Physics Class 11: Kinematics and Dynamics

Definition: Study of motion without considering its causes.
Key concepts:
- Displacement: Change in position, vector quantity.
- Velocity: Displacement per unit time, can be average or instantaneous.
- Acceleration: Change in velocity per unit time.
Equations of motion:
1. v = u + at
2. s = ut + 1/2 at²
3. v² = u² + 2as
- Where:
  - s = displacement
  - u = initial velocity
  - v = final velocity
  - a = acceleration
  - t = time

Definition: Study of forces and their effects on motion.
Newton's Laws of Motion:
1. First Law: An object at rest stays at rest, and an object in motion stays in motion unless acted upon by a net external force.
2. Second Law: F = ma (Force equals mass times acceleration).
3. Third Law: For every action, there is an equal and opposite reaction.
Key parameters:
- Mass: Measure of the amount of matter in an object.
- Weight: Force due to gravity (W = mg).

Types of forces:
- Gravitational: Attracts objects with mass.
- Normal: Perpendicular contact force.
- Frictional: Opposes motion between surfaces.
- Tension: Force transmitted through a string or rope.
Motion types:
- Uniform: Constant speed and direction.
- Non-uniform: Change in speed or direction.

Law of Conservation of Energy: Energy cannot be created or destroyed, only transformed.
Forms of energy:
- Kinetic Energy (KE): Energy of motion (KE = 1/2 mv²).
- Potential Energy (PE): Stored energy (PE = mgh).
Total mechanical energy (E): E = KE + PE.
Energy transformation examples:
- Roller coaster: PE converts to KE as it descends.
- Pendulum: PE converts to KE and vice versa.

Kinematics focuses on the study of motion while ignoring the causes of that motion.
Displacement is defined as the change in position and is a vector quantity, indicating direction.
Velocity refers to the displacement divided by time and can be either average or instantaneous.
Acceleration measures how velocity changes over time.
Key equations of motion are essential for solving kinematic problems:
- ( v = u + at ) relates final velocity, initial velocity, acceleration, and time.
- ( s = ut + \frac{1}{2} at^2 ) calculates displacement based on time and acceleration.
- ( v^2 = u^2 + 2as ) connects velocities, displacement, and acceleration.

Dynamics examines the relationship between forces and motion.
Newton’s Laws of Motion delineate fundamental principles governing dynamics:
- First Law posits that an object remains at rest or in uniform motion unless acted on by an external force.
- Second Law states that force (F) is the product of mass (m) and acceleration (a), expressed as ( F = ma ).
- Third Law affirms that for every action, there is an equal and opposite reaction.
Mass is an indicator of the quantity of matter in an object, while weight is the gravitational force acting on it, calculated by ( W = mg ).

Vector analysis studies mathematical quantities possessing both magnitude and direction.
Vector addition can be performed graphically or using component methods.
Components of a vector can be calculated as:
- ( Ax = A \cos(θ) ) for the horizontal component.
- ( Ay = A \sin(θ) ) for the vertical component.
The dot product of two vectors ( A ) and ( B ) is expressed as ( A \cdot B = |A| |B| \cos(θ) ).
The cross product, denoted ( A × B ), gives a vector perpendicular to the plane formed by ( A ) and ( B ) and is calculated with ( |A| |B| \sin(θ) ).

Forces can be categorized into various types:
- Gravitational force attracts masses toward each other.
- Normal force acts perpendicular to contact surfaces.
- Frictional force opposes the relative motion between surfaces.
- Tension is the force experienced in a string or rope under tension.
Motion can be classified into:
- Uniform motion, characterized by constant speed and direction.
- Non-uniform motion, involving changes in speed or direction.

The Law of Conservation of Energy states that energy cannot be created or destroyed, only transformed.
Kinetic Energy (KE) is the energy associated with the motion of an object, calculated by ( KE = \frac{1}{2} mv^2 ).
Potential Energy (PE) is the stored energy of an object within a gravitational field, expressed as ( PE = mgh ).
The total mechanical energy ( E ) of a system is the sum of its kinetic and potential energies: ( E = KE + PE ).
Energy transformations are illustrated in examples like roller coasters, where potential energy converts to kinetic energy as the coaster descends, and pendulums, which alternate between potential and kinetic energy.