Inertial & Gravitational Mass

Understanding Mass and Weight

Mass and weight are related but distinct concepts in physics. Understanding the difference between inertial mass and gravitational mass is crucial for grasping how objects interact with forces.

Inertial Mass

• Definition: Inertial mass is a measure of an object's resistance to changes in its state of motion. It is the "inertia" of the object.
• Role in Newton's Second Law: Inertial mass is the "m" in Newton's second law of motion: $F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration.
• Measurement: Inertial mass is determined by applying a known force to an object and measuring its acceleration.

Gravitational Mass

• Definition: Gravitational mass is a measure of the strength of an object's interaction with the gravitational field.
• Role in Gravitational Force: It appears in the universal law of gravitation: $F = \frac{Gm_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between their centers.
• Measurement: Gravitational mass is determined by comparing the gravitational force on an object to a known standard.

Newton's Law of Gravitation

Newton's law of gravitation states that every point mass attracts every other point mass by a force acting along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

The formula is:

$$F = \frac{Gm_1m_2}{r^2}$$

• $F$: Gravitational force between two masses
• $G$: Universal gravitational constant $\approx 6.674 \times 10^{-11} \text{Nm}^2/\text{kg}^2$
• $m_1, m_2$: Masses of the two objects
• $r$: Distance between the centers of the two masses

Motion Under Gravity

Motion under gravity is a special case of motion where the only force acting on an object is gravitational force. This is often approximated as $g \approx 9.8 \text{m/s}^2$ near the Earth's surface.