What Causes Angular Motion (Eccentric Force)?

Angular motion is caused when an eccentric force acts with its line of action away from an object's axis of rotation or centre of mass. This creates a torque, producing angular acceleration in accordance with Newton's second law applied to rotation.

How an Eccentric Force Produces Rotation

The turning effect depends on the force and the perpendicular distance between its line of action and the axis of rotation:

$$\tau = Fd_{\perp}$$

Here, $\tau$ is torque in newton metres, $F$ is force in newtons, and $d_{\perp}$ is the moment arm in metres. A larger force or moment arm produces greater torque.

The resulting angular acceleration is:

$$\alpha = \frac{\tau}{I}$$

where $\alpha$ is angular acceleration and $I$ is the object's moment of inertia. Therefore, the same torque produces less angular acceleration when mass is distributed farther from the axis.

For example, if a force of $500\ \text{N}$ acts with a perpendicular moment arm of $0.20\ \text{m}$, then:

$$\tau = 500 \times 0.20 = 100\ \text{N m}$$

A sporting example is an off-centre hit on a football, which causes both translation and spin. The common misconception is that an eccentric force causes only rotation. Unless the axis is fixed or other forces balance the resultant force, it can cause both linear acceleration and angular acceleration.

IB Exam Technique

For subtopic B.2.1, identify the axis, draw the force's line of action, label the perpendicular moment arm, and apply $\tau = Fd_{\perp}$. Explain the direction of rotation and connect the net torque to angular acceleration rather than merely stating that the object spins.