Moment of a Force About an Axis: Scalar

Consider a cyclist riding a bicycle and applying force on the pedal to turn the wheel. When a force is exerted on the pedal, the attached chain exerts a force on the wheel's cogs. The wheel rotates around its axle, so the axis of rotation passes through it.

The moment of a force along the axis measures how much the force causes an object to rotate around a specific point or axis.

In this case, the wheel rotates about the y-axis in the x-z plane. Here, the moment arm or the perpendicular distance between the axis of rotation and the line of action of the force is the radius of the cogs.

So the moment of a force about the y-axis is equal to Frsinθ.

Since the force is tangential, the angle between the force vector and the radius is 90 degrees.

In a bicycle, the moment of force can be multiplied by the angular velocity of the axle to obtain the power generated by the wheel rotation.