Final answer:
Both the transition of water from a gas to a solid and the cutting of hair are physical changes because they alter physical properties without changing the substances' chemical identity.
Step-by-step explanation:
The commonality between the two changes mentioned, which are indicated as a change from a gas phase to a solid phase and the shortening of long hair, is that both are considered physical changes. A physical change involves a change in physical properties such as state, shape, or size, without altering the chemical identity of the substance. In the case of water transitioning from gas (vapor) to solid (ice), and hair being cut, the composition of the substances - water molecules and hair keratin - remain unchanged even though their forms are altered.
An example that illustrates a physical change is the melting of ice. As ice melts into water, it undergoes a phase change from solid to liquid, but its chemical structure, H2O, remains the same. Similarly, when hair is cut, the structure of the hair does not change; only the length is modified. In contrast, chemical changes involve the formation of new substances with different properties and compositions, such as during the combustion of coal or the baking of bread.