Introduction to Physics: Motion and Kinematics

• Physics is the science that deals with matter, energy, motion, and force.
• Motion is the act or process of changing position or orientation in space and time. It's a fundamental concept in physics, describing how objects move and interact.

Types of Motion

• Translational Motion happens when an object moves from one point to another.
• Rotational Motion occurs when an object spins around an axis.
• Oscillatory Motion refers to repetitive motion back and forth around an equilibrium position.

Kinematics

• Kinematics is the branch of physics that describes motion without considering its causes.
• Displacement is the change in position of an object. It's a vector quantity, having both magnitude and direction.
• Velocity is the rate of change of displacement with respect to time. It's also a vector quantity, indicating both speed and direction.
• Average velocity is the total displacement divided by the total time taken.
• Instantaneous velocity is the velocity at a specific instant in time. It's the limit of the average velocity as the time interval approaches zero.
• Speed is the magnitude of velocity, without considering direction.
• Acceleration is the rate of change of velocity with respect to time. It's a vector quantity.
• Average acceleration is the change in velocity divided by the total time taken.
• Instantaneous acceleration is the acceleration at a specific instant in time, as the time interval approaches zero.

Uniform Motion

• Uniform motion is motion with constant velocity (i.e., zero acceleration).
• In uniform motion, an object covers equal displacements in equal time intervals.
• The displacement (Δx) of an object in uniform motion can be calculated as Δx = v*Δt, where v is the constant velocity and Δt is the time interval.

Non-Uniform Motion

• Non-uniform motion is motion with changing velocity (i.e., non-zero acceleration).
• Analyzing non-uniform motion is more complex than uniform motion.
• The equations of motion relate displacement, velocity, acceleration, and time for uniformly accelerated motion (constant acceleration).
• The common equations of motion are:
  • v = v₀ + at (velocity as a function of time)
  • Δx = v₀t + (1/2)at² (displacement as a function of time)
  • v² = v₀² + 2aΔx (velocity as a function of displacement)
  • where:
    • v₀ is the initial velocity
    • v is the final velocity
    • a is the constant acceleration
    • t is the time elapsed
    • Δx is the displacement

Projectile Motion

• Projectile motion is the motion of an object thrown or projected into the air, subject to gravity.
• Projectile motion can be analyzed by considering the horizontal and vertical components of motion separately.
• The horizontal component of velocity remains constant (assuming negligible air resistance).
• The vertical component of velocity changes due to gravity (constant downward acceleration).
• The trajectory of a projectile is a parabola.
• The range of a projectile is the horizontal distance it travels before hitting the ground.
• The maximum height of a projectile is the highest vertical position it reaches.
• The time of flight of a projectile is the total time it spends in the air.

Force

• Force is an interaction that, when unopposed, will change the motion of an object.
• Force is a vector quantity, having both magnitude and direction.
• Forces cause acceleration.
• Common types of forces include:
  • Gravitational force
  • Electromagnetic force
  • Strong nuclear force
  • Weak nuclear force
• Contact forces arise from direct physical contact between objects (e.g., friction, tension, normal force).

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 speed and in the same direction unless acted upon by a force.
• Inertia is the tendency of an object to resist changes in its state of motion.
• 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 (F = ma).
• Newton's third law: For every action, there is an equal and opposite reaction.
• Action-reaction pairs of forces act on different objects.

Mass

• Mass is a measure of an object's inertia, or its resistance to acceleration.
• Mass is a scalar quantity, measured in kilograms (kg).
• Weight is the force of gravity acting on an object (W = mg, where g is the acceleration due to gravity).
• Weight is a vector quantity, measured in newtons (N).

Friction

• Friction is a force that opposes motion between surfaces in contact.
• Static friction prevents an object from starting to move.
• Kinetic friction opposes the motion of an object that is already moving.
• The magnitude of static friction is variable, up to a maximum value.
• The magnitude of kinetic friction is generally constant.
• Friction depends on the nature of the surfaces and the normal force pressing them together.

Work

• Work is the energy transferred to or from an object by a force causing a displacement.
• Work is a scalar quantity, measured in joules (J).
• Work is calculated as W = Fdcosθ, where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors.
• Work is positive if the force and displacement are in the same direction.
• Work is negative if the force and displacement are in opposite directions.
• Work is zero if the force is perpendicular to the displacement.

Energy

• Energy is the ability to do work.
• Energy is a scalar quantity, measured in joules (J).
• Kinetic energy (KE) is the energy of motion (KE = (1/2)mv², where m is mass and v is velocity).
• Potential energy (PE) is stored energy due to an object's position or configuration.
• Gravitational potential energy (GPE) is PE due to an object's height above a reference point (GPE = mgh, where m is mass, g is the acceleration due to gravity, and h is height).
• Elastic potential energy (EPE) is PE stored in a deformed elastic object, such as a spring (EPE = (1/2)kx², where k is the spring constant and x is the displacement from equilibrium).

Power

• Power is the rate at which work is done or energy is transferred.
• Power is a scalar quantity, measured in watts (W).
• Power is calculated as P = W/t, where W is work and t is time.
• Power can also be expressed as P = Fv, where F is force and v is velocity.

Momentum

• Momentum is a measure of an object's mass in motion.
• Momentum is a vector quantity, measured in kilogram-meters per second (kg m/s).
• Momentum is calculated as p = mv, where m is mass and v is velocity.
• The impulse is the change in momentum of an object.
• Impulse is calculated as J = Δp = FΔt, where F is the force applied and Δt is the time interval over which it is applied.

Conservation of Momentum

• The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it.
• In collisions, momentum is conserved.
• Elastic collision is a collision in which kinetic energy is also conserved.
• Inelastic collision is a collision in which kinetic energy is not conserved (some energy is converted to other forms, such as heat or sound).

Rotational Motion

• Angular displacement (θ) is the change in angular position of an object.
• Angular velocity (ω) is the rate of change of angular displacement.
• Angular acceleration (α) is the rate of change of angular velocity.
• Torque (τ) is a twisting force that causes rotation.
• Moment of inertia (I) is a measure of an object's resistance to rotational acceleration.
• Angular momentum (L) is a measure of an object's rotational momentum.
• The equations of rotational motion are analogous to the equations of linear motion.
• Rotational kinetic energy (KErot) is the energy of rotational motion (KErot = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity).