Law of Universal Gravitation and Circular Motion

This page provides an overview of the prawo powszechnego ciążenia (law of universal gravitation) and the principles of circular motion. It introduces key concepts and formulas essential for understanding these fundamental physics topics.

Definition: Prawo powszechnego ciążenia states that every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

The gravitational force is given by the formula:

Highlight: F = G(Mm/r²)

Where:

• F is the gravitational force
• G is the gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²)
• M and m are the masses of the two objects
• r is the distance between the centers of the masses

The page also covers circular motion, introducing concepts such as centripetal force and centripetal acceleration.

Vocabulary: Centripetal force is the force that makes a body follow a curved path, directed toward the center around which the body is moving.

The formula for centripetal force is:

Highlight: F₁ = mv²/r

Where:

• F₁ is the centripetal force
• m is the mass of the object
• v is the velocity
• r is the radius of the circular path

Centripetal acceleration is given by:

Highlight: a = v²/r

The page also introduces the concept of angular velocity (ω), which is related to linear velocity (v) by the equation:

Example: v = ωr

Where ω is measured in radians per second.

Additional formulas and relationships presented include:

• Period of rotation: T = 2πr/v
• Angular displacement: θ = s/r (where s is arc length)
• Conversion between degrees and radians: 180° = π radians, 360° = 2π radians

Highlight: The concept of centrifugal force is mentioned as an apparent force in rotating reference frames, opposite to the centripetal force.

This comprehensive overview provides students with the essential knowledge to understand and apply the principles of gravitation and circular motion in various physics problems and real-world scenarios.