Definitions and Physical Constants

Kinematics in One Dimension

Kinematics describes the motion of objects without considering the causes of motion. Key quantities include displacement, velocity, and acceleration.

• Displacement:

• Average velocity:

• Average acceleration:

• Instantaneous velocity:

• Instantaneous acceleration:

Equations of motion for constant acceleration:

Quadratic equation: If , then

Kinematics in Two Dimensions & Vectors

Motion in two dimensions requires vector analysis. The position, velocity, and acceleration are all vector quantities.

• Vector notation:

• Average velocity vector:

• Instantaneous velocity vector:

Trigonometry: For , ,

Newton's Laws of Motion

First Law (Inertia)

An object at rest remains at rest, and an object in motion remains in motion at constant velocity unless acted upon by a net external force.

• Example: A ball on a frictionless surface will continue moving at constant speed unless a force acts on it.

Second Law (Force and Acceleration)

The net force acting on an object is equal to the mass of the object multiplied by its acceleration.

• Example: If a 2 kg object accelerates at , the net force is .

Third Law (Action-Reaction)

For every action, there is an equal and opposite reaction.

• Example: When you push against a wall, the wall pushes back with equal force.

Forces and Free-Body Diagrams

Types of Forces

• Frictional Force: (static), (kinetic)

• Normal Force:

• Gravitational Force:

• Tension: Force transmitted through a string, rope, or cable.

Free-Body Diagrams

Free-body diagrams are used to visualize all the forces acting on an object. Each force is represented as an arrow pointing in the direction of the force.

• Example: A block on a table has forces of gravity downward, normal force upward, and possibly friction horizontally.

Circular Motion and Gravitation

Uniform Circular Motion

Objects moving in a circle at constant speed experience a centripetal acceleration directed toward the center of the circle.

• Centripetal acceleration:

• Centripetal force:

• Period of a circular motion:

Universal Gravitation

Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Work, Energy, and Conservation

Work Done by a Force

Work is done when a force causes displacement in the direction of the force.

• Example: Lifting a box vertically:

Kinetic Energy

Kinetic energy is the energy of motion.

Gravitational Potential Energy

Potential energy due to an object's position in a gravitational field.

Work-Energy Principle

The net work done on an object is equal to its change in kinetic energy.

Conservation of Mechanical Energy

If only conservative forces act (e.g., gravity), the total mechanical energy (kinetic + potential) is conserved.

• (when no friction)

Sample Applications and Problem Types

Analyzing Motion and Forces

• Determining acceleration and velocity from position-time data

• Using free-body diagrams to resolve forces in different directions

• Calculating tension in connected blocks

• Comparing motion of objects on inclined planes

Circular Motion and Gravity

• Calculating centripetal force and acceleration for objects in circular orbits

• Using universal gravitation to find orbital masses

Work and Energy

• Finding work done by gravity or applied forces

• Applying conservation of energy to roller coasters and falling objects

• Determining coefficients of friction from energy loss

Example Table: Forces on Connected Blocks

The following table summarizes the relationships between tensions in a system of three connected blocks:

Additional Info

• Practice problems cover conceptual understanding and calculation-based questions.

• Diagrams are used to illustrate forces and motion in various scenarios.

• Students should be familiar with interpreting free-body diagrams and applying Newton's laws to solve for unknowns.