Torque

What is torque ($\tau$)?

The force exerted on a lever arm about an axis of rotation, e.g. the force you apply on a crowbar to loosen a lug nut when changing a tire.

What is torque directly proportional to?

The perpendicular distance from the axis of rotation, i.e. it is easier to close a door by pushing on the door knob instead of one inch away from the hinge.

When applying a force, what angle maximizes the effect of the force?

The angle perpendicular to the plane of the lever arm, i.e. 90$^{o}$ to the door where $\sin 90^{o} = 1$.

How do you calculate the magnitude of torque?

$$\tau = rF\sin \theta$$ (63.1)

Where $\tau$ is the torque in Newton-meters (N$\cdot$m), $r$ is the length of the lever in meters (m), $F$ is the force applied to the lever in Newtons (N) and $\theta$ is the angle between the lever arm ($r$) and the force vector $F$ in degrees ($^{o}$).