Physics: Kinematics

• Physics is the study of matter, energy, and the fundamental forces that govern the universe.
• Motion is a change in the position of an object over time.

Kinematics

• Kinematics is the branch of physics that describes the motion of objects without considering the forces that cause the motion.
• Displacement is the change in position of an object and is a vector quantity, having both magnitude and direction.
• Velocity is the rate of change of displacement and is also a vector quantity.
  • Average velocity is the total displacement divided by the total time taken.
  • Instantaneous velocity is the velocity of an object at a specific instant in time.
• Acceleration is the rate of change of velocity, also a vector quantity.
  • Average acceleration is the change in velocity divided by the total time taken.
  • Instantaneous acceleration is the acceleration of an object at a specific instant in time.
• Constant acceleration equations (SUVAT equations) relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t) when acceleration is constant.
  • v = u + at
  • s = ut + (1/2)at²
  • v² = u² + 2as
  • s = (u+v)t/2
• Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity.
  • The path of a projectile is a parabola.
  • Horizontal and vertical motions are independent.
  • Horizontal velocity remains constant, neglecting air resistance.
  • Vertical motion is subject to constant acceleration due to gravity (g ≈ 9.8 m/s²).
• Uniform circular motion is the motion of an object moving at a constant speed along a circular path.
  • Although the speed is constant, the velocity is not constant because the direction is always changing.
  • Centripetal acceleration is the acceleration directed towards the center of the circle, which causes the change in direction.
  • The magnitude of centripetal acceleration is given by a = v²/r, where v is the speed and r is the radius of the circle.
  • The period (T) is the time taken for one complete revolution.
  • The frequency (f) is the number of revolutions per unit time, and f = 1/T.
  • The speed (v) is related to the radius (r) and period (T) by v = 2πr/T.

Dynamics

• Dynamics is the branch of physics that deals with the forces that cause motion.
• Force is an interaction that, when unopposed, will change the motion of an object.
• Mass is a measure of an object's resistance to acceleration and is a scalar quantity.
• Weight is the force of gravity acting on an object and is a vector quantity.

Newton's Laws of Motion

• Newton's First Law (Law of Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same velocity, unless acted upon by a net force.
  • Inertia is the tendency of an object to resist changes in its state of motion.
• Newton's Second Law: The net force acting on an object is equal to the mass of the object times its acceleration (F = ma).
  • Force and acceleration are vector quantities, and the direction of the force is the same as the direction of the acceleration.
• Newton's Third Law: For every action, there is an equal and opposite reaction.
  • If object A exerts a force on object B, then object B exerts an equal and opposite force on object A.
  • Action and reaction forces act on different objects.
• Free-body diagrams are diagrams that show all the forces acting on an object.
  • Useful for analyzing forces and applying Newton's Second Law.
• Friction is a force that opposes motion between two surfaces in contact.
  • Static friction prevents the initiation of motion.
  • Kinetic friction opposes the motion of sliding surfaces.
  • The magnitude of friction force is proportional to the normal force between the surfaces.
  • f ≤ μsN (static friction)
  • f = μkN (kinetic friction)

Projectile Motion application of kinematics and dynamics

• Projectile motion combines kinematics concepts with the influence of gravity as a force.
• The force of gravity acts vertically downwards (F = mg) causing a constant downward acceleration (g ≈ 9.8 m/s²).
• In the absence of air resistance, there is no horizontal force, so the horizontal velocity remains constant.
• The trajectory of a projectile is a parabolic path, determined by the initial velocity and launch angle.
• Range is the horizontal distance traveled by the projectile before hitting the ground.
• Maximum height is the highest vertical position reached by the projectile.
• Time of flight is the total time the projectile is in the air.
• The range, maximum height, and time of flight can be calculated using kinematic equations, considering the initial velocity, launch angle, and acceleration due to gravity.

Circular Motion application of kinematics and dynamics

• For uniform circular motion, the net force acting on the object provides the centripetal force required to keep it moving in a circle.
• Centripetal force (Fc) is given by Fc = mv²/r, where m is the mass, v is the speed, and r is the radius of the circle.
• The centripetal force is not a new force; it is the net force that causes the centripetal acceleration and can be provided by tension, gravity, friction, or a combination of forces.
• If the centripetal force is removed, the object will move in a straight line tangent to the circle at the point where the force was removed (due to inertia).
• Examples of centripetal force include:
  • A car turning a corner (friction between tires and road)
  • A satellite orbiting a planet (gravitational force)
  • An object swung in a circle by a string (tension in the string)