11.4 - Mass and Inertia

Mass

• Mass is the quantity of matter contained in an object.
• S.I. unit: kilogram (kg).
• Mass remains constant if the quantity of matter does not change.

Inertia

• Inertia is the natural tendency of an object to resist any change in its original state, whether at rest or in motion.
• Inertia is not a physical quantity; it cannot be measured and has no value or unit.
• An object at rest tends to remain at rest; a moving object tends to continue at uniform velocity in a straight line.
• Newton’s First Law of Motion: an object will remain at rest or continue to move at uniform velocity unless acted upon by an external force.
• When a moving train stops suddenly, passengers continue moving forwards because their bodies tend to remain in motion.

Relationship between Mass and Inertia

• An empty trolley is easier to move or stop than a trolley filled with goods.
• A larger mass has greater inertia and is harder to change from its original state.
• A smaller mass has smaller inertia and is easier to move or stop.
• An inertia balance, created by NASA, can determine the mass of an object at a space station.

Experiment 11.3: Mass and Inertia

Aim: Study the relationship between mass and inertia.

Problem statement: Does the mass of an object affect its inertia?

Hypothesis: The greater the mass of an object, the greater its inertia.

Variables:

• Manipulated: mass of plasticine.
• Responding: period of oscillation.
• Constant: length of oscillating hacksaw blade and shape of plasticine.

Materials and apparatus: plasticine, hacksaw blade, G-clamp, stopwatch and electronic balance.

1. Clamp one end of a hacksaw blade horizontally to a table.
2. Attach $30\text{g}$ of plasticine to its free end.
3. Displace the blade by the same amount and release it to oscillate horizontally.
4. Measure the time, $t$, for 10 complete oscillations and calculate $T=\frac{t}{10}$.
5. Repeat using $40\text{g}$, $50\text{g}$, $60\text{g}$ and $70\text{g}$ of plasticine.
6. Plot a graph of period, $T$, against mass of plasticine.

Observation and inference: the period increases as mass increases; a longer period indicates greater inertia.

Conclusion: the greater the mass, the greater the inertia; the hypothesis is accepted.

Effects of Inertia in Daily Life

Situation	Effect and application
Loose hammer head	Striking the handle on a hard surface stops the handle, while the head continues moving downwards and tightens because of inertia.
Wet umbrella	When a rapidly rotated umbrella stops, water droplets continue moving and leave the umbrella.
Vehicle collision	Seat belts, airbags and headrests reduce injury caused by the occupants’ inertia.
Aeroplane landing	A large-mass aeroplane has large inertia and needs a very long runway to stop safely.

• Inertia can produce useful positive effects.
• Inertia can also produce negative effects; safety features and suitable stopping distances reduce them.