Question

Why does an armature of an electric motor rotate?

Answer 1

Hint Rotary motions are generated by forces acting at a distance from the axis of rotation. An armature has windings around itself which conducts current in the magnetic field created by the permanent magnet or electromagnet.

Complete step by step answer
A rotational motion can only be caused by some force acting at a distance from the axis of rotation of the body in the rotational motion. Force acting at a distance from an axis of rotation is a quantity specifically called torque.
An electric motor by definition is a device that converts electrical motion into mechanical energy, specifically rotational energy. It is often regarded as the opposite of a generator which is a device that converts mechanical energy into electricity.
An electric motor in its most basic form comprises an armature, a conductive winding, permanent magnets or electromagnets, a pair of slip rings and a pair of carbon brushes.
Two magnets with their north and south poles are placed a distance apart, the armature, with a winding looping around the armature, is placed between these magnets. When current flows through the windings, the current at one side of the loop generates a force (hence torque) in one direction, the current on the other side (flowing in the opposite direction since it is a loop) generates a force in the opposite direction. These forces are equal and opposite but have different lines of action (since they are at different sides of the armature, hence constitute what is called a couple. These couples are the agent which rotates the armature.
Hence, we can conclude that an armature rotates due to the couple generated by the current flowing in the conducting windings in the presence of a magnetic field.

Note
In a real scenario, the number of windings around the armature is way more than one, as they are wound severally to increase the force due to the magnetic field on the armature. Slip rings are used in order to change the direction of current after a half rotation so as to keep the armature rotating in the same direction.