Classical Mechanics Quiz

Definition: The branch of physics that deals with the motion of bodies under the influence of forces.
Laws of Motion: Formulated by Isaac Newton, these are three fundamental laws that describe the relationship between a body and the forces acting upon it.
1. First Law (Inertia): An object at rest stays at rest, and an object in motion remains in motion unless acted upon by an external force.
2. Second Law (F=ma): The acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass.
3. Third Law (Action-Reaction): For every action, there is an equal and opposite reaction.

Displacement: Vector quantity that refers to the change in position of an object.
Velocity: Rate of change of displacement; can be average or instantaneous.
Acceleration: Rate of change of velocity; can be uniform or variable.
Equations of Motion:
- ( v = u + at )
- ( s = ut + \frac{1}{2}at^2 )
- ( v^2 = u^2 + 2as )

Force: An interaction that changes the motion of an object; measured in Newtons (N).
Types of Forces:
- Gravitational Force: Attractive force between two masses.
- Frictional Force: Opposes motion between surfaces in contact.
- Tension Force: Force transmitted through a string or rope when pulled.
- Normal Force: Support force exerted by a surface perpendicular to the object.

Work (W): Done when a force causes displacement; calculated as ( W = F \cdot d \cdot \cos(\theta) ).
Kinetic Energy (KE): Energy of an object due to its motion; given by ( KE = \frac{1}{2}mv^2 ).
Potential Energy (PE): Energy stored in an object due to its position; gravitational potential energy is ( PE = mgh ).
Conservation of Mechanical Energy: In the absence of non-conservative forces, the total mechanical energy (KE + PE) remains constant.

Momentum (p): Product of mass and velocity; ( p = mv ).
Conservation of Momentum: In a closed system, the total momentum before an event is equal to the total momentum after the event.
Impulse: Change in momentum; given by ( J = F \cdot t ).

Angular Displacement: The angle through which an object rotates; measured in radians.
Torque ((\tau)): A measure of the force that produces or changes rotational motion; calculated as ( \tau = r \cdot F \cdot \sin(\theta) ).
Moment of Inertia (I): The rotational equivalent of mass; depends on the mass distribution relative to the axis of rotation.
Angular Momentum (L): Product of moment of inertia and angular velocity; ( L = I\omega ).

Projectile Motion: Motion of an object thrown into the air, affected by gravity; follows a parabolic trajectory.
Simple Harmonic Motion (SHM): Type of oscillatory motion where the restoring force is proportional to displacement; examples include springs and pendulums.

These notes cover the fundamental principles of classical mechanics and are essential for understanding more complex physical systems.

Classical mechanics studies the motion of bodies under the influence of forces.
Newton's Laws of Motion detail the principles governing the relationship between objects and forces.
- First Law (Inertia): Objects maintain their state of rest or uniform motion unless acted upon by an external force.
- Second Law (F=ma): Acceleration is proportional to net force and inversely proportional to mass.
- Third Law (Action-Reaction): Every action has an equal and opposite reaction.

Displacement indicates a change in position and is a vector quantity.
Velocity represents rate of displacement change; can be categorized as average or instantaneous.
Acceleration measures the rate of velocity change; it can either be uniform or variable.
Key equations of motion:
- ( v = u + at ) relates final and initial velocity, acceleration, and time.
- ( s = ut + \frac{1}{2}at^2 ) calculates displacement over time under constant acceleration.
- ( v^2 = u^2 + 2as ) connects initial velocity, final velocity, acceleration, and displacement.

Force is any interaction that changes an object's motion, expressed in Newtons (N).
Types of forces include:
- Gravitational Force: Attraction between two masses.
- Frictional Force: Resists motion between contacting surfaces.
- Tension Force: Force transmitted through a string or rope under tension.
- Normal Force: Support force from a surface acting perpendicular to an object.

Work (W) occurs when a force causes displacement: ( W = F \cdot d \cdot \cos(\theta) ).
Kinetic Energy (KE) is energy due to motion, calculated as ( KE = \frac{1}{2}mv^2 ).
Potential Energy (PE) is stored energy based on position, with gravitational potential energy expressed as ( PE = mgh ).
Conservation of Mechanical Energy states that total mechanical energy remains constant without non-conservative forces.

Momentum (p) is defined as the product of mass and velocity: ( p = mv ).
Conservation of Momentum dictates that in a closed system, total momentum before an event equals total momentum after.
Impulse represents the change in momentum, calculated as ( J = F \cdot t ).

Angular Displacement refers to the angle through which an object rotates, measured in radians.
Torque ((\tau)) quantifies the force effect producing rotational motion: ( \tau = r \cdot F \cdot \sin(\theta) ).
Moment of Inertia (I) is the rotational mass equivalent, dictated by mass distribution around the rotation axis.
Angular Momentum (L) is the product of moment of inertia and angular velocity, expressed as ( L = I\omega ).

Projectile Motion describes the trajectory of an object under gravity, typically a parabolic path.
Simple Harmonic Motion (SHM) characterizes oscillations with a restoring force proportional to displacement, like springs and pendulums.