Linear Momentum and Newton's Second Law of Motion

A set of vocabulary flashcards defining key terms, formulas, units, principles, and applications related to Linear Momentum and Newton's Second Law of Motion.

Linear Momentum

The product of a body's mass and its velocity ($p = mv$), which is a vector quantity.

S.I. Unit of Linear Momentum

$$kg\,m/s$$

Force

The physical cause which changes the state of motion of a body when applied.

Newton's Second Law of Motion

States that the rate of change of momentum of a body is directly proportional to the force applied on it, and the change in momentum takes place in the direction of the applied force.

Mathematical Expression of Force

$\text{force} = \text{mass} \times \text{acceleration}$ ($F = ma$).

1 Newton ($1\,N$)

The S.I. unit of force, defined as the force which when applied on a body of mass $1\,kg$ produces an acceleration of $1\,m/s^2$.

1 Dyne

The C.G.S. unit of force, defined as the force which when applied on a body of mass $1\,g$ produces an acceleration of $1\,cm/s^2$.

Relationship Between S.I. and C.G.S. Units of Force

$$1\,N = 10^5\,dyne$$

Conditions for $F = ma$

The mass of the body remains constant and its velocity is much smaller than the velocity of light.

Qualitative vs. Quantitative Definitions of Force

Newton's first law of motion defines force qualitatively, whereas Newton's second law of motion defines force quantitatively.

Inertia and Mass Relationship

Inertia directly depends on mass; as the mass increases, inertia also increases.

Catching a Fast-Moving Ball Application

A cricketer withdraws his hands along with the ball to increase the time taken to stop it, which decreases the force exerted on his hands and prevents injury.

Athlete Landing on Sand Application

When an athlete lands on sand, their feet push the sand for some distance, increasing the time duration to come to rest, which decreases the force exerted on their feet and saves them from getting hurt.

Glass Vessel Falling on Carpet Application

A glass vessel falling on a carpet does not break because the carpet increases the time duration in which the vessel comes to rest, causing less force to be exerted on it.