Torque
τ = r × F = rF sinθ — drag angle and watch rotation direction flip.
Key Notes
Torque τ is the rotational analog of force — measures the tendency of a force to rotate a body about an axis.
τ = r × F. Magnitude: τ = r·F·sin θ = F·r_perp = r·F_perp.
Units: N·m (same as energy units, but conceptually different — vector vs scalar).
Direction: perpendicular to plane of r and F (right-hand rule).
Rotational Newton's 2nd law: τ_net = I·α.
Equilibrium: a body is in mechanical equilibrium when Σ F = 0 AND Σ τ = 0 (both translational and rotational).
Couple: two equal-magnitude, opposite-direction forces with different lines of action — produces pure rotation (net F = 0 but τ ≠ 0).
Lever, wrench, door hinge — all use torque. Long lever arm = more rotational effect for same force.
Formulas
Torque (vector)
Cross product.
Magnitude
θ = angle between r and F. Max when θ = 90°.
Newton's 2nd (rotation)
τ and α both about the SAME axis.
Equilibrium conditions
Both must hold simultaneously.
Couple moment
d = perpendicular distance between the two lines of action.
Important Points
Torque has units N·m but is NOT energy — it's a vector quantity.
Maximum torque when force is PERPENDICULAR to lever arm.
Long wrench → more torque from same hand force ⇒ easier to loosen bolts.
Static equilibrium: BOTH F-balance and τ-balance must hold.
Couple: τ depends only on the separation d between forces, not on the chosen pivot point.
Doors: handle is far from hinges (large r) ⇒ small F produces enough τ to open.
Torque notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.