
τ=r×F
Where:
τ is the torque vector,
r is the position vector,
F is the force vector.
For a single force to produce a non-zero torque, it must act at a distance from the axis of rotation. If the force is applied directly along the axis of rotation or if its line of action passes through the axis, the lever arm (distance from the axis to the point of application of the force) becomes zero, resulting in zero torque.
In summary, a single force can only produce a non-zero torque if it acts at a distance from the axis of rotation. If the force is applied directly along the axis of rotation or if its line of action passes through the axis, the torque produced will be zero.