Physics · System Of Particles And Rotational Motion · NEET
The correct order is τ = r × F, with the position vector r written FIRST. Order matters a lot because the cross product is not commutative: r × F = -(F × r). Writing F × r gives the exact opposite direction (wrong sign). In NEET 2020 the answer was -6î N m; if you wrote F × r you would get +6î and lose the mark. Always keep r first.
r is the position vector drawn FROM the axis of rotation (usually the origin O) TO the point P where the force is applied. It is not the length of the object and not the distance moved. If the force acts at point (2, 0, 3) m and torque is taken about the origin, then r = 2î + 3k̂. Choosing a different axis changes r, so torque always depends on which point you take it about.
Use the right-hand rule for r × F: point the fingers of your right hand along r, curl them toward F, and the thumb points along τ. The torque is always perpendicular to the plane containing r and F. If the turning looks anticlockwise (in the plane of the page), τ points OUT of the page (+k̂); if clockwise, τ points INTO the page (-k̂).
When the line of the force passes through the axis, the angle θ between r and F is 0° (or 180°), so sinθ = 0 and τ = r F sinθ = 0. Physically, a push straight toward or away from the pivot cannot spin the body. This is why you push a door at the handle (far edge, θ = 90°), not near the hinges.
For torque always use SIN: τ = r F sinθ, because torque is a cross product and only the component of force PERPENDICULAR to r turns the body. The cosθ component is along r and just pushes or pulls through the axis, giving no turning. (Cosθ appears in WORK, W = F d cosθ, not in torque — do not mix them up.)
The torque about the origin when a force 3ĵ N acts on a particle whose position vector is 2k̂ m is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
τ = r × F, where r is the position vector from the axis to the point of application of force F. In component form τ = (r × F) is found using the determinant of î, ĵ, k̂ with r and F components.
The SI unit of torque is newton-metre (N m). Although it has the same dimensions as energy [M L² T⁻²], torque is a vector while work is a scalar, and we never write torque in joules.
The magnitude is τ = r F sinθ, where θ is the angle between r and F. This equals F × (perpendicular distance from the axis to the line of force), also written τ = r⊥ F or r F⊥.
Torque is maximum when θ = 90° (force perpendicular to r), giving τ = r F. It is zero when θ = 0° or 180° (force along the line of r, passing through the axis), because sinθ = 0.
Torque is a vector quantity. Its direction, given by the right-hand rule for r × F, lies perpendicular to the plane containing r and F (along the axis of rotation).
