Is torque a scalar or vector quantity?

Torque is a vector quantity because it has both magnitude and a specific direction given by the right-hand rule.

Definition of torque

Torque (?) measures the turning effect of a force acting at a distance from an axis. Mathematically ? = r x F, the cross product of position vector r and force vector F.

Using the right-hand rule, curl your fingers from r toward F; your thumb points along the torque vector. For a bolt, clockwise torque points into the page, counter-clockwise points out.

Units and magnitude

The SI unit is newton-metre (N m). Only the perpendicular component of force counts, so ? = rF sin ?. The longer the lever arm r or the greater the force F, the bigger the torque.

Applications of Torque

• Engines: Crankshaft torque tells how much rotational work can be done.
• Wrenches: A longer spanner gives more torque for the same effort.
• Bicycle pedals: Force on pedals times crank length produces wheel motion.