Chapter 6 - Momentum

6.1 - Momentum

Momentum is a fundamental concept in physics describing the quantity of motion an object possesses. It is defined as the product of an object's mass and velocity.

• Definition: Momentum is "inertia in motion".

• Formula:

• Units: Kilogram meter per second (kg·m/s)

• Example: A 2 kg ball moving at 3 m/s has a momentum of kg·m/s.

6.2 - Impulse

Impulse refers to the change in momentum resulting from a force applied over a time interval.

• Definition: Impulse is the product of force and the time over which it acts.

• Formula:

• Units: Newton seconds (N·s)

• Example: If a force of 10 N acts for 2 s, the impulse is N·s.

6.3 - Impulse-Momentum Relationship

The Impulse-Momentum Theorem states that the impulse on an object equals its change in momentum.

• Formula:

• Application: Used to stop or start objects by applying a force over time.

• Example: Catching a ball involves applying a force to change its momentum to zero.

6.4 - Bouncing

When an object bounces, its change in momentum is greater than if it simply stopped, because the direction of velocity reverses.

• Key Point: The impulse required to bounce an object is greater than to stop it.

• Formula for change in momentum: (for a bounce, is in the opposite direction)

• Example: A ball bouncing off a wall reverses its velocity, doubling the change in momentum.

6.5 - Conservation of Momentum

Conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it.

• Formula:

• Application: Used in analyzing collisions and explosions.

• Example: Two ice skaters push off each other and move in opposite directions with equal and opposite momentum.

6.6 - Collisions

Collisions are classified as elastic or inelastic based on whether kinetic energy is conserved.

• Elastic collision: Objects rebound without lasting deformation or heat generation.

• Inelastic collision: Objects become distorted and/or generate heat, possibly sticking together.

• Example: Billiard balls colliding (elastic); cars crumpling in a crash (inelastic).

Chapter 7 - Energy

7.1 - Work

Work is the effort exerted on something that will change its energy.

• Definition: Work is done when a force acts over a distance.

• Formula:

• Units: Joules (J), where

• Example: Lifting a 10 N weight 2 m upward: J.

7.2 - Power

Power measures the rate at which work is done.

• Formula:

• Units: Watts (W), where

• Example: If 100 J of work is done in 5 s, W.

7.3 - Potential Energy

Potential energy (PE) is stored energy due to position or configuration.

• Gravitational potential energy:

• Example: A 2 kg object at a height of 5 m: J.

7.4 - Kinetic Energy

Kinetic energy (KE) is energy associated with motion.

• Formula:

• Example: A 3 kg object moving at 4 m/s: J.

7.5 - Work-Energy Theorem

The work-energy theorem states that the work done on an object equals its change in kinetic energy.

• Formula:

• Application: Used to analyze energy transfer in mechanical systems.

7.6 - Conservation of Energy

Conservation of energy states that energy cannot be created or destroyed, only transformed.

• Key Point: Total energy in a closed system remains constant.

• Example: A pendulum converts potential energy to kinetic energy and back.

7.7 - Machines

Machines are devices that multiply force or change its direction, often using simple mechanisms.

• Examples: Lever, pulley, inclined plane, screw, wedge, wheel-and-axle.

• Application: Machines can increase efficiency but cannot create energy.

7.8 - Efficiency

Efficiency measures how effectively a machine converts input energy into useful output.

• Formula:

• Example: If a machine uses 100 J and delivers 40 J of useful work, efficiency is .

Chapter 10 - Projectile Motion

10.1 - Projectile Motion

Projectile motion describes the two-dimensional motion of an object under the influence of gravity.

• Key Point: Motion can be analyzed horizontally and vertically as independent components.

• Example: A ball thrown at an angle follows a parabolic path due to gravity.

Chapter 35 - Special Theory of Relativity

35.1 - Motion is Relative

All motion is measured relative to a chosen frame of reference.

• Key Point: There is no absolute rest; motion depends on the observer's frame.

• Example: A train moving past a station appears stationary to a passenger inside.

35.2 - Postulates of the Special Theory of Relativity

Einstein's theory is based on two postulates:

• Postulate 1: The laws of physics are the same in all inertial frames.

• Postulate 2: The speed of light in a vacuum is constant for all observers, regardless of their motion.

35.3 - Simultaneity

Events that are simultaneous in one frame may not be simultaneous in another.

• Key Point: Simultaneity is relative, not absolute.

• Example: Lightning strikes observed from different moving trains may appear to occur at different times.

35.4 - Spacetime and Time Dilation

Relativity links space and time into a single continuum called spacetime. Time dilation occurs when time appears to pass at different rates for observers in relative motion.

• Formula:

• Key Point: Moving clocks run slower compared to stationary ones.

• Example: Astronauts traveling at high speed age more slowly than people on Earth.

35.6 - Length Contraction

Objects moving at relativistic speeds appear shorter in the direction of motion.

• Formula:

• Key Point: Length contraction only becomes significant at speeds close to the speed of light.

• Example: A spaceship traveling at 0.8c appears contracted to an outside observer.

35.7 - Relativistic Momentum

Momentum must be adjusted for objects moving near the speed of light.

• Formula: , where

• Key Point: Relativistic momentum increases more rapidly than classical momentum as velocity approaches c.

35.8 - Mass, Energy, and

Mass and energy are interchangeable, as described by Einstein's famous equation.

• Formula:

• Key Point: Even a small amount of mass can be converted into a large amount of energy.

• Example: Nuclear reactions convert mass into energy.

35.9 - The Correspondence Principle

New theories must agree with old theories where the old theories are valid.

• Key Point: Special relativity agrees with Newtonian mechanics at low speeds.

• Application: Newton's laws break down at speeds near the speed of light.