Key Equations and Concepts

• Kinematic Equations: Used to describe motion with constant acceleration.

• Newton's Second Law:

• Weight:

Motion and Forces

Inertia and Newton's First Law

Objects remain at rest or in uniform motion unless acted upon by a net external force. This property is called inertia.

• Inertia: The tendency of an object to resist changes in its state of motion.

• Examples: A hockey puck sliding on ice continues moving until friction or another force acts on it.

• Applications: Tablecloth trick, where dishes remain at rest when the cloth is quickly pulled.

Types of Motion

• Straight-line motion: Occurs when no net force acts perpendicular to the direction of motion.

• Circular motion: Requires a net force directed toward the center of the circle (centripetal force).

• Projectile motion: Combination of horizontal and vertical motions under gravity.

Force and Acceleration

According to Newton's Second Law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

• Formula:

• Example: If the net force on a cart is doubled, its acceleration doubles.

• Example: If the mass of a cart is doubled while the force remains constant, its acceleration is halved.

Kinematics: Describing Motion

Speed, Velocity, and Acceleration

• Speed: Scalar quantity; rate of change of distance.

• Velocity: Vector quantity; rate of change of displacement.

• Acceleration: Rate of change of velocity; can be due to changes in speed or direction.

• Average speed:

• Instantaneous speed: Speed at a specific instant.

Free Fall and Gravity

• Acceleration due to gravity (Earth):

• Objects in free fall: Accelerate downward at , regardless of mass (neglecting air resistance).

• Distance fallen:

• Velocity after time :

• Example: A ball dropped from rest falls 5 m in 1 s; in 2 s, it falls 20 m (distance increases as ).

Projectile and Relative Motion

• Projectile motion: Horizontal and vertical motions are independent.

• Relative velocity: The velocity of an object as observed from a particular reference frame.

• Example: A mosquito flying at 3 m/s into a 3 m/s breeze has a resultant speed of 6 m/s (if in the same direction) or 0 m/s (if in the opposite direction).

Forces in Equilibrium and Dynamics

Equilibrium

• Static equilibrium: Object at rest; net force is zero.

• Dynamic equilibrium: Object moves at constant velocity; net force is zero.

• Example: A block sliding at constant velocity has friction force equal and opposite to the applied force.

Friction

• Friction: Force that opposes motion between two surfaces in contact.

• Kinetic friction: Acts on moving objects.

• Static friction: Acts on objects at rest.

• Example: If a block is pushed with 6 N and moves at constant velocity, friction is 6 N.

Weight and Mass

• Mass: Measure of inertia; does not change with location.

• Weight: Force due to gravity; .

• Example: An object with mass 1 kg has a weight of 9.8 N on Earth.

• On the Moon: Weight is less due to lower gravity, but mass remains the same.

Newton's Third Law: Action and Reaction

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

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

• Application: Rocket propulsion, walking, jumping.

Sample Table: Comparison of Mass and Weight on Earth and Moon

Additional info: Table values for the Moon use .

Summary of Key Points

• Objects in motion stay in motion unless acted upon by a net force (inertia).

• Acceleration is produced by net force; .

• Weight is the force of gravity on an object; .

• Friction opposes motion and is equal to the applied force at constant velocity.

• Action and reaction forces are equal in magnitude and opposite in direction.

• Projectile and relative motion require vector addition of velocities.

• Free-falling objects accelerate at ; distance fallen increases as .