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Classical Mechanics

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Classical Mechanics

Escape Velocity

The minimum speed required for a ballistic object to escape a massive body's gravitational field without further propulsion.

v_esc = √(2 G M / R) m/s
Classical Mechanics

Force

A vector interaction that, when unopposed, alters the state of motion or deforms a physical body.

F = m a = dp/dt N (kg·m/s²)
Classical Mechanics

Frequency (Mechanics)

The number of complete vibrational cycles occurring per unit time.

f = 1 / T = ω / (2π) Hz (s⁻¹)
Classical Mechanics

Friction

A resistive contact force that opposes relative sliding motion or tendency of motion between surfaces.

fs ≤ μs N, fk = μk N N
Classical Mechanics

Gravity

The universal attractive force between masses, causing mutual acceleration proportional to mass and inversely proportional to squared…

Fg = G m1 m2 / r² N
Classical Mechanics

Hooke's Law

A law of elasticity stating that restoring force exerted by a spring or elastic material is proportional to its extension or compression…

F = -k x N (k in N/m)
Classical Mechanics

Impulse

The vector quantity defined as the integral of a force over the time interval during which it acts, equal to the net change in momentum.

J = ∫ F dt = Δp = m vf - m vi N·s (or kg·m/s)
Classical Mechanics

Inclined Plane

A simple machine consisting of a flat supporting surface tilted at an angle to the horizontal.

MA = L / h = 1 / sin θ Dimensionless
Classical Mechanics

Inelastic Collision

A collision in which total linear momentum is conserved, but total kinetic energy is not conserved.

∑ p_i = ∑ p_f, KE_final < KE_initial kg·m/s, J
Classical Mechanics

Inertia

The natural resistance of any physical object to any change in its velocity or state of motion.

Quantified by Mass (m) kg
Classical Mechanics

Kinetic Energy

The scalar energy an object possesses by virtue of its motion, proportional to its mass and the square of its speed.

KE = ½ m v² J
Classical Mechanics

Maximum Height

The maximum vertical elevation reached by a projectile above its launch level, where vertical velocity momentarily becomes zero.

H = (v0² sin² θ) / (2 g) m
Classical Mechanics

Mechanical Advantage

The factor by which a simple machine multiplies input effort force to overcome load resistance.

MA = F_output / F_input Dimensionless
Classical Mechanics

Mechanical Energy

The sum of kinetic energy and potential energy in a physical system.

E_mech = KE + PE J
Classical Mechanics

Moment of Inertia

A quantitative measure of a body's rotational inertia - its resistance to changes in rotational motion about a given axis.

I = ∑ m_i r_i² = ∫ r² dm kg·m²
Classical Mechanics

Momentum

A fundamental vector quantity equal to the product of an object's mass and its velocity, representing its quantity of motion.

p = m v kg·m/s
Classical Mechanics

Newton's First Law

The principle that an object remains at rest or continues in uniform motion in a straight line unless acted upon by a net external force.

∑ F = 0 ⇒ v = constant N/A
Classical Mechanics

Newton's Second Law

The law stating that net force acting on a body equals the rate of change of its linear momentum, simplified to mass times acceleration for…

F_net = m a N
Classical Mechanics

Newton's Third Law

The law stating that whenever two objects interact, they exert forces on each other that are equal in magnitude and opposite in direction.

F_A_to_B = -F_B_to_A N
Classical Mechanics

Non-conservative Force

A force for which work done depends on the specific path taken, dissipating mechanical energy into heat, sound, or internal energy.

W_non-cons = ΔME = ΔKE + ΔPE N
Classical Mechanics

Normal Force

The perpendicular contact force exerted by a surface on an object pressing against it.

N = m g cos θ N
Classical Mechanics

Orbital Velocity

The speed required for a body to maintain a stable circular orbit around a primary gravitational mass at a given radius.

v_orb = √(G M / r) m/s
Classical Mechanics

Parallel Axis Theorem

A theorem stating that the moment of inertia about any axis parallel to a centroidal axis equals the centroidal moment of inertia plus mass…

I = I_cm + M d² kg·m²
Classical Mechanics

Pascal's Principle

The principle stating that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and container…

ΔP = F1 / A1 = F2 / A2 Pa