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Physics with Calculus: Newton's Laws and Linear Motion

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  • Aristotle's concept of natural motion

    Motion that proceeds from the "nature" of an object, depending on its elemental composition. Speed is roughly proportional to weight.

  • Aristotle's concept of violent motion

    Motion produced by external pushes or pulls. Objects remain at rest unless acted upon by a force.

  • Galileo's experiment with falling objects

    Objects of different weights fall at the same rate and hit the ground simultaneously if air resistance is negligible.

  • Galileo's concept of inertia

    Inertia is a property of matter to resist changes in motion.

  • Newton's First Law of Motion

    Every object continues in a state of rest or uniform motion in a straight line unless acted on by a nonzero net force.

  • Definition of force and its SI unit

    Force (symbol F) is an interaction that changes motion. SI unit is the newton (N).

  • Difference between vector and scalar quantities

    Vectors have magnitude and direction (e.g., force, velocity). Scalars have only magnitude (e.g., mass, temperature).

  • Net force

    The vector sum of all forces acting on an object.

  • How to find net force for forces in opposite directions

    Subtract the smaller force from the larger force and take the direction of the larger force.

  • Resultant force for perpendicular vectors

    Use the Pythagorean theorem to find the magnitude of the resultant vector.

  • Equilibrium rule

    An object is in equilibrium when the vector sum of all forces equals zero: \(\sum F = 0\).

  • Support force (normal force)

    The force perpendicular to the surface that supports the weight of an object.

  • Static vs dynamic equilibrium

    Static equilibrium: object at rest. Dynamic equilibrium: object moving at constant speed in a straight line.

  • Acceleration definition and unit

    Acceleration is the rate of change of velocity over time. Symbol: a. Unit: m/s\(^2\).

  • Acceleration when moving in a circle at constant speed

    Acceleration occurs due to change in direction even if speed is constant.

  • Free fall acceleration on Earth

    Acceleration due to gravity is approximately 9.8 m/s\(^2\).

  • Speed of a freely falling object starting from rest

    Speed increases by \(gt\), where g is acceleration due to gravity and t is time.

  • Distance fallen by a freely falling object starting from rest

    Distance is given by \(\frac{1}{2}gt^2\).

  • Velocity of an object thrown straight upward at equal elevations

    Upward and downward velocities at equal heights are equal in magnitude but opposite in direction.

  • Motion is relative

    Motion is always described relative to a reference frame, usually the Earth's surface.