Chapter 2 – One-Dimensional Kinematics

Calculating Average Speed

Average speed is a fundamental concept in kinematics, representing the total distance traveled divided by the total time taken. It is useful for analyzing motion over a period of time.

• Definition: Average speed () is given by

• Example: A runner covers 40.0 km in 1 hour 41 minutes.

Characteristics of Free Fall

Free fall describes the motion of objects under the influence of gravity alone, neglecting air resistance.

• Key Point: All objects in free fall near Earth's surface accelerate downward at approximately .

Chapter 3 – Vectors in Physics

Vector Subtraction and Components

Vectors are quantities with both magnitude and direction. Operations such as addition and subtraction are performed using components.

• Definition: The component form of a vector is .

• Example: For and ,

Chapter 5 – Newton's Laws of Motion

Apparent Weight and Action-Reaction Pairs

Newton's laws describe the relationship between forces and motion. Apparent weight is the normal force exerted by a surface, which can differ from actual weight in accelerating systems.

• Apparent Weight: (for upward acceleration)

• Action-Reaction: For every action, there is an equal and opposite reaction.

• Example: A 50.0 kg person in an elevator accelerating upward at

Chapter 7 – Work and Kinetic Energy

Work-Energy Theorem

The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy.

• Equation:

• Example: Minimum work to stop a 1000 kg car moving at 50.0 m/s:

Chapter 9 – Linear Momentum and Collisions

Types of Collisions and Conservation Laws

Collisions are classified as elastic or inelastic, depending on whether kinetic energy is conserved. Momentum is always conserved in isolated systems.

• Conservation of Momentum: (for perfectly inelastic collisions)

• Example: Two cars collide and stick together:

Chapter 10 – Rotational Kinematics

Moment of Inertia and Rotational Motion

Rotational kinematics deals with angular displacement, velocity, and acceleration. The moment of inertia quantifies an object's resistance to rotational acceleration.

• Rotational Kinetic Energy:

• Angular Acceleration:

• Example: A wheel with and :

Chapter 11 – Rotational Dynamics

Torque and Balancing

Rotational dynamics involves the study of torques and forces causing rotational motion. Balancing involves ensuring net torque is zero for equilibrium.

• Torque:

• Rotational Motion Equation:

• Example: Calculating mass to balance a mobile using torque equilibrium.

Chapter 12 – Gravity

Gravitational Force and Kepler's Laws

Gravity is the force of attraction between masses. Kepler's laws describe planetary motion.

• Newton's Law of Universal Gravitation:

• Kepler's Third Law:

• Example: Gravitational force between two 50 kg people 5 m apart:

Chapter 16 – Temperature and Heat

Thermal Expansion and Heat Transfer

Temperature and heat are central to thermodynamics. Heat transfer occurs via conduction, convection, and radiation.

• Linear Expansion:

• Heat Required:

• Heat Flow by Conduction:

• Power by Radiation:

• Example: Calculating heat required to raise temperature of a lead ball:

Summary Table: Key Equations

Additional info: These notes expand on the original problems and concepts, providing definitions, equations, and examples for each topic. The summary table consolidates key formulas for quick reference.