Fundamental Physics: Motion, Forces, and Energy

Basic Quantities and Units

• Mass (m): The amount of matter or a measure of inertia. Unit: kg.
• Weight (W): Gravitational force. Formula: W = mg. Unit: N.
• Force (F): A push or a pull. Unit: Newton (N).
• Speed: Distance divided by time (m/s).
• Velocity (v): Speed plus direction (a vector).
• Acceleration (a): Change in velocity divided by time (m/s²).

Vectors vs Scalars

• Vector: Magnitude and direction (e.g., velocity, acceleration, force, momentum).
• Scalar: Magnitude only (e.g., mass, speed, energy).

Newton’s Laws of Motion

First Law (Inertia)

An object at rest stays at rest, and an object in motion stays in motion unless acted on by a net force.

Second Law

Formula: a = F/m

• More force leads to more acceleration.
• More mass leads to less acceleration.

Third Law

For every action force, there is an equal and opposite reaction force.

• Forces are equal in size.
• Forces act in opposite directions.
• Forces act on different objects.

Forces and Equilibrium

• Normal Force (Support Force): Perpendicular to the surface.
• Equilibrium: ΣF = 0, meaning there is no acceleration.

Acceleration and Gravity

• Acceleration is a vector.
• If velocity and acceleration are in the same direction, the object is speeding up.
• If they are in opposite directions, the object is slowing down.

Free Fall

• g = 9.8 m/s² (approximately 10 m/s²) downward.
• All objects fall at the same rate when ignoring air resistance.

Momentum (p)

Formula: p = mv (also represented as p = mvp = mvp = mv, m1, m_1, m1, m2, m_2, m2, v, v, v, m1, m2).

• It is a vector quantity.
• It is conserved if no external force is applied.

Impulse

Formula: Impulse = F × t or Impulse = Δp.

• Increase time to decrease force.
• Used in safety features like helmets, airbags, and sports follow-through.

Conservation of Momentum

If there is no external force: p_before = p_after.

Energy

Kinetic Energy (KE)

Formula: KE = ½ mv²

If speed doubles, KE quadruples.

Gravitational Potential Energy (PE)

Formula: PE = mgh

• Energy stored due to height.

Elastic (Spring) Potential Energy

Formula: PE = ½ kd²

Energy Conservation

Energy cannot be created or destroyed; it only changes form.

Example: A falling object converts PE into KE.

Important Relationships

• Backing up and speeding up: Acceleration is backward.
• Upward motion in free fall: Velocity is up, but acceleration is down.
• Constant velocity: Momentum and KE remain constant.
• Bigger mass: Results in more inertia.