If we take a point of reference that is a certain distance away from where the force is applied and the force is acting on the same axis as the distance axis i.e. the force vector and the distance vector are on the same axis, only in opposite directions, would the torque of this force be zero? (using the torque eqn #3 which is equal to rFsinθ where θ=180°--angle between vectors that are tail-to-tail)
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If the sine of the angle (as in the same or opposite directions) is zero, then there is no torque.
To determine whether the torque of a force is zero in the situation you described, we can analyze the torque equation #3: τ = r × F × sin(θ), where r is the distance vector from the point of reference to the point where the force is applied, F is the force vector, and θ is the angle between the vectors.
In this case, you mentioned that the force and distance vectors are on the same axis, but in opposite directions. By stating that θ = 180°, you are indicating that the angle between the vectors is a straight line, which aligns with the force and distance being on the same axis in the opposite directions.
Since sin(180°) = 0, plugging this value into the torque equation, we get: τ = r × F × 0. Therefore, the torque in this case would indeed be zero.
To summarize, if the force vector and the distance vector are on the same axis, and the angle between them is 180° (tail-to-tail), the torque will be zero according to torque equation #3.