Kinematics: Motion and Equations

Kinematics

• Kinematics describes the motion of objects without considering the forces causing the motion.
• It focuses on the relationships between displacement, velocity, acceleration, and time.
• Displacement: The change in position of an object. It's a vector quantity, meaning it has both magnitude and direction.
• Velocity: The rate of change of displacement. It's also a vector quantity. The average velocity is the total displacement divided by the time interval. Instantaneous velocity is the velocity at a specific point in time.
• Acceleration: The rate of change of velocity. It's also a vector quantity. Average acceleration is the change in velocity divided by the time interval. Instantaneous acceleration is the acceleration at a specific point in time.
• Equations of Motion: Several equations relate displacement, velocity, acceleration, and time for constant acceleration motion. These are crucial for analyzing and solving kinematics problems. They typically involve variables like initial velocity (v₀), final velocity (v), acceleration (a), displacement (s), and time (t). Common equations include:
  • v = v₀ + at
  • s = v₀t + ½at²
  • v² = v₀² + 2as
• Uniform Motion: Motion with constant velocity (zero acceleration). In this case, displacement is linearly proportional to time.
• Uniformly Accelerated Motion: Motion with constant acceleration. This is a common type of motion in physics problems, characterized by a parabolic relationship between displacement and time.

Dynamics

• Dynamics describes the motion of objects and the forces that cause that motion.
• It combines kinematics with Newton's Laws of Motion.
• Newton's First Law: An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. This is also known as the law of inertia.
• Newton's Second Law: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This is expressed mathematically as F = ma, where F is the net force, m is the mass, and a is the acceleration.
• Newton's Third Law: For every action, there is an equal and opposite reaction. The forces act on different objects.
• Force: A push or pull that can change the state of motion of an object. Forces are vector quantities with magnitude and direction.
• Types of Forces:
  • Gravitational Force: The force of attraction between any two objects with mass. Described by Newton's Law of Universal Gravitation. It is fundamental and acts on all particles with mass.
  • Normal Force: The force exerted by a surface on an object resting on it, perpendicular to the surface.
  • Frictional Force: The force that opposes motion between two surfaces in contact. The magnitude depends on the types of surfaces and the applied normal force.
  • Applied Force: A force applied to an object by some agent.
• Free-body diagrams: Diagrams that show all the forces acting on an object. They help visualize the forces and are crucial for problem-solving.
• Equilibrium: A state where the net force on an object is zero. An object in equilibrium may be at rest or moving with constant velocity.
• Motion in a plane: Combining forces in different directions to determine the resulting motion in 2 dimensions. This requires vector addition and consideration of x and y components.
• Circular motion: The motion of an object in a circular path. Involves centripetal acceleration, which is always directed towards the center of the circle.
• Work: The scalar product of force and displacement. Work can be positive, negative, or zero depending on the angle between the force and displacement vectors.
• Energy: The capacity to do work. Different forms of energy include kinetic energy (energy of motion) and potential energy (energy stored due to position or configuration). Work-energy theorem relates work done to changes in kinetic energy.