Modern Physics- General Introduction - Newtonian Mechanics
- Recap of classical mechanics
- Limitations of classical mechanics
- Introduction to modern physics
- Key concepts in modern physics
- Newtonian mechanics in modern physics
- Importance of Newtonian mechanics in understanding the world
- Applications of Newtonian mechanics
- Examples of Newtonian mechanics in everyday life
- Equations in Newtonian mechanics
- Summary and conclusion
Newton’s Laws of Motion
- Newton’s first law: Law of inertia
- An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an external force
- Newton’s second law: Force and acceleration
- 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: Action and reaction
- For every action, there is an equal and opposite reaction
Equations of Motion
- Equations for uniformly accelerated motion
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 +2as
- s = (v + u)t/2
Free Body Diagrams
- Understanding forces acting on an object
- Representing forces using vectors
- Identifying the direction and magnitude of forces
- Examples: gravity, friction, normal force
Work and Energy
- Work done by a force
- W = F * s * cosθ, where θ is the angle between the force and the displacement
- Kinetic energy
- KE = (1/2)mv^2
- Potential energy
- Gravitational potential energy: PE = mgh
- Elastic potential energy: PE = (1/2)kx^2
- Conservation of mechanical energy
Conservation of Linear Momentum
- Linear momentum
- Momentum = mass * velocity
- p = mv
- Conservation of linear momentum
- In an isolated system, the total momentum before an interaction is equal to the total momentum after the interaction
- Examples: collisions, explosions ==
Circular Motion and Centripetal Force
- Uniform circular motion
- An object moving in a circle at a constant speed
- Centripetal acceleration: a = v^2/r
- Centripetal force: F = (mv^2)/r
- Examples of circular motion in everyday life
- Carousel, car on a curved road, planets orbiting the sun
Gravitation
- Law of universal gravitation
- Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers
- F = G(m1m2)/r^2
- Gravitational field
- Gravitational field strength: g = F/m
- Acceleration due to gravity: g = GM/r^2
- Examples: weight, satellite motion
Angular Displacement, Velocity, and Acceleration
- Angular displacement
- θ = s/r
- Angular velocity
- ω = θ/t or ω = 2πf
- Angular acceleration
- α = ω/t or α = (2πf - ωi)/t
- Relationship between linear and angular quantities
- v = rω, a = rα
- Examples: rotating objects, spinning tops
Torque and Rotational Motion
- Torque
- Torque = force * lever arm
- τ = Frsinθ
- Moment of inertia
- Moment of inertia = mass * (radius of gyration)^2
- I = mk^2
- Angular momentum
- Angular momentum = moment of inertia * angular velocity
- L = Iω
- Conservation of angular momentum
- In the absence of external torques, the total angular momentum of a system remains constant
- Examples: spinning skater, spinning ice skater throwing arms out ==
Modern Physics- General Introduction - Newtonian Mechanics Recap of classical mechanics Limitations of classical mechanics Introduction to modern physics Key concepts in modern physics Newtonian mechanics in modern physics Importance of Newtonian mechanics in understanding the world Applications of Newtonian mechanics Examples of Newtonian mechanics in everyday life Equations in Newtonian mechanics Summary and conclusion