Physics Unit 2: Two-Dimensional Motion

Unit 2: Two-Dimensional Motion

• Two-dimensional motion describes objects moving in paths that are not straight lines.
• Projectile motion is a type of two-dimensional motion where an object moves through the air, affected only by gravity.
  • Examples include a football, basketball, or water droplets from a fountain.
  • The trajectory of a projectile is curved.
  • The motion can be analyzed by separating it into horizontal and vertical components.
• Horizontal motion is independent of vertical motion.
  • Horizontal velocity remains constant (neglecting air resistance).
• Vertical motion is affected by gravity.
  • Vertical acceleration is constant (9.80 m/s² downward).
  • Vertical velocity changes.
• There are essential equations for describing projectile motion that provide information about position, velocity, and time of flight.
• Horizontal and inclined projectiles are covered separately in the unit.
  • Horizontal projectiles have zero initial vertical velocity.
  • Inclined projectiles have both horizontal and vertical components to their initial velocity.

Rotational Motion

• Rotational motion involves objects moving in circular paths around a fixed axis.
• Key quantities include:
  • Angular displacement (θ): Measured in radians.
  • Angular velocity (ω): Rate of change of angular displacement (rad/s).
  • Angular acceleration (α): Rate of change of angular velocity (rad/s²).
• The right-hand rule is used to determine the direction of angular velocity and acceleration vectors.
• Linear and angular quantities are related.
  • Example: Linear speed (v) = radius (r) × angular speed (ω).

Rotational Dynamics

• Dynamics of rotational motion concern the factors causing rotations.
• Torque (τ): The turning force, depending on force magnitude, the lever arm (distance from the axis), and the angle of force application.
  • τ = rFsin(θ)
• Moment of inertia (I): Describes an object's resistance to changes in rotational motion.
  • Depends on the mass of an object and the distribution of mass relative to the axis of rotation.
• Torque, moment of inertia, and angular acceleration are related.
  • τ = Iα

Kepler's Laws and Newton's Law of Universal Gravitation

• Kepler's First Law: Planets move in elliptical orbits around the sun, with the sun at one focus.
• Kepler's Second Law: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.
  • Planets speed up when closer to the sun and slow down when farther away.
• Kepler's Third Law: The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. (T² ∝ r³)
• Newton's Law of Universal Gravitation: Every mass attracts every other mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
  • F = G(m₁m₂)/r²
  • G is the gravitational constant.
• Newton's Law provides a theoretical foundation for Kepler's empirically derived laws.