Physics · Motion In A Plane · NEET
The correct order is tau = r x F, where r is drawn FROM the axis (pivot) TO the point where the force acts. Cross product is not commutative: F x r gives the exact opposite vector (F x r = -(r x F)). So writing the wrong order flips the sign of your answer and points the torque the wrong way. Always start from the position vector r, then cross with force F.
Torque needs a direction because rotation happens about an axis, and that axis has an orientation in space. The cross product r x F automatically gives a vector pointing ALONG the rotation axis (perpendicular to the plane of r and F). The sign of this vector tells you the sense of rotation (anticlockwise = out of page, clockwise = into page). A single number could not capture the axis direction, so torque is a vector.
Write a 3x3 determinant with i, j, k in the top row, the components of r in the middle row, and the components of F in the bottom row. Then: tau_x = r_y F_z - r_z F_y, tau_y = r_z F_x - r_x F_z, tau_z = r_x F_y - r_y F_x. Tip: for tau_y the middle term subtracts in reverse order (r_z F_x - r_x F_z), which is exactly where most students make a sign mistake.
Torque uses SIN: tau = r F sin(theta). This is because only the component of F perpendicular to r causes turning. When F is perpendicular to r (theta = 90 degrees), sin 90 = 1 and torque is maximum. When F is along r (theta = 0 or 180 degrees), sin = 0 and torque is zero - a force pushing straight toward or away from the axis cannot rotate anything. (Cos is used for the dot product / work, not for torque.)
Yes. 'Moment of a force about a point' and 'torque' mean the same physical quantity - the turning effect of a force. NEET question papers often use the phrase 'moment of the force' (as in the 2018 paper) while textbooks use 'torque'. Both are calculated the same way: tau = r x F, with SI unit newton-metre (N m).
The moment of the force F = 4i + 5j + 6k acting at the point (2, 0, -3), about the point (2, -2, -2), is given by:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The SI unit of torque is the newton-metre (N m). Although this has the same dimensions as the joule (energy), torque is never written in joules because it is a vector turning effect, not energy.
Torque is maximum when the force is perpendicular to r (theta = 90 degrees, sin = 1), giving tau = r F. It is zero when the force acts along r (theta = 0 or 180 degrees), because a force aimed straight at or away from the axis produces no turning.
Use the right-hand rule: point your fingers along r, curl them toward F, and your thumb points along the torque vector. Out of the page means anticlockwise rotation; into the page means clockwise.
Torque is the standard physics application of the cross product, so NEET uses it to test whether you can set up r = position difference and evaluate r x F correctly. This same skill reappears in the Lorentz force F = qv x B, so mastering it here pays off twice.
