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Basic principles of dynamics
The Basic Principles of Dynamics cover Newton's Laws of Motion, work-energy relationships and conservation of energy, momentum conservation, and collision theory. These principles explain in detail how objects change their motion under external forces, how energy transforms and conserves within systems, and reveal the conservation law of momentum in collisions.
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Basic principles of dynamics
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Basic principles of dynamics
Newton's Laws of Motion
First Law (Law of Inertia)
An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Second Law (Law of Acceleration)
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
F = ma
F is the net force applied
m is the mass of the object
a is the acceleration produced
Third Law (Law of Action and Reaction)
For every action, there is an equal and opposite reaction.
Forces always occur in pairs
Forces are equal in magnitude and opposite in direction
Work, Energy, and Power
Work
The product of the force applied to an object and the distance the object moves in the direction of the force.
W = F * d * cos(θ)
W is work
F is force
d is distance
θ is the angle between the force and the direction of motion
Energy
The capacity to do work.
Kinetic Energy (KE)
Energy of motion
KE = 1/2 mv^2
m is mass
v is velocity
Potential Energy (PE)
Energy due to position or state
PE = mgh
m is mass
g is acceleration due to gravity
h is height
Power
The rate at which work is done.
P = W / t
P is power
W is work
t is time
Momentum and Collisions
Momentum
The product of an object's mass and its velocity.
p = mv
p is momentum
m is mass
v is velocity
Impulse
The change in momentum of an object when it is subjected to a force over time.
J = Δp = FΔt
J is impulse
Δp is change in momentum
F is average force
Δt is time interval
Collisions
The interaction between two or more objects where they exchange momentum and energy.
Elastic Collisions
Total kinetic energy is conserved
Inelastic Collisions
Total kinetic energy is not conserved, some energy is lost as heat or sound
Rotational Motion
Angular Displacement
The angle through which a point or line has been rotated in a specified sense about a specified axis.
Angular Velocity
The rate of change of angular displacement with respect to time.
ω = Δθ / Δt
ω is angular velocity
Δθ is change in angular displacement
Δt is change in time
Angular Acceleration
The rate of change of angular velocity with respect to time.
α = Δω / Δt
α is angular acceleration
Δω is change in angular velocity
Δt is change in time
Torque
The measure of the force that can cause an object to rotate about an axis.
τ = rFsin(θ)
τ is torque
r is the distance from the axis of rotation
F is the force applied
θ is the angle between the force and the lever arm
Gravitation
Universal Law of Gravitation
Every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
F = G(m1m2)/r^2
F is the gravitational force between two masses
G is the gravitational constant
m1 and m2 are the masses
r is the distance between the centers of the two masses
Gravitational Field
The region of space around a mass where another mass experiences a force of attraction.
g = F/m
g is gravitational field strength
F is gravitational force
m is mass of the object in the field
Oscillations and Waves
Simple Harmonic Motion (SHM)
The motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law.
Periodic motion
Restoring force is proportional to the displacement and acts in the opposite direction
Waves
A disturbance that travels through a medium from one point to another.
Transverse Waves
The particles of the medium move perpendicular to the direction of the wave propagation.
Longitudinal Waves
The particles of the medium move parallel to the direction of the wave propagation.
Fluid Dynamics
Fluid Statics
The study of fluids at rest.
Pressure
The force exerted per unit area on a surface.
P = F/A
P is pressure
F is force
A is area
Fluid Dynamics
The study of fluids in motion.
Bernoulli's Principle
States that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
P + 1/2 ρv^2 + ρgh = constant
P is pressure
ρ is fluid density
v is fluid velocity
g is acceleration due to gravity
h is height above a reference point